## Math Questions and Answers

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Identify the rule of algebra illustrated by the statement. 7(1/7) = 1

In order to be relevant, accounting information should have: a. timeliness. b. verifiability. c. neutrality. d. representational faithfulness.

A customer can choose one of four amplifiers, one of six compact disc players, and one of five speaker models for an entertainment system. Determine the number of possible system configurations.

The perimeter of the pentagon below is 68 units. Find the length of side OR. Write your answer without variables.

Your friends Jim and Jennifer are considering signing a lease for an apartment in this residential neighbourhood. They are trying to decide between two apartments, one with 1,000 square feet with a...

Write an expression that represents the difference of y and 32, plus the product of y and 4.

Write 91829182 in expanded form.

Write 73 million, 5 thousand, 46 in standard form.

Who was Karl Pearson?

Which of the following is true of relevant information? a. All fixed costs are relevant. b. All future revenues and expenses are relevant. c. All past costs are never relevant. d. All fixed costs a...

What is the point of algebraic geometry?

What is the empty scheme in algebraic geometry?

What is special about curves in algebraic geometry?

What is complex algebraic geometry?

What is algebraic geometry used for?

What do sheaves explain in algebraic geometry?

What did Charles Hermite invent?

What did Alexander Grothendieck discover?

What did Alexander Grothendieck do for math?

What branches of mathematics get used in theoretical Biology?

"Variable costs are always relevant, and fixed costs are always irrelevant." Do you agree? Why?

There is about 32 pounds in a slug. If a person weighs 192 pounds, how many slugs do they weigh?

Solve for y: 6x + y = 12

Let f(x) = x^2 + 3x - 4 and g(x) = \dfrac{5x + 2}{2x^2 - x- 1}. Determine f - g and find its domain.

It is often said that statistically different does not always mean statistically important. What does this mean in terms of biological studies and experiments?

Is probability and statistics part of algebra?

Is differential geometry pure math?

Is algebraic geometry more algebra than geometry?

Is algebraic geometry just linear algebra?

Is algebraic geometry more geometry than algebra?

If a car averages 10.4 liters per 100 km of city driving, and the car averages 1800 km of city driving per month, how much fuel does it use in an average month of city driving?

If 3ax + b = c, then x equal ____.

How is algebraic geometry used in physics?

How do you simplify an expression?

How did Evariste Galois die?

Given ln(x)-x2+2x=0. Solve the equation for the smallest root, using False Position Method correct up to at least 2 decimal places i.e =0.5 10-2.

For each of the following relations, used for people, determine if the relation is complete, reflexive and transitive: (a) "Being younger and shorter" (b) "Being younger or shorter" (c) "Having the...

Evaluate the expression for the given value of the variable. \frac{2(x+3)}{10x - 60} for x = 3

Cost system design/selection should consider all but which of the following? a. Cost/benefit of a system design/selection and operation. b. A firm's strategy and information needs. c. Customer need...

Choose the best answer from the choices provided. ''Algebra a. does not vary b. Three terms c. Zero for addition and one for multiplication d. Two dimensions e. (0,0) f. Names a point in the...

Evaluate the interpret the result in terms of the area and or below the x-=axis. Integral_{-1/2}^{1} (x^3 - 2x) dx

How many molecules (not moles) of NH3 are produced from 3.86 \times 10^{-4} g of H2?

What are the challenges that teachers may foresee in teaching math?

Simplify. \frac{(9a^{3}b^{4})^{1/2}}{15a^{2}b}

Find the total area between the curve y = x^2 + 2x -3 and the x-axis, for x between x = -6 and x = 7. Also, evaluate the integral \int_{-6}^{7} f(x) dx. Interpret the value of integral in terms of...

The square root of a number plus two is the same number. What is the number?

Find the solution to the following problem: 6(-9) - (-8) - (-7) (4) + 11

Simplify: - 5 + 2(8 - 12)

What is (2)^2 \div (9)^2?

Solve for x . \frac{5x - 140}{x} = -15

Solve: 3(x-4)=12x

Solve the formula for the indicated variable. P = a + 3b + 2c, for a

Solve for x. 5(x - 6) - 7(x + 2) = -16

Simplify: {3 / 8} + {5 / 24}

Simplify: \frac{63}{2898}

Simplify: (2x^3 - 5x^2-5x) + (5x^3 - x^2 +4x+4)

Solve for y: 4 + \frac{6}{y} = \frac{5}{2}

Simplify: (1 / 4)^{-2}

Solve: \ln (4x - 2) - \ln 4 = - \ln (x-2)

Simplify: \frac{\frac{4}{x} - \frac{4}{y}}{\frac{3}{x^2} - \frac{3}{y^2}}

Simplify the following expression. 1/15 (15x - 40) - 1/3 (15x - 2y)

Simplify: \frac{9t + 3}{6t - 5} = \frac{3t + 6}{3t - 5}

What is 2 - 5 = \boxed{\space}?

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then

A set of data contains 53 observations. The minimum value is 42 and the maximum value is 129. The data are to be organized into a frequency distribution. a. How many classes would you suggest? b....

The slope of the line containing points Y and Z is ____. a. -0.5 b. -1 c. -2 d. -4

Expand the following expression. a^2z(t - a)\left(\dfrac{1}{z} + \dfrac{1}{a} \right)

Why is multicollinearity considered a "sample-specific" problem?

One example of a natural concept is a(n) ... a. ion. b. irrational number. c. appliance. d. circle.

Twenty more than four times a number is equal to the difference between -71 and three times the number. Find the number.

How can collaborating with the family of early learners be done to design math activities that are engaging, practical, and can be done at home?

Can math manipulatives be misused or overused in the early childhood classroom?

(3 * 8) - 2 + (3 + 6) = ? Calculate step by step.

A 4.36-g sample of an unknown alkali metal hydroxide is dissolved in 100.0 mL of water. An acid-base indicator is added and the resulting solution is titrated with 2.50 M HCl(aq) solution. The indi...

Select all that apply: The total differential of a function y = f(x_1, x_2) a. tells us how the dependent variable changes when one independent variable, ceteris paribus b. is written as dy = parti...

What is the value of 3 squared?

Basic arithmetic is not an easy task for Jeanne. In fact, she has to work hard at understanding mathematical concepts. She finds it hard to believe that basic math skills are: A. present in all s...

Solve for x. {2(x+5)} / {(x + 5)(x - 2)} = {3(x - 2)} / {(x - 2)(x + 5)} + 10 / {(x + 5)(x - 2)}

Find the product of 2 x + 3 y and x^2 - x y + y^2.

Find the sum of x^3 y + x^2 y^2 - 3 x y^3 and x^3 - 3 x^3 y + y^3 + 4 x y^3.

Find the expansions of (3 - 2 x) (2 x + 7) (2 x + 1).

Find the expansions of (2 x + 1) (2 x - 3) (2 x + 5).

How we can convert degree measures to radians? Convert 122^o 37' to radians.

Use the conversation factor (1.0 inch = 2.54 cm) to change these measurements into inches. (Round results to three significant digits.) 1) 5.09 mm 2) 0.711 cm 3) 3.92 cm 4) 0.472 m 5) 5.20 mm 6) 1....

Evaluate: 1) 8^{1 / 2} * 8^{-5 / 2} 2) (3^{5 / 3} / 3^{2 / 3})

Evaluate the expression ((-1)^2 + 11^2)(11^2 - {(-7)}^2).

What is the difference between a number and 20 more than that number? (Use variable "x" to solve)

Find the first derivative of the following. Do not use the product rule. Be sure to show intermediate work and do not simplify your answer. F = (1/2)S^3(2S^2 - 3S - 6)

Explain how to solve (+ 4) + 3.

What is 31/5 as a decimal?

Express 135 degrees in radians.

Express the following in radians: 1025 degrees.

Find 4/7 of a 49-degree angle.

Simplify: (v^2-36) (6 -v).

Given x is the midpoint of yz, given xy = 6x + 4 and yz = 40, find the value of x.

What is half of 72 and 0.5?

How to Convert Radians to Degrees?

Find PD if the coordinate of P is (-7) and the coordinate of D is (-1).

What is the error in finding the sum given below: \displaystyle{ \begin{align} \frac{3}{10} + \frac{\left ( -1 \right)}{10} &= \frac{3 + 1}{10} \\[0.3 cm] &= \frac{4}{10}\\[0.3 cm] &= \frac{2}{5}....

Suppose point J has coordinate of -2 and JK = 4. Then, what is the possible coordinate(s) for K?

The problem "large number of variables vs. small number of samples": a. is unavoidable in genomic studies involving the human genome. b. is important for the statisticians only. c. is typical for s...

Given two six-faced die, what is the maximum sum of numbers that you can get on these two die?

I have two U.S. coins that total 30 cents. One is not a nickel. What are the two coins?

Write in expanded form: (2a - b)^{3}

Simplify the expression 4^2 + 8 /2.

What is forecasting in biostatistics?

Construct a 95% confidence interval for the effect of years of education on log weekly earnings.

Why is it important for students to talk about math? What kinds of pre-discussion activities facilitate student discourse about math?

Calculate 4x^5- 4y, where x=-3, y=5.

How do I prove the existence of an object in math?

How to find the origin of a line?

What is the history of mathematics?

If a biologist has two treatments that are independent samples and he is not assuming a normal distribution of the data, which test(s) would be appropriate to use? 1. Mann-Whitney U-test 2. Wel...

What is the HCl of 2.00 x 10 squared mL of 0.51?

Discuss how relevant information is used to make short-term decisions and how pricing affects short-term decisions.

What is the value of the product (2i)(3i)?

Farmer Brown had ducks and cows. One day, he noticed that the animals had a total of 12 heads and 44 feet. How many of the animals were cows?

Differentiate between process improvement framework and problem-solving framework.

All work must be shown for each of the following problems, in the attachment below, thank you.

What did Stephen Hawking contribute to math?

Who are some modern male mathematicians? Discuss their contribution to the field of mathematics.

Match each concept on the left-hand side with the phrase on the right that fits best. Note that there are more items in the right column than on the left, so some answers will not be used. |I. os...

Find c1 and c2 so that y(x)=c1sinx+c2cosx will satisfy the given conditions 1. y(0)=0, y'(pi/2)=1 2.y(0)=1, y'(pi)=1

Complete the operation. (-a - 6b + 4)3ab

Examine the relationship between consumption of milk during dinner and night- time bedwetting and Examine the relationship between consumption of milk during dinner and night- time bedwetting and f...

Is it essential to have some background in math to pursue a branch of biology?

The chemistry teacher at Stevenson High School is ordering equipment for the laboratory. She wants to order sets of five weights totaling 121 grams for each lab station. Students will need to be ab...

Sam sold 39 loaves of bread in 9 days. Lucky sold 54 loaves of bread in 9 days 6 loaves per day. What is maximum number of days on which Sam sold more loaves of bread than Lucky?

What are some salient examples where systems biology has helped explain a complex process?

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is 37 ft, express the area, A, as a function of the width, x, of the w...

How is abstract algebra related to systems biology?

In systems biology, what is the difference between whole-cell simulations and metabolic models?

What are some examples of Godel's incompleteness theorem in biological systems?

Find all the sub game perfect equilibrium both in pure and mixed strategies.

How was Mayan mathematics different from math today?

The Beverton-Holt model has been used extensively by fisheries. This model assumes that populations are competing for a single limiting resource and reproduce at discrete moments in time. If we let...

Consider an experiment in which equal numbers of male and female insects of a certain species are permitted to intermingle. Assume that M(t)=(0.1t+1)ln(\sqrt {(t)}) represents the number of makin...

Find the curvature of the curve r(t). r(t) = (10 + ln(sec \ t)) \ i + (8 + t) \ k, \frac {-\Pi}{2} < t < \frac {\Pi}{2} \\r(t) = (3 + 9 \ cos \ 2t) \ i - (7 + 9 \ sin \ 2t) \ j + 2 \ k

What is: 57696978054 * 56777544 / 4?

Explain: I study engineering but I have a problem with mathematics, always when it come to mathmatic I struggle how to overcome such a problem

Construct a sample (with at least two different values in the set) of 4 measurements whose mode is smaller than at least 1 of the 4 measurements. If this is not possible, indicate "Cannot create sa...

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. A sample of 56 day-shift workers...

Suppose we are trying to model Y as a polynomial of X. Which of the following is NOT a valid reason to pick a fourth-order polynomial over a third-order polynomial? a)We believe that Y behaves acco...

Solve: h(s) = (35 - 2)^\frac {-5}{2}

If \gamma(\frac{8}{3}) = a find \gamma(\frac{1}{3}).

For each F(x,y) = 0, (i) find \frac{dy}{dx} (ii) find the points for which \frac{dy}{dx} is not defined (a) 2y+3x = 0 (b) 2x^2 + y^2 = 0 (c) x^2y + e^y + xy = 0 (d) \ln y + e^x + 5xy^2 = 0.

Find the derivative, second derivative, and curvature at t = 1. For the curve given by r(t) = (-9t, 4t, 1 + 8t^2).

What unique role does psychology play in systems biology?

A firm production function is given by q = f(k,l) = kï¿½l. q_0 = 100. w = $20, v = $5. What is the value of the Lagrange multiplier ? associated with the cost minimizing input choice? NOTE: write you...

What does a graph showing the growth of forest volume over time looks like 1) A U shape 2) An inverted U shape 3) An S shape 4) A pyramid 5) A straight line Maximizing the profit of timber harves...

! Exercise 3.5.1 : On the space of nonnegative integers, which of the following functions are distance measures? If so, prove it; if not, prove that it fails to satisfy one or more of the axioms. (...

Factor each of the following expression to obtain a product of sums TW + UY' + V

Find the average value of the function on the given interval. f(x) = x + 1; [0, 15]

Find the interval of convergence of the series \sum_{n=0}^\infty \frac{(x+5)^n}{4^n}

Show that the series is convergent.

Find curl F for the vector field F = z\sin x i -2x\cos y j +y\tan z k at the point (\pi, 0, \pi/4)

e^{3x}+2=1 implies x=

Show a separate graph of the constraint lines and the solutions that satisfy each of the following constraints: a. 3A + 2B ? 18 b. 12A + 8B ? 480 c. 5A + 10B = 200

Find the curvature for r(t) = \langle 4\cos t, t, 4\sin t \rangle

A) Find the limit: limit as x approaches infinity of arctan(e^x). B) Evaluate the integral: integral from 0 to (sqrt 3)/5 of dx/(1 + 25x^2).

Find the limit. Limit as y approaches 1 of (1/y - 1/1)/(y - 1).

Solve the given differential equation. (6x) dx + dy = 0. (Use C as the arbitrary constant.)

Find the point(s) on the surface z^2 = xy + 1 which are closest to the point (7, 8, 0).

Find an equation of the set of all points equidistant from the points A(-1, 6, 3) and B(5, 3, -3).

Find an equation of the plane. The plane through the origin and the points (2, -4, 6) and (5, 1, 3).

Given the velocity function v = t^2 + \frac{4}{\sqrt[4]{t^3}} , find the acceleration and the position function.

Find all three sides of the triangle with vertices P(2, -1, 0), Q(4, 1, 1), and R(4, -5, 4).

Let F = (6xyz + 2sinx, 3x^2z, 3x^2y). Find a function f so that F = \bigtriangledown f , and f(0, 0, 0) = 0 .

Find the volume of the parallelepiped with adjacent edges PQ, PR, PS. P(2, 0, 2), Q(-2, 3, 6), R(5, 3, 0), S(-1, 6, 4).

Solve the differential equation 2y'' -5y' -3y =0 with the initial conditions y(0) = 1, y'(0) =10

Find curl F(x,y,z) , when F(x,y,z) = x^3yz i +xy^3z j + xyz^3 k

Evaluate the integral \int \frac{1}{64x^2-9} \,dx

Find y_c and y_p by solving the differential equation x^2y'' + 10xy' + 8y = 0 using Cauchy Euler's rule.

Determine the inverse Laplace transform of F(s) = \frac{3s+5}{s^2+4s+13}

Find the slope of the curve: x^3 - 3xy^2 + y^3 = 1 at the point (2, -1).

Find the arc length of the graph of the function over the indicated interval. (Round your answer to three decimal places.) y= 1/2(e^x+e^-x) and interval [0,2]

Find an equation for the plane consisting of all points that are equidistant from the points (7, 0, -2) and (9, 12, 0).

Eliminate the parameter t to determine a Cartesian equation for: x = t^2, y = 8 + 4t.

Evaluate the integral: integral of 2sec^4 x dx.

Find all solutions of the equation in the interval [0, 2pi). 10sin^2(x) = 10 + 5cos(x).

Find the average value of the function h(x) = 6\cos^4 x \sin x on the interval [0, \pi]

Find interval of convergence and radius of convergence of the series \sum_{n=1}^\infty \frac{x^n}{9n-1}

Find an equation of the plane consisting of all points that are equidistant from (5, 3, -4) and (3, -5, -2), and having -2 as the coefficient of x.

Let f(x) = 7x^2 - 2 to find the following value. f(t + 1).

Consider the vector \mathbf F(x,y,z) = (2x+4y)\mathbf i +(4z+4x) \mathbf j + (4y + 2x) \mathbf k . a. Find a function f such that \mathbf F = \nabla f and f(0,0,0) = 0 . b. Suppose C is...

Find the radius and interval of convergence of the summation \sum_{n=1}^\infty \frac{ (x+2)^n}{n4^n}

Find all the values of x such that the series \sum_{n=1}^\infty \frac{(5x-9)^n}{n^2} would converge.

Find an equation of the tangent line to the curve y = x^3-3x+1 at the point (1,-1)

Write the equation 5x + 4y + 7z = 1 in spherical coordinates

Find the point(s) at which the function f(x) = 2 - x^2 equals its average value on the interval [-6,3] .

Let f(x) = 2x^2 - 2 and let g(x) = 5x + 1. Find the given value. f(g(-1)).

If f(2) = 15 and f '(x) \geq 2 for 2 \leq x \leq 7 , how small can f(7) possibly be?

Find an equation for the plane consisting of all points that are equidistant from the points (-5, 4, 3) and (1, 6, 7).

Solve the differential equation (\sin 2x)y'=e^{5y}\cos 2x

Find the coordinates of the point(s) on the parabola y = 4 - x^2 that is closest to the point (0, 1).

Find the derivative of the function. F(t) = e^(2t*sin 2t).

Find an equation for the plane consisting of all points that are equidistant from the points (-6, 2, 3) and (2, 4, 7).

Find the linearization of the function z = x\sqrt y at the point (2,64)

Convert from rectangular to polar coordinates: (x^2+y^2)^2 = x^2y

Find the point on the line y = 2x + 4 that is closest to the point (5, 1).

What did Ada Lovelace contribute to math?

Consider the vector field F(x, y, z) = 2xye^z i + yze^x k (a) Find the curl of the vector field. (b) Find the divergence of the vector field

Consider the vector field F(x,y,z)= \langle yz,-8xz,xy \rangle . Find the divergence and curl of F .

Find the linearization of f(x, y) = sqrt(x + e^(4y)) at (3, 0).

Find the area of the parallelogram with vertices A(-5, 3), B(-3, 6), C(1, 4), and D(-1, 1).

Find an arc length parametrization of r(t)= \langle e^t\sin(t),e^t\cos(t),6e^t \rangle

Find a particular solution to the non-homogeneous differential equation y''-4y'+4y=e^{2x} .

Find the radius of convergence and interval of convergence of the series \sum_{n=1}^\infty x^n(3n-1)

Find the curvature kappa(t) of the curve r(t) = (-1sin t)i + (-1sin t)j + (-3cos t)k.

Find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (2, 4) ?

Find the exact length of the curve. x = 6 + 12t^2, y = 5 + 8t^3, 0 leq t leq 4

Determine if this series converges conditionally, absolutely or diverges sum_{n=1}^{\infty } frac{(-1)^{(n+1)}}{n+3}.

Solve the given boundary-value problem. y double prime + 3y = 9x, y(0) = 0, y(1) + y prime (1) = 0.

Evaluate the integral \int_1^4 3\sqrt t \ln(t) \, dt

Given f'(x)=\frac{\cos(x)}{x} and f(4)=3 , find f(x)

Find the area of the parallelogram with vertices K(1, 3, 3), L(1, 4, 4), M(4, 8, 4), and N(4, 7, 3).

Evaluate the following integral. (Remember to use ln(absolute u) where appropriate. Use C for the constant of integration.) Integral of (du)/(u*sqrt(5 - u^2)).

Convert the polar equation r = -4csc(theta) into a Cartesian equation.

Evaluate the Integral \int \tan^2 x \sec^3 x \, dx

Find the points on the cone z^2 = x^2 + y^2 which are closest to the point (1, 2, 0).

Let F = (7yz)i + (6xz)j + (6xy)k. Compute the following: A) div F B) curl F C) div curl F (Your answers should be expressions of x, y, and/or z)

Evaluate the integral \int \frac{\log x}{x} \, dx

Consider the polar equation r^2 \sin \theta = 5 (1) What is the equation in Cartesian (rectangular) coordinates equivalent to this polar equation? (2) Which of the following curves is associate...

Determine whether the vector field F(x,y) = (x+5) i +(6y+5) j is path independent (conservative) or not. If it is path independent, find a potential function for it.

Consider the curve r(t) = \langle e^{-5t}\cos(-1t), e^{-5t}\sin(-1t), e^{-5t} \rangle . Compute the arclength function s(t) (with initial point t=0 )

Determine if the series converges or diverges. Justify your answer. Sum of 1/(n*(ln n)^2) from n = 2 to infinity.

Change from rectangular to spherical coordinates. A) (3, 3*sqrt(3), 6*sqrt(3)) B) (0, 5, 5)

Find velocity and position that has the acceleration a(t)= \langle 3e^t, 18t,2e^{-t} \rangle and specified velocity and position conditions: v(0)=(3,0,-6) \enspace and \enspace r(0)=(6,-1,2)

Determine whether the series \sum_{n=1}^\infty \frac{(-1)^nn^6}{7^n} converges or not.

Find T(t) \enspace and \enspace N(t) for the curve r(t) = 4t^2 i + 6t j .

Find the function represented by the following series and find the interval of convergence of the series. Sum of ((x - 5)^(2k))/(36^k) from k = 0 to infinity.

Test the series \sum_{n=1}^{\infty} (-3)^{3n} for convergence or divergence. Name the test used to determine your answer.

Find the curvature of the curve r(t)= (\cos t) i + (\sin t) j +t k at t= \pi

Determine whether the series \sum_{k=0}^{\infty}\frac{2k-1}{3k+5} converges or diverges. If the series converges, find its sum.

Find the values of x for which the series \sum_{n=1}^{\infty} \frac{x^n}{9^n} converges. Find the sum of the series for those value of x

Consider the vector field F(x,y,z)=(4z+3y) i+(5z+3x) j+(5y+4x) k . a. Find a function f such that F = \nabla f and f(0,0,0) = 0 b. Suppose, C is any curve from (0,0,0) to (1,1,1),...

Find the point on the line 5x+5y+2=0 which is closest to the point (2,4)

Determine if the series \sum_{n=1}^{\infty} (-1)^n 2n is absolutely convergent, conditionally convergent or divergent. Indicate which test you used and what you concluded from that test.

Consider the vector field F(x, y, z) = (2 z + y) i + (2 z + x) j + (2 y + 2 x) k. a) Find a function f such that F = nabla f and f(0, 0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0,...

r(t)=(2 \ln(t^2+1) i+ (\tan^{-1} t) j+8 \sqrt{t^2 + 1} k is the position vector of a particle in space at time t . Find the angle between the velocity and acceleration vectors at time t=0 .

Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = t - cube root of t, [-1, 6].

For the function g(x, y, z) = e^{-xyz}( x + y + z) , evaluate the following. (a) g(0, 0, 0) (b) g(1, 1, 0) (c) g(0, 1, 0) (d) g(z, x, y) (e) g(x + h, y + k, z + l)

Find the point of intersection of the lines r_1(t) = (-1, 1) + t (6, 10) \enspace and \enspace r_2(s) = (2, 1) + s (5, 15)

Decompose the acceleration of r(t)= (\sin (t)+3) i + (\cos(t)+4) j + t k into tangential and normal components.

Calculate the producers' surplus for the supply equation p = 7 + 2q^{1/3} at the indicated unit price p = 18

Determine whether the series \sum k \left ( {10}{11} \right )^k , where k = 1 is absolutely convergent, conditionally convergent, or divergent. please I need it step by step

Determine whether the series sum of (2^k)/(k^2) from k = 1 to infinity converges. Explain fully what test you are using and how you are using it.

Determine whether the series \sum_{n=2}^{\infty} 9n ^{-1.5} converges or diverges, Identify the test used

Determine whether the series converges or diverges and justify your answer, if the series converges state whether the convergence is conditional or absolute \sum_{n=2}^{\infty} (-1)^n \frac{3}{\s...

If the series \sum_{0}^{\infty} \left ( \frac{1}{\sqrt{13}} \right )^n converges, what is its sum?

Compute the curvature kappa(t) of the curve r(t) = (5sin t)i + (5sin t)j + (-4cos t)k.

Find the tangential and normal components of the acceleration vector. r(t) = t i + t^2 j + 5t k.

Calculate the area of the plane region bounded by x - y = 7 and x = 2y^2 - y + 3.

Find the vectors T, N, and B at the indicated point. r(t) = (t^2, (2/3)t^3, t); (4, -16/3, -2).

Estimate f(2.1, 3.8) given f(2, 4) = 2, f_x(2, 4) = 0.4, and f_y(2, 4) = -0.3.

Find the interval of convergence of the following power series. Sum of (2^k (x - 3)^k)/(k^2) from k = 0 to infinity.

Determine if the following series converges or diverges. Sum of (ln n^2)/(n) from n = 1 to infinity.

Find the radius of convergence for the following power series. Sum of (2^n (x - 1)^n)/(n) from n = 1 to infinity.

Find the area of the parallelogram whose vertices are given below. A(0, 0, 0), B(3, 2, 6), C(6, 1, 6), D(3, -1, 0).

Compute an arc length parametrization of the circle in the plane z = 9 with radius 4 and center (1, 4, 9).

Find the interval of convergence of the following series. Sum of ((x - 6)^(2n))/(36^n) from n = 0 to infinity.

Determine all values of h and k for which the following system has no solution. x + 3y = h; -4x + ky = -9.

For the function f(x, y) = 5y^2 + 3x, find a point in the domain where the value of the function is between 3 and 3.100000000.

Find the radius of convergence and interval of convergence of the following series. Sum of (x^(n + 7))/(6*factorial of n) from n = 2 to infinity.

Find the coordinates of the point(s) on the curve y = sqrt(x + 4) that are closest to the given point (4, 0).

If f(2) = 14, f prime is continuous, and integral from 2 to 5 of f prime (x) dx = 20, find the value of f(5).

Find the series' radius of convergence. Sum of ((x - 6)^n)/(factorial of (2n)) from n = 1 to infinity.

Find the exact length of the following polar curve. r = e^(8theta), 0 less than or equal to theta less than or equal to 2pi.

For what values of c is there a straight line that intersects the curve y = x^4 + cx^3 + 12x^2 - 4x + 9 in four distinct points? (Give your answer using interval notation.)

Find the radius and the interval of convergence of the power series: sum of ((-1)^n n(x + 3)^n)/(4^n) from n = 1 to infinity.

If the following series converges, compute its sum. Sum of (3 + 6^n)/(6^n) from n = 1 to infinity.

Determine if the following series converges or diverges. Sum of (5*(factorial of n)^2)/(factorial of 2n) from n = 1 to infinity.

Find the curvature of the curve r(t) = t i + t^2 j + t^3 k at the give point P(1, 1, 1).

Compute the average value of the function f(x) = x^2 - 17 on [0, 6].

Use polar coordinates to compute the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 1.

Determine if the sum of (-1)^n (n)/(sqrt(n^3 + 2)) from n = 1 to infinity converges absolutely, converges conditionally, or diverges. Show all details of your work.

Compute an arc length parametrization of r(t) = (e^t sin t, e^t cos t, 1e^t).

Does the following series converge or diverge? Sum of 1/sqrt(n^2 + 1) from n = 1 to infinity.

Solve the following initial-value problem. t*(dy/dt) + 7y = t^3, t greater than 0, y(1) = 0.

What is the average of the function g(x) = [x(ln x)^2]^(-1) over the interval x is element of [e, e^2]?

Find the interval of convergence. Sum of ((3x)^n)/(factorial of 4n) from n = 0 to infinity.

Find tangential Acceleration and Normal Acceleration.

Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges 1. sum_n=1^infi...

Compute the exact length of the polar curve described by: r = 9e^(-theta) on the interval (9/4)pi less than or equal to theta less than or equal to 6pi.

Use the Comparison Test or the Integral Test to determine whether the given series is convergent or divergent. Sum of 1/(4n^2 + 1) from n = 1 to infinity.

Find the interval of convergence of the following series. Sum of (4^n)/(factorial of (2n + 1)) x^(2n - 1) from n = 0 to infinity.

Determine two unit vectors orthogonal to both (4, 5, 1) and (-1, 1, 0).

Find the radius of convergence of the following power series. Sum of (x^(2n))/(factorial of (2n)) from n = 0 to infinity.

Find f(x). f double prime (x) = 2e^x + 3sin x, f(0) = 0, f(pi) = 0.

Find the local maximum and local minimum values and saddle point(s) of the following function. f(x, y) = 8y cos(x), 0 less than or equal to x less than or equal to 2pi.

Find the interval of convergence (give your answer in interval notation). Sum of (9^n)/(factorial of (2n + 5)) x^(2n - 1) from n = 0 to infinity.

Determine convergence or divergence of the following series and state the test used. Sum of (1/n - 1/(n + 1)) from n = 1 to infinity.

Determine whether the following series sum of 5/(k^5 + 7) from k = 1 to infinity converges or diverges.

Compute kappa(t) when r(t) = (1t^(-1), -4, 6t).

Classify the following series as absolutely convergent, conditionally convergent, or divergent. Sum of ((-8)^k e^k)/(k^k) from k = 1 to infinity.

Write the given number in the form a + bi. e^(pi + i).

Determine convergence or divergence of the alternating series. Sum of ((-1)^n)/(6n^5 + 6) from n = 1 to infinity.

Suppose f(x, y) = xy - 6. Compute the following values: A) f(x + 4y, x - 4y) B) f(xy, 6x^2 y^3)

Use the integral test to determine if sum_{k=1}^{infinity} k e^{- 3 k} converges

Find r(t) and v(t) given acceleration a(t) = (t, 1), initial velocity v(0) = (- 2, 2) and initial position r(0) = (0, 0). v(t) = r(t) =

Determine whether the series converges absolutely, converges conditionally, or diverges: Sum of ((-1)^(n + 1) factorial of n)/(n^n) from n = 1 to infinity.

Calculate the average value of f(x) = 5 x sec^2 x on the interval [0, pi/4]

For u = e^x cos y, (a) Verify that {partial^2 u} / {partial x partial y} = {partial^2 u} / {partial y partial x} ; (b) Verify that {partial^2 u} / {partial x^2} + {partial^2 u} / {partial y^2} = 0

Find the radius and interval of convergence of the series sum of (n(x + 2)^n)/(3^(n + 1)) from n = 0 to infinity.

Evaluate the integral from pi/6 to pi/3 of (tan x + sin x)/(sec x) dx.

Find f. f double prime (x) = 20x^3 + 12x^2 + 4, f(0) = 2, f(1) = 4.

Test the following series for convergence or divergence. Name the test used to determine your answer. Sum of ((-1)^(n + 1))/(n*ln n) from n = 2 to infinity.

Determine the linearization L(x) of the function at a. f(x) = x^(1/2), a = 25.

Compute the area of the triangle with vertices at (1, 2, 3), (3, 1, 4), and (4, 5, 7).

For the curve given by r(t) = (-2sin t, 4t, 2cos t), A) Find the unit tangent T(t). B) Find the unit normal N(t). C) Find the curvature kappa(t).

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x^3 - 18x^2 - 144x + 7, [-3, 5].

Show that the following equation x^5 + 3x + 1 = 0 has exactly one real root.

Find the average value of the function f(x) = 2*x^3 on the interval 2 less than or equal to x less than or equal to 6.

A) Find the interval of convergence of the series: sum of (x - 6)^n from n = 0 to infinity. B) Find the Taylor polynomial of order 3 generated by f at a. f(x) = 1/(x + 9), a = 0.

Determine the parametric equation of the line of intersection of the two planes x + y - z + 5 = 0 and 2x + 3y - 4z + 1 = 0.

Compute the following values for the given function. f(u, v) = (4u^2 + 3v^2) e^(uv^2). A) f(0, 1) B) f(-1, -1) C) f(a, b) D) f(b, a)

Does the sum diverge, converge absolutely or converge conditionally ? a) sum_{n=1}^{infinity} {(- 1)^{n + 1}} / n^3 b) sum_{n=1}^{infinity} (- 1)^n / {square root{5 n - 1}}

Find the interval of convergence of the following power series. Sum of (x^n)/(n*10^n) from n = 1 to infinity.

Show that the following series is divergent. Sum of (2n^2 + 3)/(5n^2) from n = 1 to infinity.

Determine whether the series sum of (n^n)/(factorial of n) from n = 0 to infinity converges or diverges.

Determine an arc length parametrization of r(t) = (3t^2, 4t^3). (Use symbolic notation and fractions where needed.)

Find the average rate of change of the function over the given intervals. f(x) = 11x^3 + 11; A) [4, 6] B) [-1, 1]

Find the volume of the parallelepiped with adjacent edges PQ, PR, PS. P(3, 0, 1), Q(-1, 1, 7), R(6, 3, 0), S(2, 5, 2).

Determine is it absolutely convergent, conditionally convergent or divergent. sum_{n=0}^{infinity} (- 1)^n / (2 n + 1)^2

Find all the values of x such that the given series would converge. sum_{n=1}^{infinity} {(- 1)^n (x^n) (n + 8)} / (11)^n The series is convergent from x = , left end included (enter Y or N):...

Determine the curvature kappa(t) of the given curve r(t) = (4sin t)i + (4sin t)j + (-3cos t)k.

Find the length of the curve x = 3y^(4/3) - (3/32)y^(2/3), 0 less than or equal to y less than or equal to 8.

Give the maclaurine expansion. f(x) = sqrt (x)

Determine whether the series is absolutely convergent, conditionally convergent, or divergent. sum_{n=1}^{infinity} (- 1)^{n - 1} / {n + 6}. Input A for absolutely convergent, C for conditionally...

Test the series for convergence or divergence. Name the test used to determine your answer. sum_{n=1}^{infinity} (- 2)^{2 n} / n^n

Suppose y = sqrt(6 + 4x^3). A) Find d^2(y)/dx^2. B) Write the equation of the tangent line at (-1, sqrt(2)).

Determine if the following series is convergent or divergent. Sum of k^2 e^(-k) from k = 1 to infinity.

A) Find the general solution x(t): dx/dt + 2x - 1 = 0. B) Solve the initial value problem: dy/dt = 2(4 - y), y(1) = 1.

Test the following series for convergence or divergence. (Justify your answer.) sum_{n more than or equal to 3} {1 / n} / {ln(n) sqrt{ln ^2 (n) - 1}}

Determine whether the integral is convergent or divergent. Integral from 5 to infinity of 1/(x - 4)^(3/2) dx. If it is convergent, evaluate it.

Find all the values of x such that the given series would converge. Sum of ((5x - 7)^n)/(n^2) from n = 1 to infinity. (Give your answer in interval notation.)

Solve the following differential equation: y double prime + 4y = sin^3(x).

Find the first three nonzero terms of the Taylor series for the function f(x) = sqrt(4x - x^2) about the point a = 2. (Your answers should include the variable x when appropriate.)

Find the average value of the function f(t) = t*sin(t^2) on the given interval [0, 10].

Find dy/du, du/dx, and dy/dx when y and u are defined as follows. y = 7/u and u = sqrt(x) + 7.

Find the particular solution of the differential equation dy/dx = (x - 3)e^(-2y) satisfying the initial condition y(3) = ln(3). (Your answer should be a function of x.)

Find dy/dx by implicit differentiation. e(^(x^2y))=x+y

Show how to calculate the iterated integral. int_{- 4}^{2} [ int_{pi / 2}^pi (y + y^3 cos x) d x ] d y

Integrate. (dx) / (sqrt (x^2 - 25)) , x5

Integrate the following. Integral of (t^2 multiplied by sin(Bt) multiplied by dt)

Find the first four nonzero terms of the given taylor series. a. f(x) = (1+x)^(-2) b. f(x) = e^(-3x)

Consider the power series sum of (n + 2)x^n from n = 1 to infinity. A) Find the radius of convergence, R. B) What is the interval of convergence? (Give your answer in interval notation.)

What is 33284 in expanded form?

How many integers from 0 through 30, including 0 and 30, must you pick to be sure of getting at least one integer (a) that is odd? (b) that is even?

Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x,y)inR if and only if a. x+y=0 b. x= y c. x-y is a rational numb...

Find the particular solution of the differential equation 2x*y prime - y = x^3 - x that satisfies the initial condition y = 4 when x = 4.

Find y as a function of x if (x^2)*y double prime + 2x*y prime - 30y = x^6, y(1) = 6, y prime (1) = -5.

Find the solution of the initial value problem y double prime + 2*y prime + 5y = 20e^(-t) cos(2t), y(0) = 10, y prime (0) = 0.

Find y as a function of t if 40000*y double prime - 9y = 0 with y(0) = 2, y prime(0) = 5.

Find the Taylor polynomial for x^-7x.

Find the five roots of the equation (x + 1)^5 = 32x^5.

2y'=e^x/2 +y

Evaluate the limit using L'Hospital's rule if necessary. Limit as x approaches +infinity of x^(3/x).

Solve the differential equation: sin xdy dx +(cos x)y=xsin(x^2).

Reparametrize the curve with respect to the arc length measured from the point where t=0 in the direction of increasing t. r(t)=e^6t cos(6t) i + 6 j+e^6t sin(6t) k

Evaluate the following integral: \displaystyle \int \frac{dx}{(121 + x^2)^2}.

Solve the initial value problem \displaystyle 12(t + 1) \frac{dy}{dt} - 8y = 32t, for t -1 with y(0) = 9.

Suppose R(t) = (3t^3)i - (2t^2 + 5)j + (4t^3)k. What is the curvature of R(t) if t = 2?

Find the values of the parameter r for which y = e^(rx) is a solution of the equation y double prime + 2*y prime - 3y = 0.

Solve x \, dy = x^3 \,dx - y\, dx

What is 0 divided by 0?

Determine if: A) The series is absolutely convergent. B) The series converges, but is not absolutely convergent. C) The series diverges. \displaystyle 1)\ \sum_{n=1}^{\infty}\frac{(-7)^n}{n^4}\\[5e...

Determine the convergence of the series \sum_{k=0}^{\infty} (-1)^{k+1} \frac{\sqrt k}{k+1}

Find the general solution of the following differential equations a) y''-2y'-3y = 3e^{2t} b) y''+2y'+5y = 3\sin 2t

Solve the initial-value problem t^3 \frac{\mathrm{d} y}{\mathrm{d} t} + 3t^2y = 4 \cos(t), \quad y(\pi) = 0

Determine if \displaystyle \sum_{n \ = \ 1}^{\infty} \frac{(-1)^{n + 1}}{n + \sqrt{n}} converges absolutely, converges conditionally or diverges.

Determine whether the series is absolutely convergent, conditionally convergent or divergent : \displaystyle \sum_{n \ = \ 1}^{\infty} \frac{(-1)^{n - 1}}{n + 6}.

Find equations for the following: (a) The plane which passes through the point (0,0,1) which is also orthogonal to the two planes x=2 and y=19. (b) The plane parallel to the plane 2x-3y=0 and passi...

The producer of a certain commodity determines that to protect profits, the price p should decrease at a rate equal to half the inventory surplus S-D , where S \enspace and \enspace D are r...

Why is expanded form important?

What does expanded form mean?

What is AC? Round your answer to the nearest hundredth.

Evaluate the integral. I = \int_0^\infty \frac{dx}{x^3 + 1}

Let f be a bounded function on lbrack 0,1 rbrack and P_n = left {0, {1 over n}, {2 over n}, cdots, {n-1 over n}, 1 right } be a partition of lbrack 0,1 rbrack for each n=1,2, cdots. Suppose lim {...

Use a triple integral to find the volume of the given solid. The tetrahedron is bounded by the coordinate planes and the plane z=10-2x-y.

Evaluate integral_{0}^{1} x^4e^{-x/3} dx.

Identify u and du, then give the correct answer to the integral. Integral of (5x^4 (x^5 + 1)^9) dx.

Calculate the following antiderivatives: a) the integral of (5t - 4t^6 + 6) dt b) the integral of (1/(u^(9/4)) + 7 sqrt(u) du c) the integral of (1/(2x^4)) dx

Evaluate the integral. integral_{0}^{2} x^2e^{x^3} dx

Prove the identity. sin4 x + cos4 x = 1 - 2 cos2 x + 2 cos4 x

Evaluate the following indefinite integral: integral 2x cos(x^2) dx

Find the area of the infinite region in the first quadrant between the curve y = e^(-x) and the x-axis. Give an integer or a simplified fraction.

Find the first derivative of the following function and evaluate at the given point. Product and Power Rules. h(x) = 6x^2 (3x + 4)^4; at x = 2.

Set up an integral for the length of the curve. y = x^8, 0 less than or equal to x less than or equal to 1.

Which of the following statement must be true?\\ A. If the diagonals of a quadrilateral are congruent, it is a rectangle.\\B. If a parallelogram contains a right angle, it is a square.\\C. If the d...

Evaluate: integral dy=-dx/x^2+c^2

Find the each value of theta in degrees (0 less than theta less than 90 deg ) and radians (0 less than theta less than pi/2 )

Find the derivative. \frac{d}{dx} \int_{1}^{\sqrt{x}} 16t^9 dt

Calculate the total area of the region described. Do not count the area beneath the x-axis as negative. Bounded by the line y = 6x, the x-axis, and the lines x = 4 and x = 5.

Set up an integral of the form int_a^b (f(x) - g(x)) dx for finding the area of the shaded region shown below. f(x) = g(x) =

Use the given function value(s) and the trigonometric identities to find the indicated trigonometric functions. (a) csc 30 (b) cot 60 (c) cos 30 (d) cot 30

Find two consecutive even integers such that the sum of the smaller and three times the larger is 30.

EvaluatingFind the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. sin u = 5/7, 0 less than u less than pi/2 Functions Involving Double Angles In Exercise, find the exac...

Use the Law of Sines to solve the triangle. A = 85 degrees 20', a = 35, c = 50

When a trigonometric equation has an infinite number of solutions, is it true that the equation is an identity? Explain.

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