# TayB

Popular questions and responses by TayB-
## Math

Express the function in the form f o g. (Use non-identity functions for f and g.) G(x)= cube root of (x/(9+x)) {f(x),g(x)}=?

*asked on January 28, 2015* -
## Calculus 1

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = sqrt(x), [0,16]

*asked on October 24, 2015* -
## Calculus 1

Find the numerical value of each expression. (Round your answers to five decimal places.) (a) cosh 9 (b) cosh(ln 9)

*asked on October 13, 2015* -
## Calc 1

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = 6 sin x, 0 ≤ x ≤ π

*asked on May 14, 2015* -
## Calculus 1

The curve y = |x|/(sqrt(5- x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2, 2)

*asked on September 25, 2015* -
## Calculus 1

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 5. (Round your answers to two decimal places.) f(t) = t^−1 − t *We havent learned derivative

*asked on September 12, 2015* -
## Math

Express the function in the form f compose g. (Use non-identity functions for f and g.) u(t) = cot t/(9+cot t) {f(t), g(t)}=?

*asked on January 28, 2015* -
## Calculus 1

Of the infinitely many lines that are tangent to the curve y = −4 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.

*asked on November 12, 2015* -
## Calculus 1

If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1/R= 1/R1+ 1/R2. If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how

*asked on March 29, 2015* -
## Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x^(5)e^(-6x)

*asked on October 21, 2015* -
## Calculus 1

The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function n = f(t) = a/(1 + be^−0.5t) where t is measured in hours. At time t = 0 the population is 10 cells and is

*asked on October 5, 2015* -
## Calculus 1 optimization

A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the

*asked on November 5, 2015* -
## Calculus 1

A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? (b) How much wire should be used for

*asked on November 11, 2015* -
## Calculus 1

Find the linear approximation of the function g(x)=cube root(1+x) at a=0.

*asked on October 13, 2015* -
## Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(t) = t^(3/4) − 3t^(1/4)

*asked on October 21, 2015* -
## math

Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→∞ (sqrt(49x^2+x)−7x)

*asked on February 11, 2015* -
## Calculus 1

Consider the following. B(x) = 3x^(2/3) − x (a) Find the interval of increase.(Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local maximum value(s).(Enter your answers

*asked on October 30, 2015* -
## Calc 1

Consider the position function s(t)=sin((pi)(t)) representing the position of an object moving along a line on the end of a spring. Sketch a graph of s with the secant line passing through (0,s(0)) and (0.5,s(0.5)). Determine the slope of the secant line

*asked on June 9, 2015* -
## math just for fun

A long year-end status report for work is 111 pages long. You need to print 16 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.88 each. Give your answer to the nearest cent,

*asked on August 27, 2016* -
## Calculus 1

Find the equation of the tangent line to the curve y = (9 ln x)/x at the points (1, 0) and (e, 9/e).

*asked on October 2, 2015* -
## Math

lim x→−12 sqrt(x^2 +25 −13)/x+12

*asked on February 7, 2015* -
## Calculus 1

Explain how the following graphs are obtained from the graph of y=f(x). (Select all that apply.) (d) y= -2f(x) shift 2 units upward shift 2 units downward shift 2 units to the right shift 2 units to the left stretch the graph vertically by a factor of 2

*asked on August 20, 2015* -
## Calculus 1

Find the derivative of the function. F(t) = e^(4t sin 2t)

*asked on March 13, 2015* -
## Calculus 1

Use logarithmic differentiation to find the derivative of the function. y =sqrt(x)^3x

*asked on March 12, 2015* -
## Calculus 1

If f(x)=3 sin x+ln(5x), find f '(x).

*asked on March 11, 2015* -
## calculus 2

Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.

*asked on January 22, 2016* -
## Calc 1

Evaluate the limit. lim x → 1 ln x/sin 5πx

*asked on April 26, 2015* -
## Calc 2

A hemispherical plate with diameter 10 ft is submerged vertically 2 ft below the surface of the water. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Recall that

*asked on March 24, 2016* -
## Calculus 1

A variable star is one whose brightness alternately increases and decreases. For one such star, the time between periods of maximum brightness is 4.7 days, the average brightness (or magnitude) of the star is 5.3, and its brightness varies by ±0.35

*asked on August 22, 2015* -
## Calculus 1

Related Rates: The minute hand on a watch is 9 mm long and the hour hand is 6 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)

*asked on October 8, 2015* -
## Calculus 1

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(t) = 6 cos t, −3π/2 ≤ t ≤ 3π/2

*asked on October 20, 2015* -
## Calc 1

Consider the following function. f(x) = x^6 ln x (a) Use l'Hospital's Rule to determine the limit as x → 0+. (b) Use calculus to find the minimum value. Find the interval where the function is concave up. (Enter your answer in interval notation.) Find

*asked on April 24, 2015* -
## Calculus 1

A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one

*asked on October 9, 2015* -
## philosophy

Libertarianism believes that causal determinism is true. Select one: True False I think true Whether or not we have free will seems to have implications for which of the following? Select one: a. Our idea of God b. Our idea of the physical laws of the

*asked on March 13, 2015* -
## Calculus 1

Use Newton's method with initial approximation x1 = −2 to find x2, the second approximation to the root of the equation x^3 + x + 1 = 0. *I got -1.307692 for my answer but it said that was wrong, so then I tried rounding it to two decimal places and got

*asked on November 12, 2015* -
## Calculus 1

Explain how the following graphs are obtained from the graph of y=f(x). (Select all that apply.) (a) y=7f(x) shifts 7 units upward shifts 7 units downward shifts 7 units to the right shifts 7 units to the left stretch the graph vertically by a factor of 7

*asked on August 20, 2015* -
## Calc 1

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = 5th root(x), 0 ≤ x ≤ 32

*asked on May 14, 2015* -
## Calc 1

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y =(x − 5)^2 that is closest to the origin.

*asked on May 2, 2015* -
## Calc 1

Consider the function below. f(x) = (x^2)/(x−9)^2 (a) Find the vertical and horizontal asymptotes. x=? y=? (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is

*asked on April 24, 2015* -
## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (sin^−1 x)/7x Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim

*asked on April 20, 2015* -
## calculus

Find the area of the region that lies inside the first curve and outside the second curve. r = 1 + cos(θ), r = 2 − cos(θ)

*asked on January 22, 2018* -
## Calculus 1

If tanh x=4/5, find the values of the other hyperbolic functions at x. sinh x= cosh x= coth x= sech x= csch x=

*asked on October 13, 2015* -
## Calculus 1

Related Rates Problem: Two cars start moving from the same point. One travels south at 40 mi/h and the other travels west at 30 mi/h. At what rate is the distance between the cars increasing three hours later?

*asked on October 7, 2015* -
## Calc 1

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 4 (a) Find the velocity at time t. (b) Find the distance traveled during the given time interval.

*asked on May 15, 2015* -
## Calc 1

Find f. f ''(x) = 6 + cos x, f(0) = −1, f(7π/2) = 0

*asked on May 6, 2015* -
## History

William McKinley justified annexation of the Philippines because, according to McKinley, the United States: Select one: a. Needed to bring civilization to the Filipinos. b. Needed the islands for business and trade. c. Felt the Filipinos were not ready for

*asked on February 25, 2015* -
## calc 2

Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem y' = y − 3x, y(4) = 0.

*asked on March 26, 2016* -
## Calculus 1

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = x^−3, 2 ≤ x ≤ 5

*asked on November 25, 2015* -
## Calculus 1

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x − 5)^2 that is closest to the origin.

*asked on November 13, 2015* -
## Calculus 1

simplify the expression. cos(2 tan^-1 x)

*asked on August 27, 2015* -
## Calculus 1

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a

*asked on August 18, 2015* -
## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→∞ x^7e^−x^6 Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim

*asked on April 20, 2015* -
## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (7x−sin 7x)/(7x−tan 7x)

*asked on April 20, 2015* -
## Calculus 1

Use logarithmic differentiation to find the derivative of the following equation. y = (2x+1)^5(x^4−3)^6

*asked on March 13, 2015* -
## Calculus

Differentiate the function. g(u) = sqrt(2)u+sqrt(7u) g'(u)=?

*asked on February 26, 2015* -
## Math

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 26 ft, express the area A of the window as a function of the width x of the window.

*asked on January 16, 2015* -
## calculus 2

Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (3, 45), and the x-axis.

*asked on January 25, 2016* -
## calculus 2

Sketch the region enclosed by the given curves. Find its area. y=7cos pi x, y=12x^2-3

*asked on January 25, 2016* -
## calculus 2

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. (Round your answer to two decimal places.) y = 8x^2− 3x, y = x^3−8x+ 2

*asked on January 22, 2016* -
## Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) f(θ) = 4 cos θ + 2 sin^2 θ

*asked on October 21, 2015* -
## Calculus 1

Find y' if y=ln(9x^2+7y^2).

*asked on October 2, 2015* -
## Calc 1

True or False. Explain. The graph of any function can have at most two horizontal asymptotes.

*asked on June 9, 2015* -
## Calc 1

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y =(x − 5)^2 that is closest to the origin.

*asked on May 2, 2015* -
## Calc 1

A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? (b) How much wire should be used for

*asked on April 28, 2015* -
## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0+ (sinx ln2x)

*asked on April 20, 2015* -
## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→3 (x^2+3x−18)/(x−3)

*asked on April 20, 2015* -
## Calculus 1

Water is leaking out of an inverted conical tank at a rate of 12,000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of

*asked on March 21, 2015* -
## Calculus 1

Use logarithmic differentiation to find the derivative of the function. y = x^(8cosx)

*asked on March 12, 2015* -
## History

A cause not widely championed by Progressives was: Select one: a. regulating industry b. women's suffrage c. prohibiting alcohol d. equal rights for blacks I think c or d

*asked on March 5, 2015* -
## History

At times, the Populists made remarkable efforts to unite black and white small farmers on a common political and economic program. Select one: True False I think true

*asked on February 25, 2015* -
## History

The Supreme Court's decision in Plessy v. Furguson (1896): Select one: a. Was a unanimous decision b. Sanctioned racial segregation c. Voided (undid) the Thirteenth Amendment to the Consititution d. Limited the hours that women could legally work. I think

*asked on February 25, 2015* -
## History

By the 1890s, through a network of women's clubs, temperance associations, and social reform organizations, women were exerting a growing influence on public affairs. True False I think true

*asked on February 25, 2015* -
## calc 3

Find a unit vector that is parallel to the line tangent to the parabola y = x^2 at the point (4, 16).

*asked on August 25, 2017* -
## Calc 2

Determine whether the series is convergent or divergent series symbol n=1 to infinity (n^2/(e^(3n))

*asked on April 26, 2016* -
## Calc 2

Find the solution of the differential equation that satisfies the given initial condition. du/dt= (2t + sec^2(t))/(2u), u(0) = −4

*asked on March 29, 2016* -
## calculus 2

The birth rate of a population is b(t) = 2000e^0.022t people per year and the death rate is d(t)= 1460e^0.017t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.)

*asked on January 22, 2016* -
## Calculus 1

Consider the function below. f(x)= (x^2)/((x-4)^2) Find the interval where the function is concave up. (Enter your answer using interval notation.) Find the intervals where the function is concave down. (Enter your answers using interval notation.) For

*asked on November 15, 2015* -
## Calculus 1

Of the infinitely many lines that are tangent to the curve y = −4 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.

*asked on November 13, 2015* -
## Calculus 1-Optimization

A box with a square base and open top must have a volume of 4,000 cm^3. Find the dimensions of the box that minimize the amount of material used. sides of base cm height cm

*asked on November 5, 2015* -
## Calculus 1

The curve with the equation y^2=5x^4-x^2 is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (-1,2).

*asked on September 29, 2015* -
## Calc 1

If a function is continuous, then it is differentiable.

*asked on June 9, 2015* -
## Calc1

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = sec^2 x, 0 ≤ x ≤ π/4

*asked on May 14, 2015* -
## Philosophy

Do you believe abortion is morally permissible? Why or why not?

*asked on May 2, 2015* -
## Calc 1

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)=x^3+x-4 [0,2]

*asked on April 22, 2015* -
## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (e^9x−1−9x)/(x^2)

*asked on April 20, 2015* -
## History

Can anybody help me figure out what is progressive and considered progressivism in this video. American Experience TR, The Story of Theodore Roosevelt Part4 4 PBS Documentary

*asked on March 11, 2015* -
## Calculus 1

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+y^2=(2x^2+4y^2−x)^2 (0, 0.25) (cardioid)

*asked on March 9, 2015* -
## Philosophy

If you were to sum up the Stanford Prison and Milgram experiments in a phrase that encapsulates the findings of the experiments, which of the following would it be? Select one: a. "Only the strong survive." b. "Evil acts are performed by inherently evil

*asked on March 6, 2015* -
## History

Theodore Roosevelt's taking of the Panama Canal Zone is an example of: Select one: a. his ability to "speak softly". b. his belief in intervening with the sole purpose to "uplift" the peoples of Central America. c. his belief in "liberal internationalism"

*asked on March 5, 2015* -
## Calculus 1

Find an equation of the tangent line to the curve y = 6/(1+e^−x)at the point (0,3).

*asked on March 4, 2015* -
## History

Compare and contrast the ideas and policies, domestic and foreign, of Roosevelt, Taft and Wilson. Where can I find information that compares their domestic policies? -My Answer so far: Roosevelt, Taft, and Wilson were all progressive reformers, but their

*asked on March 3, 2015* -
## Calculus

Find an equation of the normal line to the parabola y=x^2−8x+1 that is parallel to the line x−6y =7.

*asked on February 26, 2015* -
## Math

Find an expression for the function whose graph is the given curve. The top half of the circle x^2+(y-4)^2=4

*asked on January 16, 2015* -
## calc 3

Find the exact length of the curve. x = 1 + 9^t2, y = 7 + 6^t3, 0 ≤ t ≤ 2

*asked on January 18, 2018* -
## Law and ethics

On Sunday I was rear ended while waiting in line at a McDonald’s drive thru. I got out right after it happened while still in line to see if I could see any damages because I did hear and feel the impact. The person who hit me yelled at me that there was

*asked on December 12, 2017* -
## Matrices

Solve the system using matrices. Show all the row operations that you use. 3x-9y=30 2x+5y= -2

*asked on September 21, 2016* -
## calculus 2

Use Euler's method with a step size of 0.2 to estimate y(1), where y(x) is the solution of the initial value problem y' = 6x+y^2, y(0)=0. Round your final answer to 4 places, but keep more places on the intermediate steps for accuracy.

*asked on April 11, 2016* -
## calc 2

Find the orthogonal trajectories for the family of curves y=(kx)^6.

*asked on April 7, 2016* -
## Calc 2

Find the center of mass for the region bound by y= -2x+6, x=0, and y=0

*asked on April 7, 2016* -
## Calc 2

Find the solution of the differential equation that satisfies the given initial condition. dy/dx= x/y, y(0) = −7

*asked on March 29, 2016*