Friday

February 12, 2016
**Calculus**

What is the maximum volume of a closed box with a square base which can be made by bending the material? The box is to have a surface area of 100in^2.
*Sunday, October 25, 2015 by Paige*

**Calculus**

You need to do the fencing of two side by side areas with 102 meters of wood fencing. What is the maximum area that you will be able to enclose?
*Sunday, October 25, 2015 by Taylor*

**Calculus**

Hello, Tutors! I am struggling on how to do problems related to finding the volume using integrals. Could you please help me? Any easy-to understand resources? Thank You for all your help. I am thankful for you tutors!!!!!!!
*Sunday, October 25, 2015 by Anonymous*

**Calculus**

1. Calculate the population within a 7-mile radius of the city center if the radial population density is ρ(r) = 5(5 + r2)1/3 (in thousands per square mile). (Round your answer to two decimal places.) 2. A population of insects increases at a rate 280 + 8t + 1.5t2 insects...
*Sunday, October 25, 2015 by Anonymous*

**Calculus**

What is the average value of f(x) on [0,4] if the area between the graph of f (x) and the x-axis is equal to 12? I used the average value formula and got 12. But the answer key says 3. My work: M= 1/4 [12x] interval: [0,4] 48/4=12
*Sunday, October 25, 2015 by Tiffany*

**Calculus help plz**

Using the first rule of derivative find 8(x-y)12?? And how can i solve these y^x+x^y=17,x+y=5
*Saturday, October 24, 2015 by Franklin:*

**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]
*Saturday, October 24, 2015 by TayB*

**Calculus 1**

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = x^3−x^2−20x + 7, [0, 5]
*Saturday, October 24, 2015 by TayB*

**Calculus 1**

find the critical numbers of the function F(x)=x^(4/5)(x-1)^2
*Friday, October 23, 2015 by TayB*

**Calculus-Steve**

Find the area of the region between the graphs of f(x)=3x+8 and g(x)=x^2 + 2x+2 over [0,2]. I got 34/3. Calculus - Steve ∫[0,2] (x^2+2x+2) dx = 1/3 x^3 + x^2 + 2x [0,2] = 8/3 + 4 + 4 = 32/3 Why are you taking the antiderivative of x^2 +2x+2 when we are trying to find the...
*Thursday, October 22, 2015 by Tiffany*

**Calculus**

Find the area of the region between the graphs of f(x)=3x+8 and g(x)=x^2 + 2x+2 over [0,2]. I got 34/3.
*Thursday, October 22, 2015 by Tiffany*

**Calculus III**

What is the velocity vector of a particle traveling to the right along the hyperbola y=x−1 with constant speed 1 when the particle's location is (4, 14). (Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list of i, j ...
*Thursday, October 22, 2015 by Kevin*

**Calculus III**

Compute the length of the curve r(t)=5ti+8tj+(t2+4)k over the interval 0≤t≤6 Hint: use the formula ∫t2+a2‾‾‾‾‾‾‾√dt=12tt2+a2‾‾‾‾‾‾;‾√+12a2ln(t+...
*Thursday, October 22, 2015 by Steven*

**Calculus**

A long rectangle sheet of metal, 15 inches wide is to be made into a rain gutter by turning up equal amounts on each side so that they are perpendicular to the sheet. How many inches should be turned up in order to give the gutter its greatest capacity (i.e. maximize the ...
*Thursday, October 22, 2015 by Gaston College*

**Related Rates Calculus**

A man 1.8 m tall is walking at a rate of 1.5 m/s away from a streetlight. It is found that the length of his shadow is increasing at a rate of 0.9 m/s. How high above the ground is the streetlight?
*Wednesday, October 21, 2015 by Sisi*

**Calculus i need help plz plz**

Integrate:Sinxcosx/a^2cos^2(x)+b^2sin^2(x))dx??? plz i need the full working too hard for me
*Wednesday, October 21, 2015 by Collins*

**Calculus**

A graphic designer is asked to create a movie poster with a 128 in^2 photo surrounded by a 4 in border at the top and bottoms and a 2 in border on each side. What overall dimensions for the poster should the designer choose to use the least amount of paper?
*Wednesday, October 21, 2015 by Anonymous*

**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
*Wednesday, October 21, 2015 by TayB*

**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)
*Wednesday, October 21, 2015 by TayB*

**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^4/5(x − 1)^2
*Wednesday, October 21, 2015 by TayB*

**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)
*Wednesday, October 21, 2015 by TayB*

**Calculus**

Estimate the relative rate of change of f(t)=5t^2 at t=4. Use change of 0.01.
*Tuesday, October 20, 2015 by Julie*

**Math 142 (calculus)**

Determine d^2y/dx^2 for y=(5x^5+7)^4
*Tuesday, October 20, 2015 by Matt*

**Calculus**

Find constants a and b in the function ax^b/ln(x) such that f(1/5)=1 and there is a local min at x=1/5
*Tuesday, October 20, 2015 by Tanner*

**Pre-calculus**

(y-7)^2 = 12x Find the directrix
*Tuesday, October 20, 2015 by Cope*

**Calculus...need help**

Prove that the integral 1/root(ax^2+bx+c)dx=1/root(a)|n(2ax+b+2root(a(ax^2+bx+c)]+k....please i don,t no it
*Tuesday, October 20, 2015 by Collins*

**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
*Tuesday, October 20, 2015 by TayB*

**Calculus 1**

Find the derivative dy/dx for the following. Simplify your answer. y=(ln(x^2))/(x^3) I got (2/x x^3-3x^2 ln(x^2))/((x^3)^2) for the derivative is that correct? Or no?
*Tuesday, October 20, 2015 by TayB*

**Calculus**

If the velocity function of an object is v(t) = -5t4 - 20t + 100, find the displacement function given that the displacement is 50 ft when time is 1 second
*Monday, October 19, 2015 by Chong*

**Pre-calculus**

Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x, y, and z in terms of the parameter a.) x-3y+2z=21 5x-13y+12z=81 I have an answer but i'm not sure if it's ...
*Monday, October 19, 2015 by Sarah*

**Calculus**

What is the shortest distance from the surface xy+6x+z^2=33 to the origin?
*Sunday, October 18, 2015 by A*

**Calculus**

A company manufactures x units of one item and y units of another. The total cost in dollars, C, of producing these two items is approximated by the function C=7x^2+xy+1y^2+600. A) If the production quota for the total number of items (both types combined) is 182, find the ...
*Sunday, October 18, 2015 by A*

**Pre Calculus**

A park has a circular walking path with a diameter of 250 meters. a) Write the equation to describe the walking path in your diagram. b) Find the distance traveled by someone walking once around the entire path. c) Find the distance traveled by someone walking counterclockwise...
*Sunday, October 18, 2015 by Erika G.*

**Calculus i need help plz plz**

If y=ws^3/d^4 find the % increase in 'y' when 'w' increases by 2% and 's' decreases by 3% and 'd' increasee by 1%...... There a little error in the first question i post here it is plz i need the working and explanation
*Sunday, October 18, 2015 by Collins*

**Calculus**

How do I calculate the following? tan−1(tan(8)) − tan−1(tan(4))
*Sunday, October 18, 2015 by Anonymous*

**HELP CALCULUS**

Find dy/dx by implicit differentiation. tan−1(4x2y) = x + 3xy2
*Saturday, October 17, 2015 by Anonymous*

**calculus**

solve the differential equation that satisfies the given condition: dy/dx=(ycos(x))/(6+y^2), y(0)=1
*Saturday, October 17, 2015 by Lauren*

**Calculus**

The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (0,1) where f'(c)=0. f(x) = x3 - 2x2 + x, [0, 1] Round your answer to two decimal places.
*Saturday, October 17, 2015 by olga*

**Calculus**

The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (-3, -2) where f'(c)=0. f(x) = x + 6x-1 , [-3, -2] Round your answer to two decimal places.
*Saturday, October 17, 2015 by olga*

**Calculus**

The function defined below satisfies the Mean Value Theorem on the given interval. Find the value of c in the interval (1, 2) where f'(c)=(f(b) - f(a))/(b - a). f(x) = 1.5x-1 + 1.1 , [1, 2] Round your answer to two decimal places.
*Saturday, October 17, 2015 by olga*

**Calculus**

Determine the linear approximation of 21/2. Express your answer as a reduced fraction in the form a/b.
*Saturday, October 17, 2015 by olga*

**Calculus**

The measurement of the side of a square is found to be 12 cm with a possible error of 0.05 cm. Use differentials to estimate the propagated error ΔA in computing the area of the square. Please do not include the ± symbol in your answer. Round your final answer to ...
*Saturday, October 17, 2015 by olga*

**Calculus**

Which of the following is the linear approximation formula, L(x), that estimates values of y = ln(x) + 1 for values of x near 1? a) y = x - 1 b)y = x c)y = x + 1 d)y = -x
*Saturday, October 17, 2015 by olga*

**Calculus also need help plz plz plz**

If z=1/(x^2+y^2-1) is x(dz/dx)+y(dz/dy)=-2z(1+z) or -z^2(1+z) note:dz/dx=partial derivative of x and dz/dy=partial derivative of y??
*Saturday, October 17, 2015 by Collins*

**Calculus badly need help so difficult**

If y=ws^3/d^4 find the percent increase in y when w increase by 2% s decrease by 3% and s decrease by 1% plz show the full solution the question is byond my power
*Saturday, October 17, 2015 by Collins*

**Calculus**

Find c so y=4x+3 is tangent to the curve y=x^2+c
*Friday, October 16, 2015 by Matt*

**Calculus**

An open box with a capacity of 36,000 cubic inches is to be twice as long as it is wide. The material for the box is $.10/sq ft. What are the dimensions of the least expensive box? How much does it cost?
*Friday, October 16, 2015 by Matt*

**Calculus**

An open box is made by cutting squares of side w inches from the four corners of a sheet of cardboard that is 24" x 32" and then folding up the sides. What should w be to maximize volume of the box? I started by trying to get a formula for the volume which I thought ...
*Friday, October 16, 2015 by Matt*

**Pre-Calculus**

The angle of depression from the top of a 75 ft. lighthouse to a ship out in the ocean is 40*. How far out is the ship from the lighthouse? I've been stuck on this problem for an hour, I know the answer but don't know how to set it up/enter it in a calculator.
*Thursday, October 15, 2015 by Jason*

**Integral Calculus**

Initial Value Problem dy/dx = y^2 -5y+6 y(0)=1
*Thursday, October 15, 2015 by Chintu*

**Calculus**

You have been asked to determine where a water works should be built along a river between Chesterville and Denton to minimize the total cost of the pipe to the towns. (a) Assume that the same size (and cost) pipe is used to each town. (This part can be done quickly without ...
*Thursday, October 15, 2015 by Hayk *

**Calculus**

Differentiate to find critical numbers and leave function in fully factored form. g(x) = (x^2+1)^5(x^2+2)^6 g'(x) = (x^2+1)^5[6(x^2+2)^5(2x)] + (x^2+2)^6[5(x^2+1)^4(2x)] g'(x) = 2x(x^2+1)^4(x^2+2)^5[6(x^2+2)(2x) + 5(x^2+1)(2x)] g'(x) = 2x(x^2+1)^4(x^2+2)^5(11x^2+11...
*Wednesday, October 14, 2015 by Justin*

**Calculus**

Someone had helped me yesterday, but I need it broken down more because I honestly don't understand any of this? A plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. Find the rate at which the distance from the ...
*Wednesday, October 14, 2015 by Callie*

**calculus**

find the first and second derivatives for 3x^4-4xy^2+7=2y
*Wednesday, October 14, 2015 by jack*

**differential calculus**

a man 6 ft tall is walking toward a building at the rate of 4 ft/sec. if there is a light on the ground 40 ft from the building, how fast is the man's shadow on the building growing shorter when he is 30 ft from the building?
*Wednesday, October 14, 2015 by jordan*

**Calculus**

6e^3t=9e^2t
*Tuesday, October 13, 2015 by Julie*

**Calculus**

A plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station.
*Tuesday, October 13, 2015 by Callie*

**Calculus**

If a ball is thrown vertically upward with a velocity of 96 ft/s, then its height after t seconds is s = -16t^2 + 96t. What is the velocity of the ball when it is 128 ft above the ground on its way up?
*Tuesday, October 13, 2015 by Callie*

**Calculus**

The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 48 feet high is s(t) = -16t^2 - 32t + 48, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground?
*Tuesday, October 13, 2015 by nrosen*

**Calculus 1**

Find the linear approximation of the function g(x)=cube root(1+x) at a=0.
*Tuesday, October 13, 2015 by TayB*

**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=
*Tuesday, October 13, 2015 by TayB*

**Calculus 1**

Find the numerical value of each expression. (Round your answers to five decimal places.) (a) cosh 9 (b) cosh(ln 9)
*Tuesday, October 13, 2015 by TayB*

**Calculus**

The altitude attained by a model rocket t seconds into flight is given by the equation: -t^3+3t^2+20t-3 where t is greater than or equal to 0 seconds. find the maximum altitude attained by the rocket. first I found the derivative of the original equation and set it to 0. which...
*Monday, October 12, 2015 by Michelle*

**Pre-calculus**

Complete the table assuming continuously compounded interest. (Round your answers to two decimal places.) Initial Investment: Annual % Rate: Time to Double: 8 yr Amount After 10 Years: $1700 I don't understand how to get in the initial investment of annual % rate given ...
*Sunday, October 11, 2015 by Sarah*

**calculus **

Find the maximum value of the function f(x,y) = 9x2−9xy+y3 on the closed rectangle whose corners are the points (1,1), (1,−1), (−1,1) and (−1,−1)
*Saturday, October 10, 2015 by Calculus *

**Calculus**

Sketch the vector field F⃗ (r⃗ )=2r⃗ in the plane, where r⃗ =⟨x,y⟩. Select all that apply. A.All the vectors point away from the origin. B. The vectors increase in length as you move away from the origin. C. All the vectors point toward ...
*Saturday, October 10, 2015 by A*

**Calculus**

(x^2+y^2)^2=16y Find all values of x where the tangent line is vertical I found the derivative and looked for where it was undefined but it didn't work
*Saturday, October 10, 2015 by Henry*

**Math Calculus**

Postal regulations specify that a package sent by certain shipping methods may have a combined length and girth of no more than 99 inches. Find the dimensions of a CYLINDRICAL package with the greatest volume that may be sent by this shipping method. HINT* the length plus the ...
*Saturday, October 10, 2015 by Heather*

**Calculus**

what is the limit as h approaches 0 of ((x+h)^pi-x^pi)/h? Multiple choice answers: A: lnx B: lnx (x^pi) C: Pi lnx D: (pi^2) ln (x^2) E: (pi^x) lnx I know this is d/dx x^pi, or Pi x^(Pi-1)
*Saturday, October 10, 2015 by Henry*

**Calculus i need help**

Find dy/dx if x^2.y+sin(xy)+y^4.x^2+3xy=5???
*Saturday, October 10, 2015 by Collins*

**Pre-Calculus**

For the function f(x)=12x^3+4x^2-27x-9 describe the end behavior. Find the real zeros of f and determine whether the graph crosses or touches the x-axis at each x-intercept. Use the zeros of f and test numbers to find the intervals over which the graph of f is above or below ...
*Saturday, October 10, 2015 by Leizy*

**calculus**

Show that sinh (sinh^-1 x) = x
*Saturday, October 10, 2015 by ligas*

**calculus**

y = x^2 − 9x + 29/x − 5 relative maximum (x, y) = relative minimum (x, y) =
*Saturday, October 10, 2015 by akash*

**calculus**

Identify any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = x^3 + 3x^2 + 3x + 2 x-intercept (x, y) = y-intercept (x, y) = relative maximum (x, y) = relative minimum (x, y) = point of inflection (x, y) = ...
*Saturday, October 10, 2015 by akash*

**calculus**

Identify any intercepts, relative extrema, points of inflection, and asymptotes. y = 4x^2 − 24x + 34 X-intercept ? (x, y) (smaller x-value) (x, y) (larger x-value) relative minimum (x, y)
*Saturday, October 10, 2015 by akash*

**calculus**

using the two existing corner sides of an existing wall, what is the maximum rectangular area that can be fenced by a fencing material 30 ft long?
*Friday, October 9, 2015 by ligas*

**Pre-calculus**

Hi i need to find x in 9^(2x-6)=6^(8x-5) So what i did was: 3^(4x-12)=6^(8x-5) log3(3)^(4x-12)=log3(6)^(8x-5) 4x-12=(8x-5)log3(6) now i'm stuck. and i actually feel that the whole thing is wrong. help, pls
*Friday, October 9, 2015 by Lid*

**Calculus**

lim x -> pi/2 (sin(x/2)-cos(x/3)) Evaluate Please help
*Friday, October 9, 2015 by Alz*

**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 decimal place.)
*Friday, October 9, 2015 by TayB*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y=x^2, y=sqrt(x), about y=1. I have to use either the disk or washer method and i believe i use washer. i set up the integral to be pi[(1-x^3)^2 -(1-sqrt(x))^2] from 0 to 1 for my limits. i worked it out ...
*Friday, October 9, 2015 by Jedidiah*

**Calculus**

Use the FTC 1 to find the area of the region under the graph of the function f(x)= 8x-x^2 on [0,8]. I got 244/3 but the answer key says 256/3.
*Thursday, October 8, 2015 by Anonymous*

**Pre-Calculus**

Find the difference quotient usingF(x)-f(1)/x-1 1. f(x)=-3x+2 Given F(x) =2x Find f(x+🔼x) -f(x)/🔼 x
*Thursday, October 8, 2015 by Please HELP*

**Calculus 1**

Related Rates: 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 ...
*Thursday, October 8, 2015 by TayB*

**calculus**

Given the function f(x)=1/4 x^4 - 3/2 x^2 a. discuss the relative maxima, minima relative b. determine where f is increasing and where f is decreasing c. Find the points of inflection. d. Discuss the concavity
*Thursday, October 8, 2015 by zel*

**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.)
*Thursday, October 8, 2015 by TayB*

**Calculus 1**

Related Rates: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.9 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall?
*Thursday, October 8, 2015 by TayB*

**Calculus 1**

Water is leaking out of an inverted conical tank at a rate of 9,500 cm^3/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 20 cm/min when the ...
*Thursday, October 8, 2015 by TayB*

**HELP HELP CALCULUS **

y=e^(5e^x) differentiate first and second derivative
*Wednesday, October 7, 2015 by Anonymous*

**Calculus**

I've done everything I can think of to solve this, but I have no idea. Find the derivative: y = sq rt{11x + sqrt[11x + sqrt(11x)]}
*Wednesday, October 7, 2015 by Kelly*

**Calculus 1**

Related Rates: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.
*Wednesday, October 7, 2015 by TayB*

**Calculus**

A man of height 1.7 meters walks away from a 5-meter lamppost at a speed of 1.6 m/s. Find the rate at which his shadow is increasing in length. (Round your answer to three decimal places.) This problem is absolutely killing me I see a lot of examples like this on here but I ...
*Wednesday, October 7, 2015 by Jake*

**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?
*Wednesday, October 7, 2015 by TayB*

**Calculus**

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 8 sin t, where t is in seconds and x is in centimeters. The first part of the question is to find the velocity and acceleration equations, which I got to be: v...
*Tuesday, October 6, 2015 by kelly*

**Calculus/Math**

lim ((1-2x)/(√1+x^2)-1) x→∞ Find the value.
*Tuesday, October 6, 2015 by Marc*

**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 increasing at a ...
*Monday, October 5, 2015 by TayB*

**calculus**

Find the resultant vector. 1) A force of 35 grams and 45 grams applied at right angles. 57.009 g at 52° with respect to the 35 kg force 2) Velocities of 400 mph due north and 500 mph due east. 640.31 mph at 51° with respect to the 400 mph force 3) Displacements of 90 ...
*Monday, October 5, 2015 by sasha*

**Calculus**

A bright light on the ground illuminates a wall 12 meters away. A man walks from the light straight toward the building at a speed of 1.2 m/s. The man is 2 meters tall. When the man is 4 meters from the building, how fast is the length of his shadow on the building decreasing?
*Monday, October 5, 2015 by Madison C.*

**calculus**

It is desired to design a ski jump ramp. The ramp will be represented by a polynomial whose graph is a side view of the ramp. The ramp must fulfill the following specifications: The ramp begins at a height of 100 feet and ends at a height of 10 feet above the ground. From ...
*Monday, October 5, 2015 by Jennifer*

**AP Calculus AB**

Hello! I'm having trouble with this related rates problem: A 5ft tall person is walking away from a 16ft tall lamppost at a rate of (2/x) ft/sec, where x is the distance from the person to the lamppost. Assume the scenario can be modeled with right triangles. At what rate ...
*Sunday, October 4, 2015 by Andy*

**Calculus **

Differentiate. g(x) = 5e^x√x
*Sunday, October 4, 2015 by Joey*