Saturday

February 6, 2016
**Calculus AB**

If f(x) is differentiable for the closed interval [-3, 2] such that f(-3) = 4 and f(2) = 4, then there exists a value c, -3 < c < 2 such that f(c) = 0 f '(c) = 0 f (c) = 5 f '(c) = 5 Not really sure where to start here. No textbook and my teacher never explained it
*Tuesday, January 12, 2016 by Vikram*

**Calculus**

What airspeed and direction should an airplane maintain in order to continue having a ground speed of 800 km/h and a direction of 140° with wind at 130 km/h at 27°?
*Tuesday, January 12, 2016 by Geoff*

**Calculus help!!!**

X^2y+sinxy=e^xy i need solution plz
*Tuesday, January 12, 2016 by Daniel*

**Calculus**

A manufacturer of a certain brand of appliance estimates that he can sell 5000 units a year at Php 900.00 each and that he can sell 1500 units more per year for each Php 100.00 decrease in price? What price per unit will give the greatest returns?
*Tuesday, January 12, 2016 by En*

**Calculus**

Since f(x)=√(x-3) has an absolute minimum of 0 does its critical point exist? I'm really confused because someone mentioned that f(x)=√(x+3) does not have a critical point. Does that mean that if there is an end point there, there can't be a critical point?
*Tuesday, January 12, 2016 by Isabella*

**calculus**

Suppose f is a function of x. 1) find d/dx f^2 2)use the result to find the integral ∫ lnx/xdx. I did 1), and I got 2fdf, but im confused about number 2.
*Monday, January 11, 2016 by Jacob*

**Calculus**

Find all points on the graph of the function f(x) = 2 cos(x) + (cos(x))2 at which the tangent line is horizontal. Consider the domain x = [0,2π). I have pi/2 and 3pi/2 for x values. But when I plug them I get zero. Is this correct as y values or am I solving it wrong? I ...
*Monday, January 11, 2016 by Calculus*

**Calculus**

Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help.
*Monday, January 11, 2016 by Andre*

**Calculus AB**

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x(1/3) + 6x(4/3). You must justify your answer using an analysis of f '(x) and f "(x). My start to a solution: x-values: (-1/8) and (-1/4) I got -1/8 from f'(x)- ...
*Monday, January 11, 2016 by Vikram*

**Calculus AB**

What is the maximum volume in cubic inches of an open box to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative. Give ...
*Monday, January 11, 2016 by Vikram*

**Calculus**

For the following function, find the relative max's or min's using any method. I'm having a hard time finding the critical points...
*Sunday, January 10, 2016 by Isabella*

**Calculus**

For the function below, determine the intervals of concavity: f(x)=xlnx I tried doing it but the second derivative would always be f''(x)=1/x, so it would be concave up at x>0 and concave down at x<0, which is wrong. Also, for the function below, determine the ...
*Sunday, January 10, 2016 by Isabella*

**calculus**

Find a cubic function y = ax3 + bx2 + cx + d whose graph has horizontal tangents at the points
*Saturday, January 9, 2016 by Kyle*

**Physics with Calculus**

qsub1:-2.8uC qsub2: 6.6uC qsub2 sits 7.9 cm away from qsub2, and in a previous question moved up the y axis 2.7cm. The question that I am having difficulty with has added qsub3 in the middle of of qsub1 and qsub2, changing the magnitude of Fsub2net= 7.954. What is the sign and...
*Saturday, January 9, 2016 by Jessica*

**Calculus @ Henry**

I worked some on this earlier, and botched it a bit, so here goes again. A water tank is made by rotating f(x)=2^x-1 between [0,2] about the y-axis. The water tank is initially full, when a hole is opened at the bottom tip so that the water drains at a rate of 4 unit^3/second...
*Friday, January 8, 2016 by Steve*

**Calculus**

The side of a square is measured to be 10 ft with a possible error of ±0.1 ft. Use differentials to estimate the error in the calculated area. Include units in your answer.
*Friday, January 8, 2016 by Mel*

**Calculus**

Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 16cm and a height of 8cm, at the rate of 4 cm^3/min. At what rate is the depth of the water changing at the instant when the water in the tank is 6 cm deep? Show all work and include ...
*Friday, January 8, 2016 by Mel*

**Calculus**

The position function of a particle in rectilinear motion is given by s(t) = 2t^3 – 21t^2 + 60t + 3 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include units in your answer.
*Friday, January 8, 2016 by Mel*

**Calculus**

What is the maximum volume in cubic inches of an open box to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative. Give ...
*Friday, January 8, 2016 by Mel*

**Calculus**

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x^(1/3) + 6x^(4/3). Please use an analysis of f ′(x) and f ′′(x).
*Friday, January 8, 2016 by Mel*

**calculus**

A wire along 1 meter is divided into three parts . The first part is formed into a circle , the second part is formed into an equilateral triangle , and the third part is formed into a square . Determine the size of each section so that the total area of the three wake formed ...
*Friday, January 8, 2016 by jon*

**Calculus**

A water tank is made by rotating f(x)=2^x-1 between [0,2] about the y-axis. The water tank is initially full, when a hole is opened at the bottom tip so that the water drains at a rate of 4 unit^3/second. How fast is the height of the water decreasing when the height has ...
*Friday, January 8, 2016 by Henry*

**Another Calculus help plz **

Integrate:( dx/root(x^2-4x)^3 help me show it solution
*Tuesday, January 5, 2016 by Collins*

**Calculus help plz **

Integrate:(K+1/k^2+4k+8)dx
*Tuesday, January 5, 2016 by Collins*

**Calculus**

Which of the following integrals represents the volume of the solid formed by revolving the region bounded by y=x^3, y=1, and x=2 about the line y=10? a) pi*∫from (8-1) of (10-y)(2-y^(1/3))dy b) pi*∫ from (1-2) of (81-(10-x^3)^2)dx c)2pi*∫from (1-8) of y(2-y...
*Monday, January 4, 2016 by Fred*

**calculus**

the region bounded by the graph f(x)=x(2-x) and the x axis is revolved about the y axis. Find the volume of the solid. I did the integral using the shell method, but the answer wasn't correct.
*Monday, January 4, 2016 by john*

**Calculus**

Find the volume generated by rotating about the x axis the area bounded by x=0, y=2sinxcosx,, y=2cosx, and x=4, if 0≤x≤pi/2. I don't get the graph.
*Monday, January 4, 2016 by Andre*

**Calculus help plz i do not no it at all**

Integrate: xrootof(2+3.fourth rootof(x^3)/x^6.root(x) plz help i do not no it at all show working!!
*Monday, January 4, 2016 by Collins*

**Calculus**

A ball is thrown straight up from the top of a hill 30 feet high with an initial velocity of 72ft/sec. How high above level ground will the ball get? (Objects subjected to gravity adhere to s(t) = -16t^2 + v0t + so where s is the height of the object in feet v0 is the initial ...
*Monday, January 4, 2016 by Help*

**Another Calculus help plz**

Show that if y=tanx/2 dy/dx=1/sinx
*Monday, January 4, 2016 by Collins*

**Calculus help plz**

Integrate:cosmxcosnx.dx if m=n i can not solve it i have tried my best but to no avail
*Monday, January 4, 2016 by Collins*

**Calculus**

A thin plate lies in the region between the circle x^2+y^2=4 and the circle x^2+y^2=1 above the x axis. Find the centroid. For the second part, same question except the region in the first quadrant instead of above x axis. For part a, I figured out bar x is 0, and I tried to ...
*Sunday, January 3, 2016 by Andre*

**Calculus pz help urgently**

Integrate:sinxcos(x-1/4.pi)dx
*Sunday, January 3, 2016 by Collins*

**Calculus**

Last one for me. Evaluate (3x^2)/sqrt(1-x^6) dx I changed sqrt (1-x^6) into 1^(1/2)- x^(3) and let u=1^(1/2)- x^(3) then I got du/dx=3x^2 and subbed dx=du/3x^2 into the equation and got x-(x^4/4) but its not right. Options 7x^3/(3sqrt(1-x^7) + C cos-1(3x) + C sin-1(x^3) + C ...
*Saturday, January 2, 2016 by Henry*

**Calculus**

Which of the following integrals cannot be evaluated using a simple substitution? I think it is A because if you would substitute there would be nothing left in the equation? Is that right? Options ∫√(x-1) ∫1/√(1-x^2) ∫x/√(1-x^2) ∫&#...
*Saturday, January 2, 2016 by Henry*

**Calculus**

∫(x^3-x^2)/x^2 I got (x^2)/(2)-x + C but that's not one of the answers Options x - 1 + C (x^2/2)-(x^3/3) + C (x^4-x^3)/4x^2 + C (x^2/2) -x + C
*Saturday, January 2, 2016 by Henry*

**Calculus help plz**

Evaluate in (cuberootof(x+1)/(x-1)).1/(x+1)dx help plz
*Saturday, January 2, 2016 by Collins*

**Calculus**

∫((cos^3(x)/(1-sin^(2)) What is the derivative of that integral? I have been trying to use trig identities but can't find one to simplify this equation. I can't find one for (cos^3(x) or (1-sin^(2)) My options -sin(x) + C sin(x) + C (1/4)cos^(4)(x) + C None of ...
*Saturday, January 2, 2016 by Henry *

**calculus**

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 − 9x on the interval [−1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. Not quite sure how to do this one at all to be completely honest. ...
*Friday, January 1, 2016 by Jason*

**Reposting calculus help plz**

Dy/dx=(X+x^3)/y help show working
*Friday, January 1, 2016 by Collins*

**Calculus need help**

Dy/dx=x+x^3/y plz show your work
*Friday, January 1, 2016 by Collins*

**Calculus**

A 20 meter long steel cable has density 2 kg per meter. It is hanging straight down. There is a 100 kg bucket of concrete attached to the bottom. How much work is required to lift the bucket 10 meters by lifting the cable ten meters? Gravitational force equals 9.8 in this ...
*Thursday, December 31, 2015 by Andre*

**Calculus**

A cylindrical water tank has radius r=1 meter and height 10 meters. Suppose the tank is lying on its side and is filled halfway with water. How much work does it take to pump all the water out the top of the tank? The height is now 2 meters. Thanks, I'm not really sure how...
*Thursday, December 31, 2015 by Quentin*

**Calculus**

The balance in an account triples in 20 years. Assuming that interest is compounded continuously, what is the annual percentage rate? I found the equation: y=e^(xln3/20) assuming that y0=1 I got 5.64%, is that right?
*Monday, December 28, 2015 by Gary*

**Calculus**

Find the integral of 2/((2-x)(x+2)^2)dx.
*Sunday, December 27, 2015 by Henry*

**Algebra**

Over 350 students took a college calculus final exam. the scores of the students follow a normal distribution. using the information given below, determine the mean and the standard deviation for the students'scores. Give your answers to the nearest tenth of a percent. 1. ...
*Sunday, December 27, 2015 by Stephanie *

**Calculus**

Solve the following problem by separation of variables. T^2y'-t=ty+y+1 Y(1)=0 Y is a function of t.
*Friday, December 25, 2015 by Henry*

**Calculus**

Integrate sinx(cosx)^2dx using the substitution u=sinx. I know how to do this using u =cosx, but not sinx. The next problem on the homework was the same question except it asked to use u=cosx, so there couldn't have been a mistake.
*Wednesday, December 23, 2015 by Larry*

**Calculus**

Find the integral from 0 to 2 of xsqrt(5-sqrt4-x^2)). The hint said to use substitution of u=sqrt(4-x^2), and that I needed one more substitution, but I don't know how to do it.
*Wednesday, December 23, 2015 by Henry*

**Calculus**

Find a function of the form f(x)=a+bsqrtx that is tangent to the line 2y-3x=5 at the point (1, 4)
*Tuesday, December 22, 2015 by Kaitlyn*

**Calculus**

Determine whether the statement is true or false. If it is false, give an example for which the statement fails. a) if f has a relative maximum at x0, then f(x0) is the largest value that f(x) can have
*Monday, December 21, 2015 by Anonymous*

**Calculus i need help**

(Cosx)^y=x^siny find dy/dx at point pi/(4,0)
*Sunday, December 20, 2015 by Collins*

**calculus**

Find a cubic polynomial such as f(x)=ax^3+bx^2+cx+d that has horizontal tangents at the points (-5,4) and (4,-4)
*Saturday, December 19, 2015 by em*

**calculus**

A wooden artifact recovered from a tomb contains 29% of the carbon-14 that is present in living trees. The half life of carbon-14 is 5730 years. How long ago was the artifact made?
*Friday, December 18, 2015 by jeremy*

**Pre-calculus/ trig**

Given the vectors a= (-1,9) and b= (4,2) explain the difference between a-b and b-a. Thank you for your help! :)
*Thursday, December 17, 2015 by Rachel*

**Pre-calculus**

A square of size x inches is cut out of each corner of an 8in by 12in piece of cardboard, and the sides are folded up to form an open-topped box. Determine the dimensions of the cut-out squares that will produce the box of maximum volume.
*Wednesday, December 16, 2015 by jul*

**Pre-calculus: Logarithms**

ln56/ln7=ln8. Is this true or is this false? How can I find this out?
*Wednesday, December 16, 2015 by jenny*

**calculus**

A person can row at a constant speed of 6 miles per hour. If the rower wants to row directly across a river with a current of 2 mph, at what angle should they row? How fast does the boat actually cross the river?
*Tuesday, December 15, 2015 by teddy *

**Calculus **

Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the exposed surface area of the water changing when the radius is 2 feet?
*Monday, December 14, 2015 by Lacy*

**Calculus**

Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the radius of the water in the tank increasing when the radius is 2 feet?
*Monday, December 14, 2015 by Lacy*

**Calculus**

The curve y = 11x - 24 - x^2 cuts the x-axis at points A and B, and PN is the greatest positive value of the y coordinate. Show that 2 PN • AB equals three times the area bounded by that portion of the curve which lies in the first quadrant. Kinda confused on how to do this
*Monday, December 14, 2015 by Pip Paladins*

**Calculus, Physics**

The curve y = 11x - 24 - x^2 cuts the x-axis at points A and B, and PN is the greatest positive value of the y coordinate. Show that 2 PN • AB equals three times the area bounded by that portion of the curve which lies in the first quadrant. Kinda confused on how to do this
*Monday, December 14, 2015 by Pip Paladins*

**calculus**

Let Y = 7x sin-1(2x)+^3 square root 1+4x2. Find Y'. I don't know how to do the square root part. I have done y'= (7x)' (Sin^-1(2x)) + (7x)(sin^-1)'+...... y'= 7 sin^-1 + (7x)sq(2x)'/square root (1-(2x))^2 + .....
*Sunday, December 13, 2015 by Jason*

**Calculus**

A spherical balloon is being inflated so that, at the time when the radius is 5m, the radius is increasing at the rate of 0.15m/s. (A) Find the rate of increase of the volume at this time. (B) If the rate of increase of volume thereafter remains constant, find the rate at ...
*Sunday, December 13, 2015 by John*

**Calculus**

Consider the curve below. x = (cos(t))^2 y = cos(t) 0 ≤ t ≤ 6π (a) Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. (b) What is the length of the curve? I have no idea on how to evaluate this integral. I ...
*Saturday, December 12, 2015 by Jed*

**calculus**

Anti-Derivatives 2x^6-x^3/x^2
*Friday, December 11, 2015 by Jason*

**Calulus**

Fundamental Theorem of Calculus 1. (4e^x-3)dx plus the number in x (6,1)
*Friday, December 11, 2015 by Daniel*

**Calculus**

As an ice cube melts its surface area in decreasing at a rate of 6 cm^2 / sec. Find the rate at which the length of each side is decreasing at the moment when each side has length 2 cm.
*Friday, December 11, 2015 by Daniel*

**Pre-calculus**

A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 34.53 units of niacin and 25,430 units of retinol. She uses two types of commercial pellet foods. Food A ...
*Thursday, December 10, 2015 by Gift*

**Calculus**

A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The concentration C(x), in parts per million,is approximately given by the function: C(x)= 0.5/x^2, where x is the distance away from the plant in miles. The instantaneous rate of change ...
*Wednesday, December 9, 2015 by Anonymous*

**Calculus**

The area of a square with a side s is A(s)=s^2.What is the rate of the change of the area of a square in respect to its side?
*Wednesday, December 9, 2015 by Anonymous*

**Calculus**

Determine the values of x for which the function is continuous: f(x)= 10x^2-10
*Wednesday, December 9, 2015 by Anonymous*

**calculus**

find the area of the region: y=4 y=2sqrt(x) y=3-x
*Wednesday, December 9, 2015 by georges*

**Calculus**

A parabolic arch bridge has a 60ft base and a height of 24ft. Find the height of the arch at a distance of 5, 10, and 20 ft from the center
*Tuesday, December 8, 2015 by Net*

**Calculus**

I am standing on the roof of a building with a pea shooter, and I shoot a pea up into the air from a height of 80 feet. The pea reaches its maximum height 2 seconds after I shoot, then falls to the ground. Give the position of the pea as a function of time
*Tuesday, December 8, 2015 by Jose*

**Calculus AB**

If f(x) is continuous on the interval [4, 7], how many of the following statements are true? A. f(x) has a maximum value on [4, 7]. B. f(x) has a minimum value on [4, 7]. C. f(7) > f(4) D. lim f(x) = f(6) ᵡ¨6
*Tuesday, December 8, 2015 by Billy*

**Calculus**

Find the sum of the squared errors for the linear model f(x) and the quadratic model g(x) using the given points. f(x) = 2.0x − 3, g(x) = 0.09x^2 + 1.6x − 3 (−1, −4), (1, −2), (2, 0), (4, 6), (6, 9) linear model-? quadratic model- ?
*Tuesday, December 8, 2015 by Calculus Help *

**Calculus**

Find the sum of the squared errors for the linear model f(x) and the quadratic model g(x) using the given points. f(x) = −0.7x+3, g(x)=0.06x^2−0.6x+2 (−3, 5), (−1, 3), (1, 2), (3, 1) linear model-? quadratic model -?
*Tuesday, December 8, 2015 by Calculus Help *

**Mulitvariable Calculus**

How to proof tangential and normal components of a vector Thank you
*Tuesday, December 8, 2015 by cal*

**Calculus**

A spotlight on the ground is shining on a wall 24\text{m} away. If a woman 2\text{m} tall walks from the spotlight toward the building at a speed of 0.6\text{m/s}, how fast is the length of her shadow on the building decreasing when she is 2\text{m} from the building?
*Tuesday, December 8, 2015 by Spencer*

**Calculus **

A home owner wants to fence in his yard of 600 sq. feet. Three sides are to be constructed with chain link fence at a cost of 3.25 per linear feet. The fourth side is to be constructed with a wood stockade fence at a cost of $5.45 per linear foot. A) what is a complete model ...
*Monday, December 7, 2015 by Jen*

**calculus**

Find the critical numbers x1 and x2 of y=(9x^2+3)/4x.
*Monday, December 7, 2015 by beth*

**calculus**

Use implicit differentiation to find the slope of the tangent line to the graph of 18*x^(1/2)+5y^(1/2)+14 at(81/324,1)
*Monday, December 7, 2015 by beth*

**calculus**

Find the derivative of y=(7x^(1/3))/(x^2+9)
*Monday, December 7, 2015 by beth*

**calculus**

Find the derivative of 4sinx(6cosx+9sinx) at x=¦Ð/6.
*Monday, December 7, 2015 by beth*

**Calculus**

Compute the surface area of revolution about the x-axis over the interval. y = x^2, [0, 4] Is it (pi/12)(65^2 - 65)^(3/2)?
*Monday, December 7, 2015 by Sanaya*

**Calculus**

Find the derivative of f(x)=(2x)^(1/2)ln(15x)
*Monday, December 7, 2015 by Erik*

**Calculus**

Find the derivative of y=(2*x^(3/2))/(x^2+5)
*Monday, December 7, 2015 by Erik*

**Calculus**

A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15 ft/sec. At what rate is the player's distance from home base increasing when he is half way from first to second base?
*Monday, December 7, 2015 by Erik*

**calculus**

Sam has 1200 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Express the area of the field as a function of its dimension. Find the dimensions of the field that has the largest area.
*Monday, December 7, 2015 by hartati*

**Calculus**

How do I integrate sqrt of (1+e^(2x)) if doing u-sub.. u=sqrt of (1+e^(2x)) and ten using partial fraction...?
*Sunday, December 6, 2015 by Sanaya*

**Calculus**

Set up a double integral for calculating the flux of the vector field F⃗ (r⃗ )=r⃗ , where r⃗ =⟨x,y,z⟩, through the part of the upward oriented surface z=9(x^2+y^2) that lies above the disk x^2+y^2≤25.
*Sunday, December 6, 2015 by A*

**Calculus**

Find the surface area of the part of the sphere x2+y2+z2=81 that lies above the cone z=√(x2+y2)
*Sunday, December 6, 2015 by A*

**calculus**

what point of f(x)= e^(1-x^2) is concave down? I think it is 1/2 but I'm not sure
*Sunday, December 6, 2015 by tedd*

**calculus**

A satellite is free falling from a distance "d" of the surface of the moon with radius "r", with zero initial velocity. At what rate does the area of the portion of the moon visible to the satellite decrease at a time "t" after the free fall ...
*Saturday, December 5, 2015 by Steve*

**Calculus**

The approximate rate of change in the number of subscribers to wireless service is given by f’(t) = 1.498t + 1.626, where t represents the number of years since 1990. In 1992 (t = 2) there were approximately 8.893 million subscribers. Find the function that gives the ...
*Saturday, December 5, 2015 by Corey*

**Calculus**

Given dy/dt=4y and y(2)=400. Find y(7).
*Friday, December 4, 2015 by Erik*

**calculus**

The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.3. The initial population is 40. (1) What is the population after 30 days? (2) How long does it take for the ...
*Friday, December 4, 2015 by E*

**Calculus**

The rate of change of the population of a small town is dP/dt=kP Where P is the population, t is the time in years and k is the growth rate. If P=20000 when t=3 and P=30000 when t=5, what is the population when t=10? Round your answer to the nearest integer.
*Friday, December 4, 2015 by E*

**Pre calculus**

Use the given conditions to write an equation for the line in point-slope form. Passing through (-5, -7) and (-8, -6)
*Thursday, December 3, 2015 by maddie*