Monday
August 3, 2015

# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

Calculus
The mass, M, of a child can be approximated based on the height, H, of the child. The height of the child can be projected based on the child's age, A. a) State the chain rule for the derivative of the mass with respect to age (ie. find dM/dA) b) Suppose that an allometric...
Tuesday, October 28, 2014 by Anonymous

Calculus 1
The resistance of blood flow, R, in a blood vessel is dependent on the length of the blood vessel, the radius of the blood vessel, and the viscosity of the blood. This relationship is given by R = 8Lη/πr^4 where r is the radius, L is the length, and the positive ...
Tuesday, October 28, 2014 by Anonymous

Calculus
A ball is thrown up on the surface of a moon. Its height above the lunar surface (in feet) after t seconds is given by the formula h=308t−(14/6t^2) Find the time that the ball reaches its maximum height. Answer = Find the maximal height attained by the ball Answer =
Tuesday, October 28, 2014 by Hailey

Calculus
The top and bottom margins of a poster are 2 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 380 square centimeters, find the dimensions of the poster with the smallest area. Width = Height =
Tuesday, October 28, 2014 by Hailey

Calculus
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 49 feet?
Tuesday, October 28, 2014 by Hailey

Calculus
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=4−x^2. What are the dimensions of such a rectangle with the greatest possible area? Width = Height =
Tuesday, October 28, 2014 by Hailey

Calculus 1
The resistance of blood flow, R, in a blood vessel is dependent on the length of the blood vessel, the radius of the blood vessel, and the viscosity of the blood. This relationship is given by R = 8Lη/πr^4 where r is the radius, L is the length, and the positive ...
Tuesday, October 28, 2014 by Anonymous

Calculus 1
The mass, M, of a child can be approximated based on the height, H, of the child. The height of the child can be projected based on the child's age, A. a) State the chain rule for the derivative of the mass with respect to age (ie. find dM/dA) b) Suppose that an allometric...
Tuesday, October 28, 2014 by Anonymous

calculus
3) f(x)=x^(2)/6x^(2)+4. List the x values of the inflection points of f.
Tuesday, October 28, 2014 by Hailey

Calculus
The top of a 13 foot ladder is sliding down a vertical wall at a constant rate of 4 feet per minute. When the top of the ladder is 5 feet from the ground, what is the rate of change of the distance between the bottom of the ladder and the wall
Monday, October 27, 2014 by John

Calculus: need clarification to where the #'s go
A particle is moving along the curve y= 2 \sqrt{4 x + 4}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant. *I just need step by ...
Monday, October 27, 2014 by Alessandra

Calculus: need clarification to where the #'s go
Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 \mbox{cm}^3\mbox{/s}. How fast is the surface area of the balloon increasing when its radius is 14 \mbox{cm}? Recall that a ball of radius r has volume \displaystyle V=\frac{4}{3}\pi r^3 ...
Monday, October 27, 2014 by Alessandra

Calculus: need clarification to where the #'s go
When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^{1.4}=C where C is a constant. Suppose that at a certain instant the volume is 330 cubic centimeters and the pressure is 79 kPa and is decreasing at a ...
Monday, October 27, 2014 by Alessandra

Calculus
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 19 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
Monday, October 27, 2014 by Alessandra

Find al points where tangent lines to: (x^2+y^2)^(3/2) = sqrt(x^2+y^2) + x is either horizontal or vertical using implicit differentiation.
Monday, October 27, 2014 by Al

Calculus
A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at 4 feet per second. If the height of the streetlight is 15 feet, what is the rate at which the person's shadow is lengthening?
Monday, October 27, 2014 by Anonymous

Calculus
If y=sqrt (x^2+16), then d^2y/dx^2=?
Monday, October 27, 2014 by Anonymous

Calculus
A sphere is increasing in volume at the rate of 3(pi) cm^3/sec. At what rate is the radius changing when the radius is 1/2 cm? The volume of a sphere is given by V=4/3(pi)r^2 A. pi cm/sec B. 3 cm/sec C. 2 cm/sec D. 1 cm/sec E. .5 cm/sec
Monday, October 27, 2014 by Anonymous

Calculus
If (x+2y)dy/dx=2x-y, what is the value of d^2y/dx^2 at the point (3,0)? A. -10/3 B. 0 C. 2 D. 10/3 E. Undefined
Monday, October 27, 2014 by Anonymous

Calculus
If f(x)=sqrt (x^2-4) and g(x)=3x-2, then the derivative of f(g(x)) at x=3 is A. 7/sqrt 5 B. 14/sqrt 5 C. 18/sqrt 5 D. 15/sqrt 21 E. 30/sqrt 21
Monday, October 27, 2014 by Anonymous

Calculus
A sphere is increasing in volume at the rate of 3(pi) cm^3/sec. At what rate is the radius changing when the radius is 1/2 cm? The volume of a sphere is given by V=4/3(pi)r^3. A. pi cm/sec B. 3 cm/sec C. 2 cm/sec D. 1 cm/sec E. .5 cm/sec
Sunday, October 26, 2014 by Anonymous

Calculus
If y=sqrt (x^2+16), then d^2y/dx^2= A. 1 / (4(x^2+16)^3/2) B. 4(3x^2+16) C. x / ((x^2+16)^1/2) D. (2x^2+16) / ((x^2+16)^3/2) E. 16 / ((x^2+16)^3/2)
Sunday, October 26, 2014 by Anonymous

Calculus
Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = -2x2-2x+1 (-1, -2)
Sunday, October 26, 2014 by Duane

calculus
Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 8A square centimeters
Sunday, October 26, 2014 by liz

Calculus
Let f(x)=(2x+1)^3 and let g be the inverse function of f. Given f(0)=1, what is the value of g'(1)? A. -2/27 B. 1/54 C. 1/27 D. 1/6 E. 6
Sunday, October 26, 2014 by Anonymous

Calculus
Find al points where tangent lines to: (x^2+y^2)^(3/2) = sqrt(x^2+y^2) + x is either horizontal or vertical.
Sunday, October 26, 2014 by Al

Calculus
If f(x)=sinx and g(x)=cosx, then the set for all x for which f'(x)=g'(x) is: A. Pi/4 + k(pi) B. Pi/2 + k(pi) C. 3pi/4 +k(pi) D. Pi/2 + 2k(pi) E. 3pi/2 + 2k(pi)
Sunday, October 26, 2014 by Anonymous

Calculus
If r is positive and increasing, for what value of r is the rate of the increase of r^3 twelve times that of r? A. Cubed root 4 B. 2 C. Cubed root 12 D. 2 sqrt 3 E. 6
Sunday, October 26, 2014 by Anonymous

Calculus
A 12-ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder away from the wall at the rate of 0.5ft/s. What is the configuration of the ladder at the instant that the vertical speed of the top of the ladder equals the horizontal speed of ...
Sunday, October 26, 2014 by Zoe

Calculus
Find al points where tangent lines to: (x^2+y^2)^(3/2) = sqrt(x^2+y^2) + x is either horizontal or vertical.
Sunday, October 26, 2014 by Al

Calculus
The radius of a circle is increasing. At a certain instant, the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference. What is the radius of the circle at that instant? A. 1/2 B. 1 C. Sqrt 2 D. 2 E. 4
Sunday, October 26, 2014 by Anonymous

Calculus 1
Given f(x)= 3e^(1-x^2)*ln(x), find the equation of the tangent line at x = 1.
Sunday, October 26, 2014 by Ben

calculus
A 6 foot tall man walks at a rate of 5 feet per second along one edge of a road that is 30 feet wide. On the other edge of the road is a light atop a pole 18 feet high. How fast is the length of the man's shadow increasing when he is 40 feet beyond the point directly ...
Sunday, October 26, 2014 by Bryce

calculus
a. find an equation for the secant line through the points where x has the given values. b. find a equation for the line tangent to the curve when x has the first value. y=9square root(x); x=16, x=25
Sunday, October 26, 2014 by Duane

Calculus 1
A right triangle has a fixed base of length 6 meters and a height that is increasing at a rate of 2 meters/second. At what rate is the length of the hypotenuse increasing when the height is 8 meters?
Sunday, October 26, 2014 by Ben

calculus
for f(x)=5/8, a. find an equation for the secant line through points where x=4 and x=5.b. find an equation for the line tangent to the curve when x=4. I can solve part a., but I am confused on part b. please help. I don't understand how to plug the numbers into the ...
Sunday, October 26, 2014 by Duane

Calculus
We are going to fence in a rectangular field and have a maximum of 200 feet of material to construct the fence. Determine the dimensions of the field that will enclose the maximum area?
Sunday, October 26, 2014 by Fareed

Calculus
a hyperbola passing through (8,6) consists of all points whose distance from the origin is a constant more than its distance from the point (5,2). find the slope of the tangent line to the hyperbola at (8,6).
Sunday, October 26, 2014 by Al

Calculus
The graph of the equation x2 − xy + y2 = 9 is an ellipse. Find the lines tangent to this curve at the two points where it intersects the x-axis. Show that these lines are parallel.
Sunday, October 26, 2014 by Al

Calculus
400 feet of fencing is to be used to enclose four adjacent pieces of land. What dimensions will produce the largest area?
Saturday, October 25, 2014 by Rick

Calculus/pre-trig
Write the formula for the discriminant. State the types of roots for a quadratic equation, explaining how the discriminant helps you determine the type.
Saturday, October 25, 2014 by Anonymous

Calculus (math)
A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 12 feet deep?
Saturday, October 25, 2014 by mariel

calculus
A spherical snowball is placed in the sun. The snowball melts so that it's surface area decreases at a rate of 2 cm2 /min. Find the rate at which the diameter decreases when the diameter is 8 cm
Friday, October 24, 2014 by Jocelyn

Calculus
Given x^2+y^2=4, find the equation of the tangent line at the point (-1,sq.rt.3). Then, at what point is the slope 0? What point is the slope -1? I have no clue what to do!
Friday, October 24, 2014 by Matilda

The power, P, dissipated when a 6-volt battery is put across a resistance of R ohms is given by P=36R. What is the rate of change of power with respect to resistance?
Thursday, October 23, 2014 by lauren

Calculus
I need help determining the intervals of increase, decrease and the intervals of upward and downward concavity given f prime. f'(x)=(64x^4 - 125x) ^(-2/3). Im not sure how to solve this. I know that the function has no intervals of decrease, its the rest im having trouble ...
Thursday, October 23, 2014 by Sam

Calculus
Let f be a function such that f(−6)=−6, f(6)=6, f is differentiable for all real values of x and −1≤f'x≤1 for all real values of x. Prove that f(x)=x for all −6≤x≤6 I tried applying the mean value theorem here but I'm not...
Thursday, October 23, 2014 by Ss

calculus
Let \lambda be a positive real number. Evaluate \sin^{-1}(\lambdai)
Tuesday, October 21, 2014 by siri

Calculus
Find f'(a). f(x)=(x^2+1)/(x-2) Is it (x^2-5x+2)/(x-2)^2 ?
Tuesday, October 21, 2014 by Anonymous

Calculus
Use linear approximation, i.e. the tangent line, to approximate \sqrt[3] { 7.9 } as follows: The equation of the tangent line to f(x) at x = 8 can be written in the form y = Using this, we find our approximation for \sqrt[3] {7.9} is
Tuesday, October 21, 2014 by Ashley

calculus
find the absolute maximum and minimum of the function y=2cos(t)+sin(2t) on the interval of [0, pi/2] I have taken the derivative but I have no clue how to solve it for 0
Monday, October 20, 2014 by Kenneth

calculus
Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)
Monday, October 20, 2014 by Duane

Calculus
Find the critical numbers of the function f(x)=x^1/6−x^−5/6.
Monday, October 20, 2014 by Hailey

Calculus
Consider the function f(x)=ln(x)/x^6. For this function there are two important intervals: (A,B] and [B,∞) where A and B are critical numbers or numbers where the function is undefined. Find A Find B For each of the following intervals, tell whether f(x) is increasing or...
Monday, October 20, 2014 by Hailey

calculus
9) Find all critical numbers of the function f(t)=9t^2/3+t^5/3
Monday, October 20, 2014 by Hailey

Calculus
7) Consider the function f(x)=x2e4x. For this function there are three important intervals: (−∞,A], [A,B], and [B,∞) where A and B are the critical numbers. Find A and B For each of the following intervals, tell whether f(x) is increasing (type in INC) or ...
Monday, October 20, 2014 by Hailey

Calculus
f(x)=4x3−18x2−480x−2 is decreasing on what interval? It is increasing on what interval(s) ? The function has a local maximum at ?
Monday, October 20, 2014 by Hailey

Calculus
18) Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use. f(x)=2x/6x+12,[1,4]
Monday, October 20, 2014 by Hailey

Calculus
A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is increasing by 0.4 centimeters per second. What ...
Monday, October 20, 2014 by Cookie Monster

Calculus
Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 3 cubic feet per minute. If the pool has radius 6 feet and height 10 feet, what is the rate of change of the height of the water in the pool when the depth of the...
Monday, October 20, 2014 by Dan the Man

Calculus
Consider the closed curve in the day plane: 2x^2-2xy+y^3=14 a) show that dy/dx=2y-4x/3y^2-2x (I got this part) b) find equation lines to the curve when y=2 c) if the point (2.5, k) is on the curve, use part b to find the best approximation of the value of k
Monday, October 20, 2014 by Marie

calculus
A lamp post 3m high is 6m from a wall. A 2m man tall is walking directly from the post toward at 2.5m/s. How fast is his 1.5 from the wall
Monday, October 20, 2014 by James

Calculus
An inverted conical tank is being filled with water, but it is discovered that it is also leaking water at the same time. The tank is 6 meters high and its diameter at the top is 4 meters. The water is being added to the tank at a constant rate. Some of this water is found to ...
Sunday, October 19, 2014 by Ryan

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 2.3 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?
Sunday, October 19, 2014 by Ryan

Calculus
A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than ...
Sunday, October 19, 2014 by Ryan

Calculus
Find the value of a so that the tangent line to y = ln(x) at x = a is a line through the origin. I am unsure how to go about this.
Sunday, October 19, 2014 by Mel

Calculus
find y' of 4(cos(x^3))^2 when x = 1. I got -24(1)(cos(1)(sin(1) = -0.4187 but the answer is -10.9.
Sunday, October 19, 2014 by Dave

Calculus
Find an equation of the tangent line to the curve f(x) = (sins)^2 + 2tanx at x= pi/4. I worked through it and got y = 5x + 5/2 for my answer, but the answer key says that it is y - 5/2 = 5(x - pi/4). Why is the pi/4 in the answer? Thanks for any help!
Sunday, October 19, 2014 by Lucy

calculus
find the x-coordinate of all points on the curve y=12Xcos(5X)-(30*sqrt3*X^2) + 16, pi/5<X<2pi/5 where the tangent line passes through the point (0,16), (not on the curve) I have absolutely no idea how to solve this one
Sunday, October 19, 2014 by jake

Calculus
Find f''(1/2) using f(x) = ln(1-x). f'(x) = 1/(1-x) * -1 = -1/(1-x) so then using quotient rule: f''(x) = ((-1*-1) - ((1-x)(0))) / (1-x)^2 f''(1/2) = 1/(1-(1/2))^(2) = 4 Is this correct?
Sunday, October 19, 2014 by Tom

Calculus
What is the derivative of (ln(x))^x ? I have: f(x) = ln(x)^x f(x) = xlnx f'(x) = x/x + 1 * ln(x) f'(x) = 1 + ln(x) Is this correct?
Sunday, October 19, 2014 by Tom

calculus
can anyone help me with that question what is the domain of log(log(x)the base is 0.2)
Saturday, October 18, 2014 by rania

calculus
Use polar coordinates to find the volume of the given solid. Inside the sphere x^2+y^2+z^2=25 and outside the cylinder x^2+y^2=1
Saturday, October 18, 2014 by siri

calculus
Find the points of the paraboloid z=x^{2}+y^{2}-1 at which the normal line to the surface coincides with the line joining the origin to the point. What is the acute angle betwwen the normal and the z-axis at these points?
Saturday, October 18, 2014 by RAJ

calculus
A cable runs along the wall from C to P at a cost of $3 per meter, and straight from P to M at a cost of$5 per meter. If M is 16 meters from the nearest point A on the wall where P lies, and A is 50 mters from C, find the distance from C to P such that the cost of installing ...
Saturday, October 18, 2014 by RAJ

calculus
Find the points of the paraboloid z=x^{2}+y^{2}-1 at which the normal line to the surface coincides with the line joining the origin to the point. What is the acute angle betwwen the normal and the z-axis at these point
Saturday, October 18, 2014 by RAJ

calculus
use differentials to determine by approximately how many centimeters does the diagonal of a square table increase if its area is increased from 50 square centimeters to 54.45 square centimeters? Area= s^2 Diagonal= sqrt(2s^2) so, D= sqrt(2A) dD=A^(-1/2) dA dD= 50^(-1/2)* 4.45 ...
Saturday, October 18, 2014 by anonymous

Calculus
If G(x)=(x)/(1+2x), find G'(a) and use it to find an equation of the tangent line to the curve y=(x)/(1+2x) at the point (-1/4,-1/2). My answer: G'(a)=1/(1+2x)^2 Equation of tangent line: y= 4x+0.5
Saturday, October 18, 2014 by Anonymous

Calculus
A pebble is dropped from an open window 100 meters above the ground. a) What is the velocity of the pebble after 2 seconds? b) What is the velocity of the pebble when it hits the ground?
Saturday, October 18, 2014 by Anonymous

Calculus
Find the slope of the curve f(x)=1/(x^2+3). My answer: (-2x)/(x^2+3)^2
Saturday, October 18, 2014 by Anonymous

Calculus
The number of bacteria after t hours in a controlled laboratory experiment is n=f(t). Suppose there is an unlimited amount of space and nutrients for the bacteria. Which do you think is larger, f'(5) or f'(10)? If the supply of nutrients is limited,would that affect ...
Saturday, October 18, 2014 by Anonymous

calculus
2 given s(t)=3t +5t+3, find the instantaneous velocity when t i= 5.
Saturday, October 18, 2014 by Duane

calculus
how would you represent the area outside given y= 4cos(2theta) but outside y=4 ?
Saturday, October 18, 2014 by RAJ

Calculus
A rectangular field is to be enclosed by a fence and divided into three lots by fences parallel to one of the sides. Find the dimensions of the largest field that can be enclosed with 800 feet of fencing. Help me please!!!!!!!!!!! THANK YOU
Saturday, October 18, 2014 by Lex

Calculus
The cost of producing x ounces of gold from a new gold mine is C=f(x) dollars. Do you think the values of f'(x) will increase or decrease in the short term? What about the long term? Explain.
Saturday, October 18, 2014 by Anonymous

DIFF CALCULUS
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end. Water is being pumped into the pool at ¼ cubic meter per minute, and there is 1 meter of water at the deep end. a. What percent of the pool is filled? ...
Saturday, October 18, 2014 by JR

calculus
a ladder 6 feet long leans against a vertical building. the bottom of the ladder slides away from the building horizontally at rate of 1/2 ft/sec. A) at what rate is the top of the ladder sliding down the wall when the bottom of the ladder is 3 feet from the wall? b)at what ...
Saturday, October 18, 2014 by fadea

Calculus
The number of bacteria after t hours in a controlled laboratory experiment is n=f(t). Suppose there is an unlimited amount of space and nutrients for the bacteria. Which do you think is larger, f'(5) or f'(10)? If the supply of nutrients is limited,would that affect ...
Friday, October 17, 2014 by Anonymous

Calculus
The cost of producing x ounces of gold from a new gold mine is C=f(x) dollars. Do you think the values of f'(x) will increase or decrease in the short term? What about the long term? Explain.
Friday, October 17, 2014 by Anonymous

calculus
ind the point(s) on the cone z^2 = x^{2}+3y^{2} that are closest to the point (-1,-7,0)
Friday, October 17, 2014 by RAj

Calculus
what is the limit of arcsinx as x approaches 1 from the left
Friday, October 17, 2014 by Ginger

Calculus
1. If the tangent line to y=f(x) at (4,3) passed through the point (0,2), find f(4) and f'(4). My answer: f(4)=3 f'(4)=1/4
Friday, October 17, 2014 by Anonymous

calculus
A sample poll of 100 voters revealed the following information concerning three candidates A, B, and C who were running for three offices. 10 voted in favor of both A and B, 35 voted in favor of A or B but not C, 25 voted in favor of B but not A or C, 65 voted in favor of B or...
Friday, October 17, 2014 by RAj

Calculus
Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid x^2/81+y^2/25+z^2/49=1
Friday, October 17, 2014 by Siri

calculus
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x^2y+3y^2-y subject to the constraintx^2+y^2less than or equal to 10
Friday, October 17, 2014 by RAJ

calculus
Given g(x) = (x + cosx)/(e^x - 2x^3 + 5). Find g'(x). Do not need to simplify.
Friday, October 17, 2014 by RAJ

calculus
Find the point on the surface z = 2x2+xy+3y2 where the tangent plane is parallel to the plane 8x-8y-z=5.
Friday, October 17, 2014 by RAJ

CALCULUS
Hi guys can you help me! Please teach me step by step.. I really need it. pls! Thank you......... A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end. Water is being pumped into the pool at ¼ cubic meter ...
Friday, October 17, 2014 by Jane

A theatre company allows a group of 10 people to buy theatre tickets at a price of $28 per person. For each person in excess of 10, the price is decreased by$2 per person for everyone down to a minimum of \$10 per person. What number of people will produce the maximum revenue ...