Wednesday
October 1, 2014

# Homework Help: Math: Calculus

Calculus
Posted by MG on Wednesday, March 26, 2014 at 6:54pm. The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at ...
Thursday, March 27, 2014 at 3:36am

Calculus
If e^x = 243 and e^y = 32 then e^((3x + 4y)/5) =? The answer is 432, but I don't understand why.
Thursday, March 27, 2014 at 3:34am

pre calculus
A taxi company charges $2.00 for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 < x < 2 Thursday, March 27, 2014 at 12:07am Calculus The height in feet above the ground of a ball thrown upwards from the top of a building is given by s=-16t^2 + 160t + 200, where t is the time in seconds. If the maximum height is 600 feet, what is v^-1(32)? The answer is supposed to be 4 seconds, but I don't understand ... Wednesday, March 26, 2014 at 11:07pm Calculus You are given a piece of sheet metal that is twice as long as it is wide an has an area of 800m^2. Find the dimensions of the rectangular box that would contain a max volume if it were constructed from this piece of metal by cutting out squares of equal area at all four ... Wednesday, March 26, 2014 at 9:49pm Calculus Use a tangent line approximation at x=0 to estimate the value of sin(-0.1). I got 0.1 Wednesday, March 26, 2014 at 8:56pm Calculus The vertical position of an object is modeled by the function h(t)=-16t^2 +5t+7, where h is measured in feet and t is measured in seconds. Find the object's initial velocity (that is, the velocity at t=0). Is it 5 feet per second? Wednesday, March 26, 2014 at 8:46pm Pre calculus For the most part, will a law of cosines always be one triangle? As in one triangle to solve? Wednesday, March 26, 2014 at 8:35pm College Calculus The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at a rate of _______ m/hr at 9:00? I tried several times... Wednesday, March 26, 2014 at 6:54pm Calculus If position is given by p(t)=t^2 +1, find the velocity v(t) at t = 2. I'm completely lost as to where to even start with this problem. Wednesday, March 26, 2014 at 4:25pm Calculus The amount of carbon-14 still present in a sample after t years is given by the function where C0 is the initial amount. Estimate the age of a sample of wood discovered by an archeologist if the carbon level in the sample is only 18% of its original carbon-14 level. Wednesday, March 26, 2014 at 10:31am Calculus If 40 milligrams of strontium-90 radioactively decays to 12 milligrams in 30 years, find its half-life (the number of years it takes until half of it remains). Use the formula A = p ⋅ e−kt, where p is the amount and A the (smaller) final amount. Wednesday, March 26, 2014 at 10:29am pre calculus Find the exact values: tan(7pi/4) - tan (pi/6) Wednesday, March 26, 2014 at 1:42am Calculus Find a positive number such that the sum of the square of the number and its reciprocal is a minimum. Tuesday, March 25, 2014 at 9:25pm Grade 12 Calculus For an outdoor concert, a ticket price of$30 typically attracts 5000 people. For each $1 increase in the ticket price, 100 fewer people will attend. The revenue, R, is the product of the number of people attending and the price per ticket. a) Let x represent the number of$1 ...
Tuesday, March 25, 2014 at 8:46pm

Calculus
There are 50 apple trees in an orchard, and each tree produces an average of 200 apples each year. For each additional tree planted within the orchard, the average number of apples produced drops by 5. What is the optimal number of trees to plant in the orchard? I mostly need ...
Tuesday, March 25, 2014 at 8:09pm

A rectangular piece of paper with perimeter 100 cm is to be rolled to form a cylindrical tube. Find the dimensions of the paper that will produce a tube with maximum volume. I have made it up to getting an equation for V(w).
Tuesday, March 25, 2014 at 7:49pm

Calculus Rate of Change
Find the average rate of change h(x)=2x^2-4 from x=2 to x=6 Simplify your answer as much as possible
Tuesday, March 25, 2014 at 10:27am

calculus
Recall that the volume of a sphere of radius r is V(r) =4\, \pi\, r^3 /3. Find L, the linearisation of V(r) at r=50
Tuesday, March 25, 2014 at 2:05am

Calculus A
Find all relative extrema and points of inflection for the function; h(x)=(x^2+5x+4)/(x-1)
Monday, March 24, 2014 at 11:20pm

Calculus
Find dy/dx implicitly in terms of x and y only for the following function; x+ 4xy=y^2
Monday, March 24, 2014 at 11:17pm

Calculus A
Find all relative extrema and points of inflection for the following function... h(X)= X^2+5X+4/ X-1 min= max= inflection points=
Monday, March 24, 2014 at 7:16pm

calculus
Suppose that a particle moves along a line so that its velocity v at time t is given by this piecewise function: v(t)=5t if 0≤t<1 v(t)=6((t)^(1/2))-(1/t) if 1≤t where t is in seconds and v is in centimeters per second (cm/s). Estimate the time(s) at which the ...
Sunday, March 23, 2014 at 8:17pm

Calculus
Find the slope of the tangent line to the ellipse x^2/4 + y^2/16= 1 at the point (x,y)
Sunday, March 23, 2014 at 8:11pm

Calculus
Suppose you have a hot cup of coffee in a room where the temp is 45 Celcius. Let y(t) represent the temp. of coffee as a function of the number of minutes t that have passed since the coffee was poured a) write a differential equation that applies to newtons law of cooling. ...
Sunday, March 23, 2014 at 6:16pm

find y' and y” by implicit differentiation. 2x^3 + 3y^3 = 8
Saturday, March 22, 2014 at 3:53pm

Calculus
A rancher wants to build a rectangular fence next to a river, using 100 yd of fencing. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the rancher should not fence the side next to the river.)
Saturday, March 22, 2014 at 5:45am

Calculus
A ball is thrown vertically upward with an initial velocity of 135 feet per second, the ball’s height after t second is s(t) = 135t – 22t How to calculate average velocity from 1 to 3 seconds?
Saturday, March 22, 2014 at 12:34am

Calculus
Evaluate the improper integral or state that it diverges: integral from -inf to inf (2xe^-x) dx. Please help!
Thursday, March 20, 2014 at 8:39pm

Calculus Help STEVE
find y'' by implicit differentiation. 2x^3 + 3y^3 = 8 I got the first derivative as you but the problem was asking for second derivative by implicit diff. this is where i got confused. Thank you!!!
Thursday, March 20, 2014 at 5:51pm

Calculus Help
find y'' by implicit differentiation. 2x^3 + 3y^3 = 8
Thursday, March 20, 2014 at 3:28pm

find the derivative of the function. Simplify where possible. F(theta)=arcsin(square root of (sin9(theta)))
Thursday, March 20, 2014 at 2:42pm

CALCULUS HELP
Let r(x)= f(g(h(x))), where h(1)=4, g(4)=5, h'(1)=3 , g'(4)=5 and f'(5)=7. find r'(1).
Thursday, March 20, 2014 at 2:04pm

Find an equation of the tangent line to the curve at the given point. ((pi/6),(2 square root of (3)/3)) y = sec (x)
Thursday, March 20, 2014 at 1:54pm

Calculus :(
Differentiate with respect to (t). y = d cos(t) + (t^2)sin(t)
Thursday, March 20, 2014 at 1:52pm

calculus
Evaluate the improper integral or state that it diverges: integral from 6 to infinity (1/t^2-5t)dt. I need help on solving this and what does it mean by converges and diverges?
Thursday, March 20, 2014 at 2:10am

Calculus Help
use logarithmic diff. to find the derivative of the function. Show steps please! so I can see how it is done. Thank you so much! y=(e^(-x)cos^(2)(x))/(x^(2)+x+1)
Tuesday, March 18, 2014 at 10:47pm

AP Calculus
Approximating the integral from 0 to 6 of (e^x dx) by 3 circumscribed rectangles of equal width on the x-axis yields ____. a) 2e^2 + 4e^4 + 6e^6 b) 2(e^2 + e^4 + e^6) c) 2(e + e^3 + e^5) d) e + 3e^3 + 5e^5 e) e^2 + 3e^4 + 5e^6
Monday, March 17, 2014 at 4:40pm

Calculus Help
Use logarithmic differentiation to find the derivative of the function. y = (tan x)^(7/x)
Sunday, March 16, 2014 at 7:43pm

Calculus
Solve the initial-value problem. y'' - 2y' + y = 0 , y(2) = 0 , y'(2) = 1
Sunday, March 16, 2014 at 6:40pm

Calculus
Solve the boundary-value problem. y'' + 5y' - 6y = 0 , y(0) = 0 , y(2) = 1
Sunday, March 16, 2014 at 6:39pm

AP Calculus
The average area of all squares with sides between a inches and b inches (b>a) is ____ in^2.
Sunday, March 16, 2014 at 6:14pm

AP Calculus
The base of a solid is bounded by y =|x|+a, 0<a<3, and the line y=3. find in cu. units in terms of a, the volume of the solid if every cross section perpendicular to the y-axis is an equilateral triangle.
Sunday, March 16, 2014 at 6:13pm

Calculus Help
Use logarithmic differentiation to find the derivative of the function. show steps please! y=(e^-xcos^2(x))/(x^2+x+1)
Sunday, March 16, 2014 at 4:12pm

Use implicit diff. to find dy/dx of each of the following. In the following x,y and (a) are all variables. Show step by step please! Thank you! 1) y^2 = x^2+a^2 2) y^2+ay = x^2+ax+a^2
Sunday, March 16, 2014 at 3:54pm

calculus
using the method of shells, set up, but dont evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1
Sunday, March 16, 2014 at 2:30pm

Pre-Calculus
Express the complex number in polar form. 5-12i
Saturday, March 15, 2014 at 6:51pm

Pre-Calculus
Find this quotient. Express the result in rectangular form. 9(cos3π/2 + isin3π/2) ÷ 3(cosπ/4 + isinπ/4)
Saturday, March 15, 2014 at 6:49pm

Pre-Calculus
Express the number in rectangular form. 3(cosπ/3+isinπ/3)
Saturday, March 15, 2014 at 6:40pm

Pre Calculus
Find each product or quotient. Express the result in rectangular form. 2(cosπ/6+isinπ/6) X 4(cos2π/3 +i2π/3)
Saturday, March 15, 2014 at 6:39pm

Calculus
Find equations of both the tangent lines to the ellipse x^2 + 4y^2 = 36 that pass through the point (12, 3). smaller slope y= larger slope y=
Friday, March 14, 2014 at 5:24pm

Calculus Help and Check
Find dy/dx by implicit differentiation. x^5(x + y) = y^2(9x − y) this is what i've got so far but I dont think it is the right answer. y'= 9y^2-6x^5-5x^3y/x^5+9y^2-18xy
Friday, March 14, 2014 at 3:53pm

Calculus
Find four other forms of the point (4, 105°) Two of the four must include a negative r value.
Friday, March 14, 2014 at 12:02am

Calculus Help
In the following x,y and (a) are all variables. Show steps please! Thank you! 1) y^2 = x^2+a^2 2) y^2+ay = x^2+ax+a^2
Thursday, March 13, 2014 at 8:19pm

CALCULUS ECONOMICS
Consider the problem of a competitive firm which has fixed costs of $1000, semi-fixed-costs of$1000, and variable costs given by q^2. QUESTION: What is the maximum market price at which the firm decides to supply zero?
Thursday, March 13, 2014 at 4:10pm

CALCULUS ECONOMICS
Consider the problem of a competitive firm which has fixed costs of $1000, semi-fixed-costs of$1000, and variable costs given by q2. QUESTION: What is the maximum market price at which the firm decides to supply zero?
Thursday, March 13, 2014 at 4:09pm

CALCULUS ECONOMICS
Consider a market in which consumption of the good being traded generates a positive externality. There are 100 identical consumers, each with a utility function given by (1/2)*(q^(1/2))+m +(G^(1/2)) where G denotes the total level of consumption in the market. The good is ...
Thursday, March 13, 2014 at 4:08pm

CALCULUS ECONOMICS
Consider a market in which consumption of the good being traded generates a positive externality. There are 100 identical consumers, each with a utility function given by (1/2)*(q^(1/2))+m +(G^(1/2)) where G denotes the total level of consumption in the market. The good is ...
Thursday, March 13, 2014 at 4:06pm

CALCULUS ECONOMICS
Consider an oligopolistic market with two firms. Each of them produces using a cost function given by c(q)=q^2. The aggregate demand in the market is given by 1000−p. Suppose that, in order to increase production, the government gives the firms a $100 per-unit produced ... Thursday, March 13, 2014 at 3:58pm CALCULUS ECONOMICS Consider the same setting as in the previous question. Suppose that firms are NOT owned by consumers. Let s denote the size of the per-unit subsidy/tax given to the firms. Let positive values of s denote subsidies, and negative values of s denote taxes. QUESTION: What is the ... Thursday, March 13, 2014 at 3:54pm CALCULUS ECONOMICS Consider an oligopolistic market with two firms. Each of them produces using a cost function given by c(q)=q^2. The aggregate demand in the market is given by 1000−p. Suppose that, in order to increase production, the government gives the firms a$100 per-unit produced ...
Thursday, March 13, 2014 at 3:53pm

CALCULUS ECONOMICS
Consider an economy in which a monopolistic firm serves two identical, but separate markets, called A and B. The aggregate inverse demand in each market is given by 1000−q. The cost function for the monopolist is given by (qA+qB)^2, where qA andqB denotes the amount sold...
Thursday, March 13, 2014 at 3:52pm

CALCULUS ECONOMICS
Consider a market in which aggregate demand is given by 1000−10p, and aggregate supply is given by 10p, where p denotes the market price. QUESTION: What is the maximum amount of revenue that the government can raise using a per-unit sales tax on consumers?
Thursday, March 13, 2014 at 3:50pm

CALCULUS ECONOMICS
Consider the problem of a rational consumer with an experienced utility function given by 8*x^(1/2)+m. Let p=$1 p/unit denote the market price of good x. Suppose that, initially, the firm selling the good matches his purchases as follows: for every x units that he buys, he ... Thursday, March 13, 2014 at 3:49pm CALCULUS ECONOMICS Consider the problem of a rational consumer with an experienced utility function given by 8x√+m. Let p=$1 p/unit denote the market price of good x. Suppose that, initially, the firm selling the good matches his purchases as follows: for every x units that he buys, he ...
Thursday, March 13, 2014 at 3:47pm

Pre-Calculus
Write the polar equation in rectangular form... r=5sintheta
Thursday, March 13, 2014 at 3:28pm

Pre-Calculus
Find the polar coordinates of each point with the given rectangular coordinates. Use degrees. (-4,-3)
Thursday, March 13, 2014 at 3:25pm

Pre Calculus
Write the rectangular equation in polar form... x=3
Thursday, March 13, 2014 at 3:17pm

Pre-Calculus
Find the rectangular coordinates of the point with the given polar coordinates. (3, 150°)
Thursday, March 13, 2014 at 3:15pm

Calculus
Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc. 1. Int. of (xlogx)dx from 0 to 1. ...
Thursday, March 13, 2014 at 2:45am

CALCULUS HELP
Find the derivative of the following function showing your work and fully simplifying your answer. STEP BY STEP PLEASE!!! f(x)=(8x-3)^5/(6x+7)^12 THANK YOU SO MUCH!!!
Wednesday, March 12, 2014 at 2:34pm

Calculus
Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc. 1. Int. of (xlogx)dx from 0 to 1. ...
Wednesday, March 12, 2014 at 6:13am

Calculus
Show, using limits, that f(x) = x2 – x + 3, is continuous at x = 2.
Wednesday, March 12, 2014 at 2:15am

Calculus
A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes three 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.)
Tuesday, March 11, 2014 at 10:12pm

Calculus
Two people start from the same point. One walks east at 5 mi/h and the other walks northeast at 7 mi/h. How fast is the distance between the people changing after 15 minutes? (Round your answer to three decimal places.)
Tuesday, March 11, 2014 at 10:11pm

Calculus
Can you tell me if im doing this right? Find the volume of the region obtained by revolving the area below about the line x=3. y=x3, x=2, y=0 v=pi[2,0] (x^3)^3dx= pi[2,0] x^9 v=pi/10 x^10(2,0)= 1024/10 pi
Tuesday, March 11, 2014 at 9:46pm

Find the area between the curves y= x^2/2 +2 and y = –x – 3 on the interval –4 ≤ x ≤ 4. I got 40/3 is that correct?
Tuesday, March 11, 2014 at 9:43pm

Calculus
Can someone help me with finding the derivative of this function? y = -( csc x)2 (cos-1(1-x2))
Tuesday, March 11, 2014 at 9:42pm

Calculus Help
Find the derivative of the following function showing your work and fully simplifying your answer. f(x)=(8x-3)^5/(6x+7)^12 Thank you!!!
Tuesday, March 11, 2014 at 3:36pm

calculus
Find the surface area of the part of the sphere x^2+y^2+z^2=a^2 inside the circular cylinder x^2+y^2=ay (r=a*sin(θ) in polar coordinates), with a>0. First time posting on this website, sorry for the lack of details on my attempts but I am really not sure where to start...
Monday, March 10, 2014 at 10:22pm

Calculus
Determine the equation of the inverse function if f(x) = 2x^2+3, and x≥0. The answer is supposed to be f^-1(x)=[√(2x-6)]/2. This is what I did: x=2y^2+3 2y^2=x-3 y^2=(x-3)/2 y=√[(x-3)/2] Did I do something wrong? Thanks!
Monday, March 10, 2014 at 5:37pm

Calculus
If f(x)= -4x^2+7 and x≤0, what is the equation of the inverse function? The answer is supposed to be f^-1(x)= -[√(7-x)]/2, but this is what I did: x=-4y^2+7 -4y^2=x-7 y^2=(x-7)/-4 y= √[(x-7)/-4] Did I do something wrong? By the way, for the original function...
Monday, March 10, 2014 at 2:12pm

Calculus
Find all points on the graph of the function f(x) = 2 cos x + cos^2 x at which the tangent line is horizontal. (Use n as your arbitrary integer.) smaller y-value (x,y)= larger y-value (x,y)=
Sunday, March 9, 2014 at 10:40pm

Calculus Help
A model for the length of daylight (in hours) in Philadelphia on the tth day of the year is L(t) = 12 + 2.8 sin[(2π/365)(t − 80)]. Use this model to compare how the number of hours of daylight is increasing in Philadelphia on March 21 and April 21. (Assume there are...
Sunday, March 9, 2014 at 9:56pm

Calculus
It requires 8 inch pounds of work to stretch a certain spring 2 inches from its rest position. Assuming that the spring follows hooke's law, what is k? Please answer this question. Thanks for your answers in advance.
Saturday, March 8, 2014 at 8:13pm

Integral calculus
It requires 8 inch pounds of work to stretch a certain spring 2 inches from its rest position. Assuming that the spring follows hooke's law, what is k? Thanks for your answers! :)
Saturday, March 8, 2014 at 7:36pm

calculus
The velocity of a skateboard is v(t) = t^2 - 4 t + 3 m/s when moving in a straight line. A. Find the the change in displacement of the skateboard between 4 seconds and 6 seconds. (Note this may or may not be negative, meaning it goes in the opposite direction, if so then be ...
Saturday, March 8, 2014 at 6:03pm

calculus
\int_{4}^{13} f(x) \,dx - \int_{4}^{11} f(x) \,dx = \int_{a}^{b} f(x) \,dx where a= and b= .
Saturday, March 8, 2014 at 6:02pm

calculus
A long narrow piece of land gets flooded each year by a river. The flooded area is in the shape of the area under the curve y = 2.3 x^3 and above the x-axis, for 0 \le x \le 3.2. All the distances are in metres.
Saturday, March 8, 2014 at 6:01pm

calculus
a. The value of \displaystyle \int_{-2}^{-1} \frac{14}{ 4 x } dx is b. The value of \displaystyle \int_{1}^{2} \frac{14}{ 4 x } dx is
Saturday, March 8, 2014 at 6:01pm

calculus
The following definite integral can be evaluated by subtracting F(B) - F(A), where F(B) and F(A) are found from substituting the limits of integration. \int_{0}^{4} \frac{1600 x +1200 }{(2 x^2 +3 x +1)^5}dx After substitution, the upper limit of integration (B) is : and the ...
Saturday, March 8, 2014 at 6:00pm

calculus
At a summer campfire, the radius of a marshmallow on a stick expands at the rate of \ {r ' (t)} = \frac{2.4 }{3 t + 6} mm/s where t is the time of heating in seconds. Initially the radius was 3.8 mm. Find the radius after 16 seconds using the following steps: When ...
Saturday, March 8, 2014 at 6:00pm

calculus
Ice cream drips out of the bottom of an ice cream cone on a hot day at a rate of r(t) mL per second, as a child eats it slowly, where t is in seconds. If r(t) = 10 e^{-k t}, complete the definite integral expressing the quantity of ice cream lost in the first 3 minutes(s). (...
Saturday, March 8, 2014 at 5:59pm

calculus
At a summer campfire, the radius of a marshmallow on a stick expands at the rate of \ {r ' (t)} = \frac{2.1 }{1 t + 5} mm/s where t is the time of heating in seconds. Initially the radius was 3.8 mm. Find the radius after 27 seconds using the following steps: When ...
Saturday, March 8, 2014 at 5:59pm

calculus
Find the area of the region under the curve y = 16 e ^{4 x} between x = -1.4 to x =1.4 .
Saturday, March 8, 2014 at 5:58pm

calculus
A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 7 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle \theta between the beam and the line ...
Friday, March 7, 2014 at 7:13pm

calculus
A hot air balloon rising vertically is tracked by an observer located 4 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is \frac{\pi}{3} , and it is changing at a rate of 0.1 rad/min. How fast is the ...
Friday, March 7, 2014 at 7:00pm

Calculus
for what values of r does the function y=e^rx satisfy the differential equation y''-4y'+y=0 Show steps please! Thank you!
Friday, March 7, 2014 at 6:43pm

calculus
A man of height 1.5 meters walk away from a 5-meter lamppost at a speed of 1.8 m/s. Find the rate at which his shadow is increasing in length.
Friday, March 7, 2014 at 6:30pm

calculus
A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 1.4 \text{m}^3\text{/min}. How fast is the water level rising when it is 2.6 m?
Friday, March 7, 2014 at 5:53pm

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