Wednesday

April 23, 2014

April 23, 2014

**Recent Homework Questions About Calculus**

Post a New Question | Current Questions

**College Calculus**

let Ø be the angle between them the angular velocity of the minute hand = 2π/60 rad/min = π/30 rad/min the angular velicity of the hour hand = 2π/(12(60)) or π/720 rad/min then, so dØ/dt = (π/30 - π/720) rad/min dØ/dt = 23&#...
*Wednesday, March 26, 2014 at 8:25pm*

**College Calculus**

I followed this example, where am i missing something or going about it wrong? If we let y be the angle between the two hands and x be the distance between the two tips, then, by the law of cosines, we have: x^2 = 5^2 + 1.5^2 - 2*5*1.5cos(y) x^2 = 27.5 - 15cos(y) Take the ...
*Wednesday, March 26, 2014 at 6:58pm*

**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**

dp/dt = v = 2 t at t = 2 v = 2*2 = 4
*Wednesday, March 26, 2014 at 4:26pm*

**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**

I did one for you. Now you do this one. By the way you left the half life of carbon 14 or exponential decay function out of your statement of the problem making it impossible without looking that up.
*Wednesday, March 26, 2014 at 10:38am*

**Calculus**

12 = 40 e^(-kt) .3 = e^-30 k ln .3 = -30 k -1.20 = -30 k k = .04013 so .5 = e^-.04013 t -.6931 = -.04013 t t = 17.3 years
*Wednesday, March 26, 2014 at 10:35am*

**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*

**calculus**

A rectangular field is to be enclosed and divided into 4 equal lots by fences parallel to one of the sides. A total of 10,000 meters of fence are available. Find the area of the largest field that can be enclosed.
*Wednesday, March 26, 2014 at 10:15am*

**pre calculus**

-1 - 1/√3
*Wednesday, March 26, 2014 at 5:45am*

**pre calculus**

Find the exact values: tan(7pi/4) - tan (pi/6)
*Wednesday, March 26, 2014 at 1:42am*

**Calculus**

let the number be x, and the sum as stated be S S = x^2 + 1/x dS/dx = 2x - 1/x^2 = 0 for a max/min 2x = 1/x^2 2x^3 = 1 x^3 = 1/2 x = (1/2)^(1/3) or the cube root of 1/2
*Tuesday, March 25, 2014 at 9:47pm*

**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**

thx!
*Tuesday, March 25, 2014 at 9:14pm*

**Grade 12 Calculus**

I hope your function looks something like this: R(x) = (5000 - 100x)(30 + x) = 150000+ 5000x - 3000x - 100x^2 = -100x^2 + 2000x + 150000 this is a standard parabola opening dowwards , so it will have a maximum the x of the vertex is -b/(2a) = -2000/-200 = 10 So there should be...
*Tuesday, March 25, 2014 at 9:06pm*

**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 - good catch bob**

Dang - forgot the restriction on the domain.
*Tuesday, March 25, 2014 at 8:35pm*

**Calculus**

now if you are allowed to remove trees, and for each tree removed, the average goes up by 5, then the optimal is to remove five trees.
*Tuesday, March 25, 2014 at 8:29pm*

**Calculus**

number apples=average*number trees let x be the nubmer of trees 50<x<inf number apples=(200-(x-50)*5)(x) where x is the number of trees, 50<x<infinity N=200x-5x^2 +250x dN/dx=0=200-10x+250 10x=450 x=45 but x>50, so look at optimal check x=50 N=50*200=10000 ...
*Tuesday, March 25, 2014 at 8:28pm*

**Grade 12 Calculus**

if the sheet is x by y, and is rolled along the y axis, 2x+2y = 100 v = pi r^2 y where 2pi r = x, or r = x/(2pi), so v = pi (x/(2pi))^2 (100-2x)/2 = x^2(50-x)/(4pi) dv/dx = x(100-3x)/(4pi) dv/dx=0 when x = 100/3 at that point, max v is pi*(50/3)^3
*Tuesday, March 25, 2014 at 8:21pm*

**Calculus**

the number of apples is yield/tree * # trees. With x trees, yield per tree is 200 - 5(x-50) for x > 50 So, total crop is c(x) = x(200-5(x-50)) = x(450-5x) = 450x - 5x^2 c'(x) = 450-10x c' = 0 at x=45 So, the max yield is achieved with 45 trees
*Tuesday, March 25, 2014 at 8:16pm*

**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*

**Grade 12 Calculus**

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**

average=(finalvalue-initial value)/chngeinX final value= h'(6)=4*6=24 initial vealue=h'(2)=4*2=8 average h'=16/4=4 units unknown
*Tuesday, March 25, 2014 at 10:52am*

**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**

v = 4π/3 r^3 v' = 4π r^2 at r=50, v = 500π/3 and v' = 100π So, the tangent line at r=50 is v - 500π/3 = 100π(x-50)
*Tuesday, March 25, 2014 at 4:58am*

**Calculus**

recall that the voulme of a sphare of radius r is v(r)=(4pir^3)/3. find l, ther linearisation of v(r) at r=50. A sphare of radius 50 centimeters is covered with a layer of point of thickness 0.31 millimeters. use the linearisation of v at r=50 to estimate the volume of point ...
*Tuesday, March 25, 2014 at 2:13am*

**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*

**Trigonometry**

http://www.wolframalpha.com/input/?i=y%3D2sin%28x-2pi%2F3%29 for x-intercepts, y = 0 2sin(x-2pi/3) = 0 sin(x-2pi/3)=0 but sin 0 = 0 and sin π =0 and sin 2π = 0 so x - 2π/3 = 0 and x -2π/3 = π and x - 2π/3 = 2π x = 2π/3 or x = &#...
*Tuesday, March 25, 2014 at 12:11am*

**Calculus**

fre
*Monday, March 24, 2014 at 11:59pm*

**Calculus**

x + 4xy = y^2 1 + 4y + 4xy' = 2yy' y' = (1+4y)/(2y-4x)
*Monday, March 24, 2014 at 11:59pm*

**Calculus A**

h' = (x^2-2x-9)/(x-1)^2 h" = 20/(x-1)^3 Clearly there are no inflection points, since f" is never zero h' is zero at two places, since the numerator is. So, there will be two extrema, one on each side of x=1. So, one will be a max, the other a min, depending ...
*Monday, March 24, 2014 at 11:58pm*

**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**

17
*Monday, March 24, 2014 at 8:47pm*

**Calculus A**

I will assume you meant: h(x) = x^2 + 5x + 4/(x-1) h ' (x) = 2x + 5 - 4/(x-1)^2 = 0 for max/min 2x + 5 = 4/(x-1)^2 (2x+5)(x^2 - 2x + 1) = 4 2x^3 - 4x^2 + 2x + 5x^2 - 10x + 5 = 4 2x^3 + x^2 - 8x + 1 = 0 hard to solve, Wolfram has this http://www.wolframalpha.com/input/?i=2x...
*Monday, March 24, 2014 at 7:32pm*

**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**

Nevermind I didn't read the question correctly. I got it! Thank You!
*Monday, March 24, 2014 at 1:43am*

**Calculus**

after this, i am to solve the differential but I am confused as to what I would make T air. dT/dt=-k(45-Tair) what do i do with the other 2 variables since k is a constant of proportionality. and T air is a constant
*Monday, March 24, 2014 at 12:49am*

**Calculus 12 Optimization**

120
*Sunday, March 23, 2014 at 9:35pm*

**calculus**

Assuming an initial position of zero, s(t) = 5/2 t^2 for 0<=t<1 so, at t=1, s = 5/2 Now, using the 2nd function, s(t) = 5/2 + 4t^(3/2) - log(t) solve that for s(t) = 4
*Sunday, March 23, 2014 at 8:21pm*

**Calculus**

use implicit differentiation: x/2 + y/8 y' = 0 y' = -4x/y
*Sunday, March 23, 2014 at 8:18pm*

**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**

the heat flow is proportional to the difference in temperature. dT/dt= -k(T-Tair) T air is a constant,
*Sunday, March 23, 2014 at 7:24pm*

**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*

**CALCULUS ECONOMICS**

How did you get to that number?I have 5000 (wrong solution) and I can't figure out q7 because i don't know the right value for q.opt (q.eq=625?)
*Sunday, March 23, 2014 at 3:21pm*

**CALCULUS ECONOMICS**

And for q7??It's my last chance...
*Sunday, March 23, 2014 at 2:46pm*

**CALCULUS ECONOMICS**

right for Q6!!!!!!!thankssssss
*Sunday, March 23, 2014 at 2:26pm*

**CALCULUS ECONOMICS**

2750? right or wrong?
*Sunday, March 23, 2014 at 10:55am*

**CALCULUS ECONOMICS**

Yes, they are right! Have you the answers of question 5,6,7? Thanks very very much!
*Sunday, March 23, 2014 at 9:13am*

**CALCULUS ECONOMICS**

Nothing?I need a clue in this one!
*Sunday, March 23, 2014 at 6:54am*

**CALCULUS ECONOMICS**

thanks
*Sunday, March 23, 2014 at 4:55am*

**CALCULUS ECONOMICS**

QUESTION: In this case, what is the difference between the optimal level of total consumption and the level of total consumption in equilibrium?
*Sunday, March 23, 2014 at 4:18am*

**CALCULUS ECONOMICS**

If Q = 440, shouldn't P = 560?
*Sunday, March 23, 2014 at 1:55am*

**Calculus Help Please!!!**

6x^2 + 9y^2 y' = 0 y' = -2x^2 / 3y^2 now for y", do it again: 12x + 18y (y')^2 + 9y^2 y" = 0 y" = -2(2x+3y(y')^2) / 3y^2 Now just substitute in y' and you're done Or, you can use the quotient rule on y': y' = -2/3 (x^2 / y^2) y&...
*Saturday, March 22, 2014 at 4:02pm*

**Calculus Help Please!!! **

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

**Calculus**

if two resistors with resistances r1 and r2 ohms are connected in parallel in an electric circuit to make an r-ohms resistor , the value of r can be found from the equation 1/r=1/r1+1/r2. if r1 is decreasing at the rate of 1 ohm/sec , and r2 is increasing at the rate of 0.5 ...
*Saturday, March 22, 2014 at 3:22pm*

**CALCULUS ECONOMICS**

WRONG s is not -300
*Saturday, March 22, 2014 at 2:32pm*

**CALCULUS ECONOMICS**

second: -300
*Saturday, March 22, 2014 at 1:57pm*

**CALCULUS ECONOMICS**

440
*Saturday, March 22, 2014 at 9:04am*

**CALCULUS ECONOMICS**

Thanks!
*Saturday, March 22, 2014 at 9:03am*

**CALCULUS ECONOMICS**

??
*Saturday, March 22, 2014 at 8:19am*

**Calculus**

If the length (parallel to the river) is y, 2x+y = 100 a = xy = x(100-2x) = 100x-2x^2 max a at x = 100/4 = 25 So, the yard is 25x50 As usual, max area when the fence is divided equally among lengths and widths.
*Saturday, March 22, 2014 at 5:49am*

**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**

According to my knowledge of physics, s(t) = 135t - 16t^2 Anyway, average velocity = total.distance/total.time So, that would be (s(3)-s(1))/(3-1)
*Saturday, March 22, 2014 at 5:36am*

**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 ECONOMICS**

Thanks
*Friday, March 21, 2014 at 1:36pm*

**CALCULUS ECONOMICS**

correct!!!! thnks dude
*Friday, March 21, 2014 at 9:48am*

**CALCULUS ECONOMICS**

Wrong!!!
*Friday, March 21, 2014 at 1:40am*

**Calculus**

∫2x e^-x dx = -2 e^-x (x+1) = -2(x+1)/e^x Now, e^x grows so much faster than x that the limit is zero as x -> ∞. That can be justified by using lHospital's Rule, to show that the limit is the same as -2/e^x -> 0 However, as x -> -∞ e^x grows very...
*Thursday, March 20, 2014 at 11:31pm*

**calculus**

d
*Thursday, March 20, 2014 at 8:50pm*

**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 ECONOMICS**

First question: Q=440 and P=660. Second question: s=100
*Thursday, March 20, 2014 at 7:35pm*

**Calculus Help STEVE**

oops. Well, if you got y', y" is just a bit down the road There are two ways to do it. First, use y' directly: y' = -2x^2 / 3y^2 by the quotient rule, y" = ((-4x)(3y^2) - (-2x^2)(6yy')] / 9y^4 = ((-12xy^2 + 12x^2y(-2x^2/3y^2)) / 9y^4 = -12xy(y - x(-2x...
*Thursday, March 20, 2014 at 6:05pm*

**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**

The question is asking for the second derivative by implicit diff. That's where I got confused. thank you so much!!!
*Thursday, March 20, 2014 at 5:30pm*

**Calculus :(**

y' = -d sin(t) + 2t sin(t) + t^2 cos(t)
*Thursday, March 20, 2014 at 4:37pm*

**Calculus Help Please!!!**

y = secx y' = secx tanx at x = pi/6, y' = 2/√3 * 1/√3 = 2/3 so, now we have a point and a slope, so the line is y - 2/√3 = 2/3 (x-pi/6) http://www.wolframalpha.com/input/?i=plot+y%3Dsec%28x%29+and+y+%3D+2%2F3+%28x-pi%2F6%29+%2B+++2%2F%E2...
*Thursday, March 20, 2014 at 4:36pm*

**CALCULUS HELP**

r = f(g(h(x)) r'(x) = f'(g(h(x))) g'(h(x)) h'(x) r'(1) = f'(g(h(1))) g'(h(1)) h'(1) = f'(g(4)) g'(4) (3) = f'(5) (5)(3) = (7)(5)(3) = 105
*Thursday, March 20, 2014 at 4:32pm*

**Calculus Help Please!!!**

f(θ) = arcsin(√sin9θ) since d/dx arcsin(x) = 1/√(1-x^2), f'(θ) = 1/√(1-sin9θ) * 9cos9θ/2√sin9θ = 9cos9θ / 2√(sin9θ)√(1-sin9θ) nasty, but that's how it is
*Thursday, March 20, 2014 at 4:28pm*

**Calculus Help**

6x^2 + 9y^2 y' = 0 y' = -2x^2 / 3y^2
*Thursday, March 20, 2014 at 4:21pm*

**Calculus Help**

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

**Calculus Help Please!!! **

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*

**Calculus Help Please!!! **

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*

**Math - PreCalc (12th Grade)**

ok so far, though they already told you that f(2)=3 because the point (2,3) is on the graph. As you know, the slope at any point (x,y) on the graph is 2x+2 So, the slope at x=2 is 6 Though, if this is pre-calc, how do you know the slope of the tangent to a curve? That's ...
*Thursday, March 20, 2014 at 1:21pm*

**calculus**

I think you missed a t in the denominator ∫ 1/(t^2-5t) dt = 1/5 log((5-t)/t) the definite integral is log(6)/5
*Thursday, March 20, 2014 at 5:14am*

**calculus**

integral = -(2t-5)/(t^2-5)^2 at infinity ---> -2t/t^2 = 2/t = 0 at 6 = (5-2)/31^2 = .00312 It does not diverge but has a finite answer. If t = sqrt(5) were included, we would have had a problem with a zero denominator.
*Thursday, March 20, 2014 at 4:38am*

**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*

**Math (algebra)**

V = pi r^2 h = 500 so h = 500/(pi r^2) area of side = 2 pi r h area of top and bottom togethr = 2 (pi r^2) =2 pi r^2 cost = C = .11(2 pi r^2) +.06(2 pi r h) C = .22 pi r^2 + .12 pi r [500/(pi r^2)] C = .22 pi r^2 + 60/r C = .691 r^2 + 60/r I need to use calculus to find the ...
*Wednesday, March 19, 2014 at 6:52pm*

**Math (algebra)**

Area = x y A = x (36 - x^2) = 36 x - x^3 domain is 0 </= x </= 6 assuming that it has to be on the POSITIVE x axis( the function would work fine for negative x but you specified + x) for largest I have to use calculus dA/dx = 0 at max = 36 -3 x^2 x^2 = 12 x = 2 sqrt 3 ...
*Wednesday, March 19, 2014 at 6:02pm*

**Calculus ll - Arc Length/Simpson's Rule**

3
*Wednesday, March 19, 2014 at 9:56am*

**CALCULUS ECONOMICS**

Ok, The correct answer should be 12,500. Let me know if you are happy with this.
*Wednesday, March 19, 2014 at 5:33am*

**CALCULUS ECONOMICS**

This is the total social welfare available.
*Wednesday, March 19, 2014 at 3:17am*

**CALCULUS ECONOMICS**

So what's correct?
*Wednesday, March 19, 2014 at 3:17am*

**Calculus Help**

log y = log (e^-x) + log cos^2(x) - log(x^2+x+1) log y = -x + 2log cos x - log(x^2+x+1) 1/y y' = -1 - 2tanx - (2x+1)/(x^2+x+1) y' = -(1 + 2tanx + (2x+1)/(x^2+x+1)) * (e^-x cos^2x)/(x^2+x+1) Now, you can massage that for a few more steps, to get something that pleases you
*Tuesday, March 18, 2014 at 11:15pm*

**Calculus Help**

y = (e^-x) (cosx)^2 (x^2 + x + 1) take ln of both sides ln y = ln e^-x + ln (cosx)^2 + ln(x^2 + x + 1) = -x + 2 ln(cosx) + ln(x^2 + x + 1) now differentiate y' / y = -1 + 2(-sinx/cosx) + (2x+1)/(x^2 + x + 1) = -1 - 2tanx + (2x+1)/(x^2 + x + 1) y' = y(-1 - 2tanx + (2x+1...
*Tuesday, March 18, 2014 at 11:12pm*

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