Wednesday
April 23, 2014

# Homework Help: Math: Calculus

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

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

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

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

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

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%3​D2sin%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

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

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

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=plo​t+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

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

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

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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