School and Work

Differentiate the function with respect to x:
f'(x) = 24x^2 - 24

When f'(x) = 0

24(x^2 -1) = 0
==> x = 1 or x=-1

Matey before me didn't do the last part HA!!!!

you need to plug your values of x into the f(x)

when x = 1, f(x) = 8 -24 +3 = -13
when x = -1, f(x) = -8+24+3 = 19

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A uniformly charged square whose side is 2s with surface charge density +s is lying in the xy plane. Find the electric field at point P lying on the axis collinear with the center of the square and a distance b from the center. Show that the electric field E at point P is

E = Q log {[b + s] x [s + (s^2 + (b - s)^2)^1/2]} (i^) /
16 {[b - s] x [s + (s^2 + (b + s)^2)^1/2]}

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related rates problems. I do not remember how to do them so if you could please explain how you got an answer that would be much appreciated

problem 1:
The radius of a circle is increasing at a nonzero rate, and at a certain instant, the rate of increase in the are of the circle is numerically equal to the rate of increase in its circumference. at this instant, the radius of the circle is?

problem 2:
The diameter and height of a paper cup in the shape of a cone are both 4 inches. water is leaking out at a rate of 1/2 cubic inch per second. Find the rate at which the water level is dropping when the diameter of the surface is 2 inches.

problem 3:
A railroad track and a road cross at right angles. An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60meters per second. At how many meters per second is the train moving away from the observer 4 seconds after it passes the intersection?

problem 4:
A family standing on the ground is watching a jet approach. The jet is approaching at a rate of 12 miles per minute at an altitude of 8 miles.
a) At what rate is the straight-line distance between the family and the jet changing when the jet is 16 miles from the family?

b) At what rate (in radians per minute) is the angle of altitude changing when the straight-line distance from the jet to the family is 36 miles?

please help me with these problems. my AP exam is coming up in a few weeks and I don't remember how to do this stuff.

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f(x) = (1 + 2x)¹° so f '(x) = 10(1 + 2x)? •2 = 20(1 + 2x)?

Since the point is (0,1) the slope at that point is f '(0) = 20(1)? = 20

So using the point-slope form of the line

y – 1 = 20(x – 0) or y = 20x + 1

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Home >All Categories > Science & Mathematics >Mathematics >Open Question Matt Member since:July 16, 2009Total points:108 (Level 1)In the bottom of an hourglass, a conical pile of sand is formed at the rate of 12 in.³ per minute. The radius of the base of the pile is always equal to one-half its altitude. How fast is the altitude rising when it is 6 in. deep?P.S.: Report the person who answered this first. He is simply ranting and that is against the community guidelines!2 minutes ago

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The Internet is not something that you just dump something on. It's not a big truck. It's a series of tubes. And if you don't understand, those tubes can be filled and if they are filled, when you put your message in, it gets in line and it's going to be delayed by anyone that puts into that tube enormous amounts of material, enormous amounts of material.

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I = ? [ v(3-5x) / (2x) ] dx ......................... (1)
_______________________

Let : x = (3/5) sin² F.

Then : dx = (3/5) 2 sin F cos F dF.

Also : v(3-5x) = v3. cos F.
________________________

From (1), then,

I = ? [ ( v3. cos F ) / ( 2(3/5) sin² F ) ] · (3/5) 2 sin F cos F dF

= v3. ? ( cos² F / sin F ) dF

= v3. ? [ ( 1 - sin² F ) / sin F ] dF

= v3. ? ( csc F - sin F ) dF

= v3. { ln | csc F - cot F | - ( - cos F ) } + C

= v3. { ln | csc F - cot F | + cos F } + C

= v3. ln | (v(5x/3) - v(3-5x)/v(5x) | + v(3-5x) + C .......... Ans.
________________________________

Happy To Help !
________________________________

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Sorry, I could not read the content fromt this page.

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Let,
present population = x

After time, t years it is = 3x, then,

3x = x(1 +2.5/100)^t = x(1.025)^t

(1.025)^t = 3

Taking log both sides, we get,

t = log(3) / log(1.025) = 0.477 / 0.0107

t = 44.492 years >======================< ANSWR

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You have to draw the picture to see this.

If you cut squares which are s x s in each corner, then fold up the flaps to make a box, then

- the height of the box is s
- the bottom of the box is (10 - 2s) x (8 - 2s) because you've taken 2s from each side.

So V = s(10-2s)(8 - 2s)

Multiply that out. Take the derivative with respect to s. Set it equal to 0.

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a. use newtons method to find all the values x such that x^2 - 2v2x+1 = 0 (the 2x + 1 is under the radical).

b. Use Newton's Method to approximate the positive solution to the equation ln(x + 4) = x to three
decimal places.

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Roger is breeding tropical fish to sell to hobbyists. He feels that his supply curve looks like
y1 = 0.06x2 + 5.06,
where x is the number of fish, in hundreds, sold at y1 dollars each. Articles in his trade newsletters lead him to believe that the demand curve is given by the portion of the quadratic curve
y2 = 0.2x2 - 4.8x + 31.8
that is a decreasing function of x.

(a) Check that the equilibrium quantity is 7. Calculate the producer surplus if Roger sells at y1(7).
(b) What is the consumer surplus?

Any help is greatly appreciated.

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Suppose that a firm makes two products A and B that use the same raw materials. Given a fixed amount of raw materials and a fixed amount of manpower, the firm must decide how much of its resources should be al- located to the production of A and how much to B. The management is aware of the production possibilities curve:

9x2 + 4y2 = 18, 000

...which reflects the limitations on personnel and raw materials available to the firm. A point (x, y) on this curve is called a production schedule for the firm, committing it to produce x units of A and y units of B. The sale of each unit of A yields a $3 profit, whereas each unit of B yields a $4 profit. Assuming that all units produced are sold, find the production schedule that maximizes the profit of the firm.

Would anyone be able to help me out? Thank you in advance.

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Question is:
An office contains 1000 ft^3 of air initially free of carbon monoxide. Starting at time = 0, cigarette smoke containing 4% carbon monoxide is blown into the room at the rate of 0.5 ft^3/min. A ceiling fan keeps the air in the room well circulated and the air leaves the room at the same rate of 0.5ft^3/min. Find the time when the concentration of carbon monoxide reaches 0.01%.

I'm always having trouble setting up this equation
I know s = smoke;
so DS/dt = in - out
[4% * 0.5ft^3/min] - [0.01% * 0.5ft^3/min ] I know I'm missing some variables such as t, to find the time when concentration of smoke is 0.01%

My assumption is 4% of 1000ft^3 so that there is 9060ft^3 = air while 40ft^3 = smoke in.
0.01% of 1000 is 9090 = air and 10 = smoke.
Just need help setting up the question and understanding how to get it.

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Sorry, I could not read the content fromt this page.

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Sorry, I could not read the content fromt this page.

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Recall that 4^-2=1/4^2

So e^-x = 1/e^x

thus e^x^e^-x=e^x/e^x = 1

so you have integral of dx from 0 to 1 which has the anti-derivative of just x

so x evaluated at the limits is
1 - - 0 = 1

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Pretty sure f(5) = f(7) in this case. I am not going to do the arithmetic. You can do that.

Rolle's theorem basicly says that if the two end points are equal. There must be a point c between the two end points that have a tangent slope of 0. It's pretty intuitive if you think about it. If the two points have the same y coordinate, than it's either a straight line between them or a curve that goes up then down or etc. There must be a 0 tangent slope somehwere.

To get that point, you set the derivative of f(x) to 0 and solve for x, which is would be the point c.

df/dx = -48 + 8x = 0
x=48/8.... c = 48/8

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ln(8)? ..... i posted the full problem but everyone's avoiding that like the plague. anybody know what i can do with ln(8)?

my final answer was ln(3) - ln(8), but the book answer was just ln(3). check my work in the other problem if you want, or if you know something about ln(8) that i dont, feel free to share.

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Home >All Categories > Science & Mathematics >Mathematics >Open Question Ryan Member since:December 12, 2007Total points:15,067 (Level 6)I want to know if its better to take it during the summer or the fall year. And how rigorous would the course be on a scale of 1-10 if you did pretty decent (mostly B's and A's) on calc I and II?Answer Question

Be the first to answer this question.

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