PLEASE HELP

Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min. It forms a pile in the shape of a right circular cone whose

Norma-Jean [14]

Answer:

$\frac{dh}{dt}=\frac{160}{169\pi } ft/min$

Step-by-step explanation:

This is a classic related rates problem. Gotta love calculus!

Start out with the formula for the volume of a cone, which is

$V=\frac{1}{3}\pi r^2h$

and with what we know, which is $\frac{dV}{dt}=40$

and the fact that the diameter = height (we will come back to that in a bit).

We need to find $\frac{dh}{dt}$ when h = 13

The thing we need to notice now is that there is no information given to us that involves the radius. It does, however, give us a height. We need to replace the r with something in terms of h. Let's work on that first.

We know that d = h. Because d = 2r, we can say that 2r = h, and solving for r gives us that $r=\frac{h}{2}$ .

Now we can rewrite the formula with that replacement:

$V=\frac{1}{3}\pi (\frac{h}{2})^2h$

Simplify that all the way down to

$V=\frac{1}{12}\pi h^3$

The derivative of that function with respect to time is

$\frac{dV}{dt}=\frac{1}{12}\pi(3h^2)\frac{dh}{dt}$

Filling in what we have gives us this:

$40=\frac{1}{12}\pi (3)(13)^2\frac{dh}{dt}$

Solve that for the rate of change of the height:

$\frac{dh}{dt}=\frac{160}{169\pi } \frac{ft}{min}$

or in decimal form:

$\frac{dh}{dt}=.95\pi \frac{ft}{min}$

8 0

3 years ago

Find the slope.<br> y = -9x +4<br> m<br> [?]

faust18 [17]

Answer:

-9

Step-by-step explanation:

with the equation y=mx+b, m equals the slope and b equals the y-intercept. whatever is in the place of m is the slope. in this case, -9.

5 0

3 years ago

Which one of these is not congruent to angle 5?

Artemon [7]

Answer:

Step-by-step explanation:

The answer is 1 and 3

7 0

3 years ago

Which expression is equal to (x+2)(−3x2+3x+1)?

padilas [110]

Multiply everything in the second parenthesis by x.

-3x^3 + 3x^2 + x

Multiply everything in the second parenthesis by 2.

-6x^2 + 6x + 2

Combine these two equations together.

-3x^3 + 3x^2 + x - 6x^2 + 6x + 2

Combine like terms.

-3x^3 - 3x^2 + 7x + 2

Hope this helps!
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7 0

4 years ago

Please answer quickly this is due today and I just can’t figure it all out!!

Bumek [7]

Answer:

A. You may set the variables in either order. But for argument sake, let's set as follows:

x = Amount of bookshelves

y = Amount of tables

B. Because of the amount of things you need to make, the following is an inequality using those variables.

x + y > 25

Plus you can determine a second inequality based on the amount of money that you have to spend.

20x + 45y < 675

Finally you may also add in that each value must be greater than or equal to zero, since they cannot have negative tables.

C. By solving the system and looking at basic constraints when graphed, you can see the feasible region has 4 vertices.

(0,0)

(18, 7)

(0, 15)

(33.75, 0) or (33, 0) if you insist on rounding.

Step-by-step explanation: Good luck and hope this helps :)

4 0

3 years ago