Added instead of distributing or multiplying
Answer:

Step-by-step explanation:
If
, then
and
are alternate interior angles.
This means that line segment AC is a transversal.
This implies that line segment AD is parallel to line segment BC.
The second choice is the correct answer.
Answer:
Step-by-step explanation:
Here's the formula for the volume of a right circular cylinder:

Here's what we are given and what we need to find:
Given that d = 10 cm, h = 20 cm, dd/dt = 1 cm/sec
Need to find dh/dt when V is constant
Since our formula has a radius in it and not a diameter but the info given is a diameter, we can use the substitution that
so

Now we can rewrite the formula in terms of diameter:
which simplifies down to

Now we will take the derivative of this equation with respect to time using the product rule. That derivative is
![\frac{dV}{dt}=\frac{\pi }{4}[d^2*\frac{dh}{dt}+2d\frac{dd}{dt}*h]](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D%5Bd%5E2%2A%5Cfrac%7Bdh%7D%7Bdt%7D%2B2d%5Cfrac%7Bdd%7D%7Bdt%7D%2Ah%5D)
Now we can fill in our values. Keep in mind that if the volume is constant, there is no change in the volume, so dV/dt = 0.
and

Multiply both sides by pi/4 to get
and solve for dh/dt:

Interpreted within the context of our problem, this means that the volume will be constant at those given values of diameter and height when the liquid in the cylinder is dropping at a rate of 4 cm/sec.
Answer:
b
Step-by-step explanation: