Answer:
y=2x-2
Step-by-step explanation:
y=mx+b is point slope form.
let m= the slope
b=y intercept
the y intercept is -2
y=mx-2
then after finding the slope (2) put that in
y=2x-2
Easy, so absolute value makes anything inside into positive
|x|=2
therefor x=-2 or x=2 since it would be made posotive
answer is -2 and 2
78 gallons is the same as 312 quarts
Question:
Find the point (,) on the curve
that is closest to the point (3,0).
[To do this, first find the distance function between (,) and (3,0) and minimize it.]
Answer:

Step-by-step explanation:
can be represented as: 
Substitute
for 

So, next:
Calculate the distance between
and 
Distance is calculated as:

So:


Evaluate all exponents

Rewrite as:


Differentiate using chain rule:
Let


So:



Chain Rule:




Substitute: 

Next, is to minimize (by equating d' to 0)

Cross Multiply

Solve for x


Substitute
in 

Split

Rationalize



Hence:

Answer:
.
Step-by-step explanation:
We have been given that a sphere has a radius of 8 centimeters. A second sphere has a radius of 2 centimeters. We are asked to find the difference of the volumes of the spheres.
We will use volume formula of sphere to solve our given problem.
, where r is radius of sphere.
The difference of volumes would be volume of larger sphere minus volume of smaller sphere.





Therefore, the difference between volumes of the spheres is
.