Answer:
V = 120.6796
LA = 110.8513
SA = 174.8513
Step-by-step explanation:
Let me know if you need more of an explanation for any of these
First we need the height, one way to find that out is to use the diagonal of the and one of the diagonal edges of the pyramid. Specifically we will need half of the diagonal of the square. We will call the diagonal of the square d.

Gonna leave it like that for ease of writing. So then half of the diagonal is 
The height, h, will be
. Plugging everything in gets us 
last, we need to find slant height, which we will call s.

s is also the height of the triangles for purposes of finding area. Now for the volume and areas.
Volume is area of the base times height divided by 3, so 
Lateral area is the sum of the four areas of the triangles, and each of those are
so the whole lateral area is 4 times that. So we get 
Total surface area is the lateral surface area + the area of the base, so 110.8513 + 64 = 174.8513
So our equation currently is ⇒ 
<u>Let's first move all the constant to one side and group 'like variables' together</u>:

<u>Now lets complete the square of both equations</u>

<u><em>Now we know the circle's general equation format is</em></u>:
⇒
- (h, k) ⇒ coordinate of the center of the circle
- r ⇒ length of radius of circle
<u>Thus the radius of the circle is 7</u>
<u></u>
Hope that helps!
Answer:
The domain that makes sense for this function is all values greater than or equal to 0.
Step-by-step explanation:
A ball is thrown into the air from a height of 4 feet at time <em>t</em> = 0. It is modeled by the function:

The domain of the function is time <em>t</em>. The range of the function is the ball's height in the air <em>h</em>.
Since time is our domain, we must restrict our domain to values equal to or greater than 0 since time cannot be negative.
Therefore, the domain that makes sense for this function is all values greater than or equal to 0.
In interval notation, this is:

And as an inequality:

Answer:
x³ - 10x² + 31x - 30
Step-by-step explanation:
Given
(x - 2)(x - 3)(x - 5) ← expand the second pair of factors using FOIL
= (x - 2)(x² - 8x + 15) ← distribute
= x³ - 8x² + 15x - 2x² + 16x - 30 ← collect like terms
= x³ - 10x² + 31x - 30