For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:

Answer:
9x²-3x-25, Domain is all real numbers
Step-by-step explanation:
f(g(x)) = 3(3x²-x-10)+5
= 9x²-3x-30+5
= 9x²-3x-25
Domain is all real numbers
Answer: see proof below
<u>Step-by-step explanation:</u>
Given: cos 330 = 
Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

Proof LHS → RHS:
LHS cos 165
Double-Angle: cos (2 · 165) = 2 cos² 165 - 1
⇒ cos 330 = 2 cos² 165 - 1
⇒ 2 cos² 165 = cos 330 + 1
Given: 

Divide by 2: 

Square root: 
Scratchwork: 

Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

LHS = RHS 
Hi!
Here's your answer:
x=3 and y=0
I hope this helps!
Feel free to mark brailiest!