ANSWER
A. 22 in
EXPLANATION
The volume of a cone is calculated using the formula:

It was given that: the volume is 2,279.64 in³
The height of the cylinder is also given as: h=18 in.
We substitute, the given values into the formula to get:




We take positive square root to get;


Therefore the diameter is 2(11) which is equal to 22 inches.
Answer:
It would be the second option
Step-by-step explanation:
z:28 is the ratio of the shorter triangle's side to the larger triangle's side, so is 27:45.
a. Parameterize
by

with
.
b/c. The line integral of
over
is




d. Notice that we can write the line integral as

By Green's theorem, the line integral is equivalent to

where
is the triangle bounded by
, and this integral is simply twice the area of
.
is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.
Answer:
b. not similar
Step-by-step explanation:
The given sides* have the ratio 30:39 = 10:13 in one triangle and the ratio 20:27 = 10:13.5 in the other triangle. Since these ratios are different, the triangles cannot be similar.
____
* These are the sides bracketing the vertical angles at T. If the triangles were similar, the three sides would have to have the ratios 10 : 13 : 13.5.
However, the geometry shown would require that the angle opposite side 13.5 in one triangle have the same measure as the angle opposite side 13 in the other triangle. That is not possible, so it is not possible for these triangles to be similar.
Answer:
a. y = -x² + 2x - 8
b. y = 
c. y = x³+ 3
Step-by-step explanation: