Answer:
x = 18
m<A = 166°
Step-by-step explanation:
The parallel lines are cut by a transversal, so corresponding angles A and B are congruent.
7x + 40 = 3x + 112
4x = 72
x = 18
m<A = 7x + 40 = 7(18) + 40 = 126 + 40 = 166
Answer:
The coordinates of point S are (8,-2)
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to

Let
Point S(x2,y2)
substitute the given values

<em>Solve for x2</em>

<em>Solve for y2</em>

therefore
The coordinates of point S are (8,-2)
I assume the cone has equation
(i.e. the upper half of the infinite cone given by
). Take

The volume of the described region (call it
) is

The limits on
and
should be obvious. The lower limit on
is obtained by first determining the intersection of the cone and sphere lies in the cylinder
. The distance between the central axis of the cone and this intersection is 1. The sphere has radius
. Then
satisfies

(I've added a picture to better demonstrate this)
Computing the integral is trivial. We have

Since the average of 6 tests is 6, and we know that the average is found by dividing the total score by the number of tests, we can just multiply the average by the number of tests to find the total score. Doing this, we get 82 * 6 which simplifies to 492.