Answer:
x = 6
Step-by-step explanation:
We have to make the bottom eqivilent to the top.
10 + 30 = 40
5 x 6 = 30
10 + 30 = 40
from the question, (-2,2) and (1,2) have the same y value so you can use that as your base and easily find the perpendicular height using the y axis since it's parallel to the x axis.
the third point, (0,-6), to the base is your height
use the sum of the positive of the y values to find your height (because height can't be negative): 6+2 = 8
area of a triangle = 1/2 bh = 1/2 x 3 x 8 = 12
Note: 1/2 bh only works because (-2,2) and (1,2) form a line parallel to the x axis
Answer:
a) y = (x+2)/3
b) 5
Step-by-step explanation:
f^-1(x) means "f inverse of x". To find the inverse, we simply:
a ) f(x) = 3x -2
y = 3x - 2 --> because f(x) is the same thing as y
x = 3y - 2 --> to find the inverse, we simply just switch x and y
x + 2 = 3y
y = (x+2)/3
b) f^-1(13)
f^-1(13) = [((13) + 2)/3]
f^-1(13) = (15)/3
f^-1(13) = 5
Answer:
756π cm^3.
Step-by-step explanation:
Volume of the cone
270π = 1/3 π r^2 h
270π = 1/3 π r^2 * 10
r^2 = 270 / ( 10/3 )
r^2 = 81
r = 9 cm.
So the volume of the hemisphere = 1/2 * 4/3 * π * 9^3
= 486π cm^3.
So the volume of the whole solid = 270π + 486π
= 756 π cm^3.
