Apyramid is placed inside a prism as shown. the pyramid has the same base area, b, as the prism but half the height of the prism. the height of the prism is 30 feet. which expression gives the volume of the pyramid

Base area = b (ft^2)

Height of prism = 30 ft.

Volume of the prism = 30b ft^3

Height of pyramid = 30/2=15 ft

Base area of pyramid = b ft^2

Volume of pyramid = (1/3)bh=(1/3)b(15) =5b ft^3

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

choose (5, 1.5) and (-1.5,-3.5)

step-by-step explanation:

5 - 1.5 =3.5

-1.5 - (-3.5) = 2

3.5 + 2 =5.5

hope this !