Answer:
Step-by-step explanation:
<em>(17).</em> g(x) = x³ + 4x
f(x) = 4x + 1
( f × g )( x ) = ( x³ + 4x )( 4x + 1 ) = <em>4 </em><em> + x³ + 16x² + 4x</em>
<em>(19).</em> f(t) = 4t - 4
g(t) = t - 2
( 4f + 3g )( t ) = 4(4t - 4) + 3(t - 2) = 16t - 16 + 3t - 6 = <em>19t - 22</em>
<em>(21).</em> h(t) = t + 3
g(t) = 4t + 1
h(t - 2) + g(t - 2) = ( t - 2 ) + 3 + 4( t - 2 ) + 1 = t + 4t - 2 + 3 - 8 + 1 = <em>5t - 6</em>
Answer:
The volume of the shaded figure is 252π feet³ ⇒ 1st answer
Step-by-step explanation:
* <em>Lets revise how to find the volume of the sphere</em>
- The volume of any sphere is , where
r is the radius of the sphere
- There is a large sphere of diameter 12 feet
- The diameter of the sphere is twice its radius
∵ The length of the diameter is 12 feet
∴ The length of the radius = feet
- There is a smaller sphere with a radius of 3 feet
- The smaller sphere is cut out of the center of the larger sphere
- <em>The volume of the shaded part is the difference between the </em>
<em> volumes of the larger sphere and the smaller sphere</em>
* <em>Lets find the volume of each sphere</em>
- The volume of the larger sphere:
V larger = = 288π feet³
- The volume of the smaller sphere:
V smaller = = 36π feet³
∴ The volume of the shaded figure = 288π - 36π = 252π feet³
* The volume of the shaded figure is 252π feet³
