Jean-Paul Sovique, the famous sculptor, is building a solid conical sculpture. He has 1,178.1 cubic feet of clay to work with, and he wants his sculpture to be three times as high as its radius. What will the radius and height of his cone be?

Radius = 7.21 feet.

Height = 21.63 feet

- to the nearest hundredth.

Step-by-step explanation:

Let the radius be r feet, then the height will be 3r feet.

So the volume = 1,178.1 = 1/3 π r^2 h

1.178.1 = 1/3  π r^2 3r

1/3 π 3 r^3 = 1178.1

 π r^3 = 1178.1

r^3 = 1178.1/ π

r^3 =   375

r = 7.211 feet.

So the height = 3 * 7.211 ft

= 21.633 ft

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.