Jim is 4 ft from a lamppost that is 16 ft tall and he is 6 foot tall his shadow is ft long?

To solve this, let us first imagine a smaller triangle created by the head of Jim (A), the top of the lamp post (B), and somewhere on the body of the lamp post which is directly perpendicular to the head of Jim (C).

CB = 16 – 6 = 10 ft

AC = 4 ft

Calculate for angle B using tan function:

tan B = AC / CB

B = tan^-1 (4 / 10)

B = 21.8°

Now imagine a bigger triangle created by the tip of shadow (D), the top of the lamp post (B), and the base of the lamp post (E).

BE = 16 ft

B = 21.8°

We can calculate for DE using tan function:

tan B = DE / BE

(16 ft) tan 21.8 = DE

DE = 6.4 ft

Since Jim is 4ft away from the base of the lamp post, therefore the length of the shadow is:

6.4 ft – 4 ft

= 2.4 ft

Therefore the length of Jim’s shadow is 2.4 ft long

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.