A tree that is 35 feet tall casts a shadow 42 feet long at 4:00PM. A man standing near the tree at that same time casts a shadow that is 7.5 feet long. How tall is the man?

The man's height is 6.25ft

Step-by-step explanation:

Given

Represent the height of the tree with H, the height of the tree's shadow with S

Represent the height of the man with h, the height of the man's shadow with s

So, we have:

H = 35ft

S = 42ft

s = 7.5ft

Required

Solve for h

To answer this, we make use of the following ratio

h/s = H/S

Substitute values for S, H and s

h/7.5 = 35/42

Multiply both sides by 7.5

h = 7.5 * 35/42

h = 262.5/42

h = 6.25

..

step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: