Please help need ASAP

Answers:

Explanation:

We'll use the cosine ratio to find side AT

cos(angle) = adjacent/hypotenuse

cos(A) = AR/AT

cos(24) = 33/AT

AT*cos(24) = 33

AT = 33/cos(24)

AT = 36.1229971906996

AT = 36.122997  approximately

We could use the sine or tangent ratio to find side TR, but let's use the pythagorean theorem instead.

a^2 + b^2 = c^2

(AR)^2 + (TR)^2 = (AT)^2

33^2 + (TR)^2 = (36.1229971906996)^2

1089 + (TR)^2 = 1304.8709260393

(TR)^2 = 1304.8709260393 - 1089

(TR)^2 = 215.8709260393

TR = sqrt(215.8709260393)

TR = 14.6925466151821

TR = 14.692547  also approximate

We could use any of the trig ratios of sine, cosine, or tangent to solve for angle T.

However, it's easiest to take advantage of the fact that angles A and T are complementary.

So,

A+T = 90

T = 90-A

T = 90-24

T = 66 degrees

This value is exact.

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: