A rectangles base is 2in. Shorter than twice its height. The rectangles area is 40in^2. Find it's dimensions.

5 in by 8 in

Step-by-step explanation:

Given that :

Area, A of rectangle = 40 in²

Let

height = x

Base = 2x - 2

Area of rectangle = L * B

40 = x * (2x - 2)

40 = 2x² - 2x

2x² - 2x - 40 = 0

x² - x - 20 = 0

x² - 5x + 4x - 20 =0

x(x - 5) +4(x - 5) = 0

x - 5 = 0 or

x + 4 = 0

x = 5 or x = - 4

X cannot be negative

X = 5

Height = 5

Base = 2*5 - 2 = 8

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92