The total surface area of this cuboid is 112cm^2. Find the value of x. Please explain, don’t just give the answer.

The value of x is 3

Step-by-step explanation:

Let us study the face of the cuboind

∵ The cuboid has 6 rectangular faces

∵ Each opposite faces area equal in areas

∴ 2 faces of dimensions 10 cm and 2 cm

∴ 2 faces of dimensions 10 cm and x cm

∴ 2 faces of dimensions 2 cm and x cm

∵ The total surface area of the cuboid is the sum of the areas of the 6 faces

∵ The area of the rectangle = length × width

∴ The total surface area = 2(10 × 2) + 2(10 × x) + 2(2 × x)

∴ The total surface area = 2(20) + 2(10x) + 2(2x)

∴ The total surface area = 40 + 20x + 4x

→ Add the like terms 20x and 4x

∴ The total surface area = 40 + 24x

∵ The total surface area of this cuboid is 112 cm²

→ Equate the two sides of the total surface area

∴ 40 + 24x = 112

→ Subtract 40 from both sides

∵ 40 - 40 + 24x = 112 - 40

∴ 24x = 72

→ Divide both sides by 24

∴ x = 3

∴ The value of x is 3

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