The amount of metal he will need to cover the back of the shelves is 180 inches².
The figure above is like a composite figure. Therefore, lets find the area.
<h3>Area of the composite figure</h3>
The area of the figure is the sum of the whole individual 2 dimensional shapes in the composite figure.
Therefore, two rectangles can be drawn from it.
area of rectangle = lw
where
l = length
w = width
Therefore,
area of rectangle 1 = 9 × 8 = 72 inches²
area of rectangle 2 = 6 × 18 = 108 inches²
Total area = 108 + 72 = 180 inches²
Therefore, the amount of metal he will need to cover the back of the shelves is 180 inches².
learn more on area here: brainly.com/question/25849553
For # 9, the answer is 4 pants and 11 shirts, see in the comments for my explanation
Answer:
9/2
Step-by-step explanation:
Assume 0 < <em>x</em>/2 < <em>π</em>/2. Then
tan²(<em>x</em>/2) + 1 = sec²(<em>x</em>/2) ===> sec(<em>x</em>/2) = √(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - <em>t</em> ²)
We also know that
sin²(<em>x</em>/2) + cos²(<em>x</em>/2) = 1 ===> sin(<em>x</em>/2) = √(1 - cos²(<em>x</em>/2))
Recall the double angle identities:
cos(<em>x</em>) = 2 cos²(<em>x</em>/2) - 1
sin(<em>x</em>) = 2 sin(<em>x</em>/2) cos(<em>x</em>/2)
Then
cos(<em>x</em>) = 2/(1 - <em>t</em> ²) - 1 = (1 + <em>t</em> ²)/(1 - <em>t</em> ²)
sin(<em>x</em>) = 2 √(1 - 1/(1 - <em>t</em> ²)) / √(1 - <em>t</em> ²) = 2<em>t</em>/(1 - <em>t</em> ²)
