Answer:
the dimensions of the most economical shed are height = 10 ft and side 5 ft
Step-by-step explanation:
Given data
volume = 250 cubic feet
base costs = $4 per square foot
material for the roof costs = $6 per square foot
material for the sides costs = $2.50 per square foot
to find out
the dimensions of the most economical shed
solution
let us consider length of side x and height is h
so we can say x²h = 250
and h = 250 / x²
now cost of material = cost of base + cost top + cost 4 side
cost = x²(4) + x²(6) + 4xh (2.5)
cost = 10 x² + 10xh
put here h = 250 / x²
cost = 10 x² + 10x (250/ x² )
cost = 10 x² + (2500/ x )
differentiate and we get
c' = 20 x - 2500 / x²
put c' = 0 solve x
20 x - 2500 / x² = 0
x = 5
so we say one side is 5 ft base
and height is h = 250 / x²
h = 250 / 5²
height = 10 ft
See attached picture.
Break the shape up into 4 different shapes and find the seperate areas then add them together.
Answer = C. 146
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❖ A composite number is 27. 27 is composite because there are more numbers than 1 and itself that can be multiplied to create 27. The two other numbers to make 27 are 3 x 9. All the other answer choices are prime numbers because no other numbers besides 1 and itself can be multiplied to make that number.
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Factor <span><span><span><span>2<span>x3</span></span>+<span>7<span>x2</span></span></span>−<span>3x</span></span>−18</span><span><span><span><span>2<span>x3</span></span>+<span>7<span>x2</span></span></span>−<span>3x</span></span>−18</span><span>=<span><span><span>(<span>x+2</span>)</span><span>(<span>x+3</span>)</span></span><span>(<span><span>2x</span>−3</span>)</span></span></span>Answer:<span><span><span>(<span>x+2</span>)</span><span>(<span>x+3</span>)</span></span><span>(<span><span>2x</span>−3</span><span>)</span></span></span>
15,000
3 multiplied by 5,000 is 15,000
