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Afina-wow [57]
4 years ago
11

A man drove 16 mi directly east from his home, made a left turn at an intersection, and then traveled 2 mi north to his place of

work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
Mathematics
1 answer:
svlad2 [7]4 years ago
8 0

Answer:

16. 1 miles

Step-by-step explanation:

Using Pythagorean Theorem,

a^2 + b^2 = c^2

Since the road that goes from his home to work directly is c^2...

Plug in the rest of the numbers

16^2 + 2^2 = c^2

256 + 4 = c^2

260 = c^2

The reverse square of 260 is

16. 1 miles

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A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base.
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Width = 4ft

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Step-by-step explanation:

Given

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Required

The dimension that minimizes the cost

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Volume = LWH

This gives:

128 = LWH

Substitute L = 2W

128 = 2W * WH

128 = 2W^2H

Make H the subject

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The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

A = LW + 2(WH + LH)

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Cost = 9 * LW + 6 * 2(WH + LH)

Cost = 9 * LW + 12(WH + LH)

Cost = 9 * LW + 12H(W + L)

Substitute: H = \frac{64}{W^2} and L = 2W

Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)

Cost =18W^2 +  \frac{768}{W^2}*3W

Cost =18W^2 +  \frac{2304}{W}

To minimize the cost, we differentiate

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Rewrite as:

36W = 2304W^{-2}

Divide both sides by W

36 = 2304W^{-3}

Rewrite as:

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Solve for W^3

W^3 = \frac{2304}{36}

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Take cube roots

W = 4

Recall that:

L = 2W

L = 2 * 4

L = 8

H = \frac{64}{W^2}

H = \frac{64}{4^2}

H = \frac{64}{16}

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Width = 4ft

Height = 4ft

Length = 8ft

8 0
3 years ago
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