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3 years ago

8

Which of the following is equivalent to 10 3/2?

2 answers:

Aleksandr-060686 [28]3 years ago

6 0

Answer:

D) $\sqrt{10^3}$

slava [35]3 years ago

4 0

Answer:

D

Step-by-step explanation:

Raising a number to a power in fraction simply means getting the appropriate root of the number. Hence,

${10}^{3 \times \frac{1}{2} } \\ \sqrt{ {10}^{3} }$

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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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Answer:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

Step-by-step explanation:

Given

$Volume = 128ft^3$

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$Sides\ Cost = \$6/ft^2$

Required

The dimension that minimizes the cost

The volume is:

$Volume = LWH$

This gives:

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Substitute $L = 2W$

$128 = 2W * WH$

$128 = 2W^2H$

Make H the subject

$H = \frac{128}{2W^2}$

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

The surface area is:

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So, we have:

$A = LW + 2(WH + LH)$

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

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

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

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$C' =2*18W + -1 * 2304W^{-2}$

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$2*18W + -1 * 2304W^{-2} =0$

$36W - 2304W^{-2} =0$

Rewrite as:

$36W = 2304W^{-2}$

Divide both sides by W

$36 = 2304W^{-3}$

Rewrite as:

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

Solve for $W^3$

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

$W^3 = 64$

Take cube roots

$W = 4$

Recall that:

$L = 2W$

$L = 2 * 4$

$L = 8$

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

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

$H = \frac{64}{16}$

$H = 4$

Hence, the dimension that minimizes the cost is:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

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