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2 years ago

14

The length around a rectangle

2 answers:

USPshnik [31]2 years ago

8 0

Perimeter is the length around an object

Rashid [163]2 years ago

5 0

Perimeter is correct

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What is the factored form of 15x - 6

alexandr402 [8]

Answer:

3(5x - 2)

Step-by-step explanation:

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3 years ago

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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.

noname [10]

Answer:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

Step-by-step explanation:

Given

$Volume = 128ft^3$

$L = 2W$

$Base\ Cost = \$9/ft^2$

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

Required

The dimension that minimizes the cost

The volume is:

$Volume = LWH$

This gives:

$128 = LWH$

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:

Area = Area of Bottom + Area of Sides

So, we have:

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

The cost is:

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

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

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

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

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

Then set to 0

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

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

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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2 years ago

Is square root of 100 irrational or rational?

viva [34]

<span>Square root of 100 is a rational number. Because sqaure rooot 100 = 10. And, 10 can be written in the form rational number. Any number that can be written in the form of p/q where p and q are integers and q in not zero is called a rational number.</span>

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2 years ago

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How do you turn 3/10 into a decimal

xxTIMURxx [149]

Answer:

do 3 divided by 10 to get the decimal

Step-by-step explanation:

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3 years ago

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In Exercise,find the balance in the account after 10 years.

Vesnalui [34]

Answer: $ 3462.03

Step-by-step explanation:

The exponential equation for growth (compounded continuously) is given by :-

$A=Pe^{rt}$

, where P= Present value

r= growth rate ( in decimal)

t= time

As per given , we have

P=$1900, r = 6% =0.06 and t= 10

Substitute all the values in the above equation , we get

$A=1900e^{0.06(10)}$

$A=1900e^{0.6}$

$A=1900(1.8221188)=3462.02572\approx3462.03$ [To the nearest cent]

Hence, the balance in the account after 10 years = $ 3462.03

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3 years ago