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3 years ago

9

A National Hockey League rink is 115 feet longer than it is wide. If the perimeter of the rink is 570 feet, find the dimensions

of the rink.

1 answer:

kirza4 [7]3 years ago

7 0

Check the picture below.

what's the length? well, l = w + 115.

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An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne

lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

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3 years ago

Does anyone know how to solve this <br> The answer is B but can anyone explain why

Lana71 [14]

Answer:

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Step-by-step explanation:

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3 years ago

(4x+2)=102+44 solve for x

sergiy2304 [10]

<h3>Solution:</h3>

(4x + 2) = 102 + 44
or, 4x = 102 + 44 - 2
or, 4x = 144
or, x = 144 ÷ 4
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<h3>Answer:</h3>

x = 36

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3 years ago

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Am I to assume this is for volume? The volume formula for a cylinder...oblique or not...is V = 1/3pi r^2 h. Cavalieri's principle tells us that the formulas for both are the same. So V = 1/3*pi*100*11 and V = 366.67 pi

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3 years ago

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Find the area of following rhombuses. Round your answers to the nearest tenth if<br> necessary.

polet [3.4K]

Answer:

$Area =55.4ft^2$

Step-by-step explanation:

Given

The attached rhombus

Required

The area

First, calculate the length of half the vertical diagonal (x).

Length x is represented as the adjacent to 60 degrees

So, we have:

$\tan(60) = \frac{4\sqrt 3}{x}$

Solve for x

$x = \frac{4\sqrt 3}{\tan(60)}$

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So:

$x = \frac{4\sqrt 3}{\sqrt 3}$

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At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

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So, the area of the rhombus is 4 times the area of 1 triangle

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$Area =55.4ft^2$

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3 years ago