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Slav-nsk [51]
2 years ago
6

The long side of a rectangle is 3x+21 units, and it's area is 3x^2+33x+84. Find the width

Mathematics
1 answer:
ella [17]2 years ago
3 0
L*w=area
(3x+21)*w=3x^2+33x+84
w=(3x^2+33x+84)/3x+21
(3(x+4)(x+7))/3(x+7)
w=x+4
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A volleyball uniform costs $15 for the shirt, $12 for shorts, and $8 for socks. Which expression applies the distributive proper
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An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a
belka [17]
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Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s
</span>

4 0
3 years ago
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