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Leto [7]
3 years ago
11

When p = 12, t = 2, and s = 1/6, r = 18. If r varies directly with p and inversely with the product of s and t, what is the cons

tant of variation?
A: 1/8

B: 1/2

C: 4 1/2

D: 18
Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
3 0
R = kp/st
18 = 12k/(1/6 x 2)
18 = 12k/(1/3)
18 = 36k
k = 18/36 = 1/2

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Answer:

1. Find the difference between the areas.

<u>Area of the small rectangle</u>: (x+2)(x+7)=x^2+7x+2x+14=x^2+9x+14

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2.

You can solve this question just by looking at the graph.

a) The height is 4 meters.

f(d)=h=-2d^2+7d+4

To find the height of the bleachers, we should consider the moment before the shoot, when the distance is equal to 0.

f(0)=h=-2(0)^2+7(0)+4

h=4

The height is 4 meters.

b) 9 meters.

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f(1)=h=-2(1)^2+7(1)+4

f(1)=h=-2+7+4

h=9

b) The ball travels 4 meters.

But to calculate it, it is when h=0

0=-2d^2+7d+4

Using the quadratic formula:

$d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$d=\frac{-7 \pm \sqrt{7^2-4\left(-2\right)4}}{2\left(-2\right)}$

$d=\frac{-7\pm\sqrt{81}}{-4}$

$d=\frac{-7\pm9}{-4}$

It will give us to solutions, once it is a quadratic equation, but we are talking about a positive distance.

$d=-\frac{1}{2} \text{ or }d=4$

3.

In this question, we have to find the area of the cylinder and the sphere.

From the information given, we have

a = 5mm and d = 5mm, therefore the radius is 2.5 mm.

The volume of a cylinder:

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3 0
3 years ago
Calculate the mean given the frequency table
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First, multiply the midpoint of each class by its frequency, as follows:

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            10-19      14.5            20                14.5*20 = 290

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The mean is computed as the division between the addition of the "midpoint*frequency" column by the addition of "frequency" column.

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