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Anna11 [10]
3 years ago
9

PQ⊥PS , m∠QPR=7x−9, m∠RPS=4x+22 Find : m∠QPR

Mathematics
1 answer:
emmainna [20.7K]3 years ago
3 0

Given:

It is given that,

PQ ⊥ PS and

∠QPR = 7x-9

∠RPS = 4x+22

To find the value of ∠QPR.

Formula

As per the given problem PR lies between PQ and PS,

So,

∠QPR+∠RPS = 90°

Now,

Putting the values of ∠RPS and ∠QPR we get,

7x-9+4x+22 = 90

or, 11x = 90-22+9

or, 11x = 77

or, x = \frac{77}{11}

or, x = 7

Substituting the value of x = 7 in ∠QPR we get,

∠QPR = 7(7)-9

or, ∠QPR = 40^\circ

Hence,

The value of ∠QPR is 40°.

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A=4 \pi r^2
2122.64=4(3.14)r^2
2122.64=12.56r^2
Now, we just need to solve our equation for r:
\frac{2122.64}{12.56} =r^2
r^2=\frac{2122.64}{12.56}
r^2=169
r=+or- \sqrt{169}
r=13 or r=13
Since the radius of a sphere cannot be a negative number, r=13.

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On a linear X temperature scale, water freezes at −115.0°X and boils at 325.0°X. On a linear Y temperature scale, water freezes
belka [17]

Answer:

The current temperature on the X scale is 1150 °X.

Step-by-step explanation:

Let is determine first the ratio of change in X linear temperature scale to change in Y linear temperature scale:

r = \frac{\Delta T_{X}}{\Delta T_{Y}}

r = \frac{325\,^{\circ}X-(-115\,^{\circ}X)}{-25\,^{\circ}Y - (-65.00\,^{\circ}Y)}

r = 11\,\frac{^{\circ}X}{^{\circ}Y}

The difference between current temperature in Y linear scale with respect to freezing point is:

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The change in X linear scale is:

\Delta T_{X} = r\cdot \Delta T_{Y}

\Delta T_{X} = \left(11\,\frac{^{\circ}X}{^{\circ}Y} \right)\cdot (115\,^{\circ}Y)

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Lastly, the current temperature on the X scale is:

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T_{X} = 1150\,^{\circ}X

The current temperature on the X scale is 1150 °X.

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