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3 years ago

In ΔFGH, the measure of ∠H=90°, the measure of ∠F=24°, and FG = 57 feet. Find the length of HF to the nearest tenth of a foot.

Mathematics

1 answer:

Alex3 years ago

4 0

Answer: 52.1

Step-by-step explanation:

\cos F = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{x}{57}

cosF=

hypotenuse

adjacent

\cos 24=\frac{x}{57}

cos24=

57\cos 24=x

57cos24=x

Cross multiply.

x=52.0721\approx \mathbf{52.1}\text{ feet}

x=52.0721≈52.1 feet

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A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon

zmey [24]

Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.

<h3>What is the volume of a sphere?</h3>

The volume of a sphere of radius r is given by:

$V = \frac{4\pi r^3}{3}$

Applying implicit differentiation, the rate of change is given by:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

In this problem, we have that:

$\frac{dV}{dt} = 500, r = 70$

Hence the rate of change of the radius is given as follows:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

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$\frac{dr}{dt} = \frac{500}{19600\pi}$

$\frac{dr}{dt} = 0.0081$

The radius is increasing at a rate of 0.0081 cm per minute.

More can be learned about implicit differentiation at brainly.com/question/25608353

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2 years ago

There were 12 girls on the basketball team. 3 of them scored over 10 points in the game. What fraction represents the number of

Naily [24]

Answer:

1/4

Step-by-step explanation:

3 out of 12 stored over 10:

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6 0

3 years ago

If 110% of a number is 528, then the number is:

Anuta_ua [19.1K]

Answer:

c) 480

Step-by-step explanation:

Any percentage can be converted to a number ratio by dividing by 100%.

E.g. 100%/100% = 1

Following this concept, we can find the equivalent of 110% :

110%/100% = 1.1

Since 528 is 1.1 times the number we are looking for, we just need to divide 528 by 1.1 to find our number. This is because 1.1/1.1 = 1

528/1.1 = 480

Hope this helped!

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2 years ago

Read 2 more answers

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vovangra [49]

Answer:

40.49cm²

Step-by-step explanation:

I hope it helps

8 0

3 years ago

Please help me due today

Keith_Richards [23]

Answer:

To find the answer consider that this is a right triangle and we can use the tangent function in order to find the value of x

remember the acronym soh cah toa.

to use the tangent function we divide the opposite and adjacent side that is what the oa stands for in toa

setting it up looks like this

tan 72° = $\frac{x}{8\\}$

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which is about 24.62

Step-by-step explanation:

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3 years ago