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mars1129 [50]
3 years ago
12

A theme park has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumfere

nce of 558.92 yd. What is the surface area of the sphere?
Mathematics
1 answer:
DENIUS [597]3 years ago
3 0

Answer:

The surface area of the sphere is = 99426.41 yd^2

Step-by-step explanation:

The area of a sphere can be calculated using this formula:

A=4\pi r^2

However, we have a little problem: we do not have our radius yet to utilize in the formula above.

We can get our radius from the circumference of the circle which has been given to us.

circumference = 2 \times \pi \times r

r = \frac{circumference}{2 \pi} = \frac{558.92yd}{2\pi} = 88.95yd

We now have our radius. we can input it into equation 1 above

The Surface area of sphere = 4 \times \pi \times 88/95^2 =  99426.41yd^2

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3. Two cars are parked, 150m apart, and on opposite sides of a building. A camera on the top of the building rotates and can vie
allsm [11]

Answer:

<em>The building is 61.5 m tall</em>

Step-by-step explanation:

The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:

h = height of the building

a, b = internal angles of each triangle

x  = base of each triangle

The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:

a = 90° - 37° = 53°

b = 90° - 42° = 48°

Now we apply the tangent ratio on both triangles separately:

\displaystyle \tan a=\frac{\text{opposite leg}}{\text{adjacent leg}}

\displaystyle \tan 53^\circ=\frac{150-x}{h}

\displaystyle \tan 48^\circ=\frac{x}{h}

From the last equation:

x=h.\tan 48^\circ

Substituting into the first equation:

\displaystyle \tan 53^\circ=\frac{150-h.\tan 48^\circ}{h}

Operating on the right side:

\displaystyle \tan 53^\circ=\frac{150}{h}-\tan 48^\circ

Rearranging:

\displaystyle \tan 53^\circ+\tan 48^\circ=\frac{150}{h}

Solving for h:

\displaystyle h=\frac{150}{\tan 53^\circ+\tan 48^\circ}

Calculating:

h = 61.5 m

The building is 61.5 m tall

5 0
3 years ago
Find two positive numbers satisfying the given requirements.
Umnica [9.8K]

Answer:

8 and 19

Step-by-step explanation:

To some this, let's first list all the factors of 152. They are;

1, 2, 4, 8, 19, 38, 76, 152.

Now, let's arrange them to reflect being multiplied to get 152.

Thus;

1 × 152 = 152

2 × 76 = 152

4 × 38 = 152

8 × 19 = 152

Also, let's do the same for their sum;

1 + 152 = 153

2 + 76 = 78

4 + 38 = 42

8 + 19 = 27

Looking at the figures above, the ones that their product is 152 but have the least sum are 8 and 19

8 0
2 years ago
NEED HELP ASAP
stellarik [79]

C

because you just eliminate it

3 0
3 years ago
Carlos drunk 2740 milliliters after football practice how much liters does he drink
Anni [7]
2.74 liters since 1000mL is a liter.
7 0
3 years ago
Write as a decimal. If a repeating decimal, round to the nearest hundredth.
Mamont248 [21]

Given:

\frac{475}{80}

Let's evaluate and find the quotient.

We have:

\frac{475}{80}=5.9375

SInce it is not a repeating decimal, we are asked to leave to answer as it is.

A repeating decimal is a decimal with digits or group of digits that repeats endlessly.

The decimal 5.937

ANSWER:

5.9375

6 0
1 year ago
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