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ANEK [815]
3 years ago
10

A certain bridge arch is in the shape of half an ellipse 106 feet wide and 33.9 feet high. At what horizontal distance from the

center of the arch is the height equal to 12.3 feet
Mathematics
1 answer:
nata0808 [166]3 years ago
8 0

Answer:

The horizontal distance from the center is 49.3883 feet

Step-by-step explanation:

The equation of an ellipse is equal to:

\frac{x^2}{a^{2} } +\frac{y^2}{b^{2} } =1

Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.

Then, replacing a by 106/2 and b by 33.9, we get:

\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1

Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:

\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\\\frac{x^2}{2809} +\frac{12.3^2}{1149.21} =1\\\\\frac{x^2}{2809}=1-\frac{12.3^2}{1149.21}\\\\x^{2} =2809(0.8684)\\x=\sqrt{2809(0.8684)}\\x=49.3883

So, the horizontal distance from the center is 49.3883 feet

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A plane at an altitude of 7000 ft is flying in the direction of an island . If an angle of depression is 21 ° from the plane to
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The horizontal distance until the plan flies over the island is 2687.05 feet approximately.

<u>Solution:</u>

Given that, A plane at an altitude of 7000 ft is flying in the direction of an island

An angle of depression is 21 degree from the plane to the island

We have to find what is the horizontal distance until the plan flies over the island  

The diagram is attached below

Assume as shown in the diagram , now we can use the right angle triangle property

\tan (21)=\frac{\text {distance between plane and point above island}}{\text {height of plane}}

\tan (21)=\frac{\text {distance between plane and point above island}}{7000}

\text { Distance between plane and point above island }=7000 \times \tan (21)

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6 0
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Look up the answers with mathcam.
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<u>Solution:</u>

Given, Mel has to put the greatest number of bolts and nuts in each box so each box has the same number of bolts and the same number of nuts.  

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