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Leona [35]
3 years ago
9

A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the

dish and are reflected to a single​ point, where the receiver is located. If the dish is 14 feet across at its opening and 2 feet deep at its​ center, at what position should the receiver be​ placed?

Mathematics
1 answer:
allochka39001 [22]3 years ago
5 0

Answer:

The receiver must be placed at a distance of 6.125 ft from the center.

Step-by-step explanation:

The dish is of parabola shape with the length of 14 feet and 2 feet deep from the center.

A parabola is a curve which is a set of all points in the plane which are at equal distance away from a given point called focus and given line called directrix.

We have to find out the point at which all the waves comes to one point where the receiver must be placed is the focus of the parabola.

The above scenario is shown in the image which can be converted in mathematical graphical representation of the parabolic curve.

The extreme two end points becomes, (-7,2) and (7,2)

The general equation for such parabola is:

x² = 4ay

where, a is the distance from the center and the focus.

Since, (7,2) satisfy the equation so,

7² = 4a×2

a = 49 /8

Thus,

<u>The receiver must be placed at a distance of 6.125 ft from the center.</u>

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Answer:

Explained

Step-by-step explanation:

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Water oak gains 24 inches in height  every year and  1.5 inch growth in diameter annually, meaning if we divide 1.5 inches by 12 months we gets 0.125 inches growth monthly. So a water oak tree needs only 8 months to grow 1 inch in diameter.

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Step-by-step explanation:

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What is the slope of a line perpendicular to the line passing through (1, -3) and (-4, 7)?
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The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds
Feliz [49]

Answer:

0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 200, \sigma = 50

Find the probability that he weighs between 170 and 220 pounds.

This is the pvalue of Z when X = 220 subtracted by the pvalue of Z when X = 170.

X = 220

Z = \frac{X - \mu}{\sigma}

Z = \frac{220 - 200}{50}

Z = 0.4

Z = 0.4 has a pvalue of 0.6554

X = 170

Z = \frac{X - \mu}{\sigma}

Z = \frac{170 - 200}{50}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

0.6554 - 0.2743 = 0.3811

0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.

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3 years ago
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