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slega [8]
3 years ago
7

You stand 50 feet from a monument. The angle of depression from the top of the monument to your feet is 64 degrees. Approximatel

y how tall is the monument
Mathematics
1 answer:
Murrr4er [49]3 years ago
7 0

Answer:

The monument is approximately 86.6 feet tall

Step-by-step explanation:

The given monument parameters are;

The distance of the person from the monument = 50 feet

The angle of depression from the top of the monument to the person's feet = 64°

Given that the angle of elevation to the top of the monument from the person's feet = The angle of depression from the top of the monument to the person's feet, we have;

tan(Angle of depression) = tan(Angle of elevation) = (The height of the monument)/(The distance from the monument)

∴ The height of the monument = tan(Angle of depression) × The distance from the monument

Substituting the known values, gives;

The height of the monument = tan(60°) × 50 ≈ 86.6

The height of the monument ≈ 86.6 feet.

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Step-by-step explanation:

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a survey amony freshman at a certain university revealed that the number of hours spent studying the week before final exams was
Marat540 [252]

Answer:

Probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.

Step-by-step explanation:

We are given that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15.

A sample of 36 students was selected.

<em>Let </em>\bar X<em> = sample average time spent studying</em>

The z-score probability distribution for sample mean is given by;

          Z = \frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = population mean hours spent studying = 25 hours

            \sigma = standard deviation = 15 hours

            n = sample of students = 36

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the average time spent studying for the sample was between 29 and 30 hours studying is given by = P(29 hours < \bar X < 30 hours)

    P(29 hours < \bar X < 30 hours) = P(\bar X < 30 hours) - P(\bar X \leq 29 hours)

      

    P(\bar X < 30 hours) = P( \frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} } < \frac{ 30-25}{\frac{15}{\sqrt{36} } }} } ) = P(Z < 2) = 0.97725

    P(\bar X \leq 29 hours) = P( \frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} } \leq \frac{ 29-25}{\frac{15}{\sqrt{36} } }} } ) = P(Z \leq 1.60) = 0.94520

                                                                    

<em>So, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 and x = 1.60 in the z table which has an area of 0.97725 and 0.94520 respectively.</em>

Therefore, P(29 hours < \bar X < 30 hours) = 0.97725 - 0.94520 = 0.0321

Hence, the probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.

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Step-by-step explanation:

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3 years ago
<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \
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Answer:

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Step-by-step explanation:

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We can use Part I of the Fundamental Theorem of Calculus:

  • \displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

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We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

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We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

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We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

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Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

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For the first term, replace \text{t} with 2x, and apply the chain rule to the function. Do the same for the second term; replace

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Simplify the expression by distributing 2 and 2x inside their respective parentheses.

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Rearrange the terms to be in order from the highest degree to the lowest degree.

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This is the derivative of the given integral, and thus the solution to the problem.

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3 years ago
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