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kykrilka [37]
3 years ago
9

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 6 cubic feet per minute. The dia

meter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 2 feet high?
Mathematics
1 answer:
Alla [95]3 years ago
4 0

Answer:

0.2122\text{ ft per min}

Step-by-step explanation:

Let r be the radius ( in feet ) of the cone,

So, the diameter of the cone = 2 × radius = 2r feet,

∵ The diameter of the base of the cone is three times the height,

If h represents the height of the cone,

⇒ 2r = 3 × h,

⇒ r=\frac{3h}{2} feet,

∵ Volume of a cone,

V=\frac{1}{3}\pi R^2 H

Where,

R = radius, H = height,

Thus, the volume of the given cone is,

V=\frac{1}{3}\pi r^2 h

=\frac{1}{3}\pi (\frac{3h}{2})^2 h

=\frac{3}{4}\pi h^3

Differentiating with respect to t ( time )

\frac{dV}{dt}=\frac{9}{4}\pi h^2\frac{dh}{dt}

We have,

\frac{dV}{dt}=6\text{ cubic ft per min},h=2\text{ feet}

6=\frac{9}{4}\pi (2)^2 \frac{dh}{dt}

6=9\pi \frac{dh}{dt}

\implies \frac{dh}{dt}=\frac{6}{9\pi }\approx 0.2122\text{ ft per min}

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Sally gets a cup of coffee and a muffin every day for breakfast from one of the many coffee shops in her neighborhood. She picks
aniked [119]

Answer:

<u>A. Mean of the amount Sally spends on breakfast daily = $ 3.90</u>

<u>Standard deviation of the amount Sally spends on breakfast daily = $ 0.34 (rounding to the next cent)</u>

<u>B. Mean of the amount Sally spends on breakfast weekly = $ 27.30</u>

<u>Standard deviation of the amount Sally spends on breakfast weekly = $ 0.89 (rounding to the next cent)</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Average price of a cup of coffee = $ 1.40

Standard deviation = $0.30

Average price of a muffin = $ 2.50

Standard deviation = $ 0.15

The two prices are independent of each other

2. What is the mean and standard deviation of the amount Sally spends on breakfast daily?

Let's recall that:

1. The mean of the sum of two independent variables is the sum of their means.

2. The variance of the sum of two independent variables is equal to the sum of their variances.

Therefore,

Mean of the amount Sally spends on breakfast daily = Average price of a cup of coffee + Average price of a muffin

Replacing with the values we know:

Mean of the amount Sally spends on breakfast daily = 1.40 + 2.50

Mean of the amount Sally spends on breakfast daily = $ 3.90

Variance of the amount Sally spends on breakfast daily = Variance of the price of a cup of coffee + Variance of the price of a muffin

Replacing with the values we know:

Variance of the amount Sally spends on breakfast daily = 0.30² + 0.15²

Variance of the amount Sally spends on breakfast daily = 0.1125

Standard deviation of the amount Sally spends on breakfast daily = √0.1125

Standard deviation of the amount Sally spends on breakfast daily = $ 0.34 (rounding to the next cent)

3. What is the mean and standard deviation of the amount she spends on breakfast weekly (7 days)?

Mean of the amount Sally spends on breakfast weekly = 7 * Mean of the amount Sally spends on breakfast daily

Mean of the amount Sally spends on breakfast weekly = 7 * 3.90

Mean of the amount Sally spends on breakfast weekly = $ 27.30

Variance of the amount Sally spends on breakfast weekly = 7 * Variance of the amount Sally spends on breakfast daily

Variance of the amount Sally spends on breakfast weekly = 7 * 0.1125

Variance of the amount Sally spends on breakfast weekly = 0.7875

Standard deviation of the amount Sally spends on breakfast weekly = √0.7875

Standard deviation of the amount Sally spends on breakfast weekly = $ 0.89 (rounding to the next cent)

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3 years ago
600 is deposited in an account that pays 7% annual interest,compunded continuosly.what is the balance after 5 years?
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==========================================================

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Something like choice A is a non-answer because the term with the largest exponent 3 is buried in the middle, and not at the left side. The exponents are not in decreasing order. Choice C can be ruled out for similar reasons.

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Answer:

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