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lesya [120]
3 years ago
5

A conical tank is leaking water at the rate of 75 cubic inc/min. At the same time water is being pumped into the tank at a const

ant rate.The tanks height is 60 in whiles its top diameter is 20 inches.If the water level is rising at a rate of 5in/min when the height of the water is 10 inches high,find the rate in which water is being pumped into the tank to the nearest cubic inhes/min.The volume of a cone is given by( v= 1/3pi*r^2*h)
Mathematics
1 answer:
lubasha [3.4K]3 years ago
3 0
Since r = h/6 ; r' = h'/6; = 5/6

<span><span>V′</span>=<span><span>10(2)(5)(5) / </span><span>3(3)(6)</span></span>pi+ <span><span>5⋅<span>5^2 / </span></span><span>3⋅<span>3^2</span></span></span> pi</span> <span><span>V′</span>=<span>250 / 27</span>pi+<span>125 / 27</span>pi</span> <span><span>V′</span>=<span>375 / 27</span>pi;<span> at the given moment specified
</span></span>
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Consider the function f(x) = 3x and the function g, which is shown below.
VLD [36.1K]

Answer:

<em>B. The graph of g is the graph of f shifted 2 units down</em>

Step-by-step explanation:

<u>Graph of Functions</u>

We have two functions:

f(x)=3^x

g(x)=3^x-2

Since g(x)=f(x)-2 it will be represented as an identical graph as that for f(x), but vertically displaced 2 units down. Let's check it by plugging some points

f(0)=3^0=1

g(0)=3^0-2=-1

f(1)=3^1=3

g(1)=3^1-2=1

f(3)=3^3=27

g(3)=3^3-2=25

We can notice the values of g(x) are always 2 units below f(x), thus the correct answer is

B. The graph of g is the graph of f shifted 2 units down

7 0
4 years ago
A bowl is the shape of a hemisphere and made out of thick clay. The diameter of the outside bowl is 44.6 cm. And the diameter of
aleksandr82 [10.1K]

Answer:

Step-by-step explanation:

Ive already explained this somebody else asked if you find it you will have the answer

3 0
3 years ago
A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained p
Alekssandra [29.7K]

Using the z-distribution and the formula for the margin of error, it is found that:

a) A sample size of 54 is needed.

b) A sample size of 752 is needed.

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of \alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which z is the z-score that has a p-value of \frac{1+\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

90% confidence level, hence\alpha = 0.9, z is the value of Z that has a p-value of \frac{1+0.9}{2} = 0.95, so z = 1.645.

Item a:

The estimate is \pi = 0.213 - 0.195 = 0.018.

The sample size is <u>n for which M = 0.03</u>, hence:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}

0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}

\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}

(\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2

n = 53.1

Rounding up, a sample size of 54 is needed.

Item b:

No prior estimate, hence \pi = 0.05

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}

0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}

\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}

(\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2

n = 751.7

Rounding up, a sample of 752 should be taken.

A similar problem is given at brainly.com/question/25694087

5 0
3 years ago
Is this figure an example of a line
ivann1987 [24]

Answer:

No , It has two endpoints.

Explanation: A line segment has two end points with a definite length.

A straight line has neither starting nor end point and is of infinite length.

5 0
3 years ago
Read 2 more answers
Find the LCM and solve, it's very very urgent. ​
xeze [42]

Answers:

<h3>1. 1050</h3><h3>2. 1200</h3><h3>3. 1200</h3><h3>4. 3360</h3><h3>5. 1080</h3><h3>6. 480</h3>

please see the attached picture for full solution..

Hope it helps....

Good luck on your assignment...

7 0
3 years ago
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