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barxatty [35]
3 years ago
13

An 14-meter-tall cylindrical tank with a 2-meter radius holds water and is half full. Find the work (in mega-joules) needed to p

ump all of the water to the top of the tank. (The mass density of water is 1000 kg/m3. Let g = 9.8 m/s2. Round your answer to two decimal places.)
Mathematics
1 answer:
agasfer [191]3 years ago
3 0

Answer:

to two decimal places

= 6.04 mega joules

Step-by-step explanation:

The volume of the half tank

= πr²h

r= 2 m

h= 14/2= 7 m

Volume= 22/7 *2² *7

Volume= 88 m³

work (in mega-joules) needed to pump all of the water to the top of the tank

= Volume*mass density *acceleration*distance

= 88*1000*9.8*7

= 6036800 joules

In mega joules

= 6.036800 mega Joules

to two decimal places

= 6.04 mega joules

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Answer:

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Step-by-step explanation:

We are given the following information in the question:

f(x) = kx^2, 0\leq x \leq 2\\~~~~~~~= 0, \text{ otherwise}

where x is the time elapses between the end of the hour and the end of the lecture.

We have to find the values of k.

Since, f(x) is the pdf, then,

\displaystyle\int^\infty_{-\infty} f(x) = 1\\\\\displaystyle\int^2_{0} f(x) = 1\\\\\displaystyle\int^2_{0} kx^2 = 1\\\\k\bigg[\frac{x^3}{3}\bigg]^2_0 = 1\\\\k\times \frac{8}{3} = 1\\\\k = \frac{3}{8}

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4 0
3 years ago
1. $200 is deposited into an account that earns 6% simple interest
katen-ka-za [31]

Answer:

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Step-by-step explanation:

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3 0
3 years ago
What is the solution of the equation x2 + 8x = 4?
d1i1m1o1n [39]

Answer:

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4 0
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P(x) = x2 – 1 and q(x)=5(x-1), which expression is equivalent to (p – q)(x)?
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3 0
4 years ago
Read 2 more answers
The temperature inside a certain industrial machine at time t seconds after startup, for 0 < t < 10, is given by h(t) = 42
frutty [35]

Answer:

t= \frac{125}{38} s

Step-by-step explanation:

We are given the temperature inside the machine from startup until 10 seconds later, the formula is:

h(t)= 42 \cdot t +1 - 4\cdot t +2  (degrees \, C)

We want to know at what time t the temperature inside the machine will be equal to 128 °C.

So we set:

h(t)=128

42\cdot t+1-4\cdot t+2=128

Now, we rearrange the equation to keep terms with t on the left hand side and terms without t on the right hand side

42\cdot t-4\cdot t=128-1-2

and we simplify:

(42-4)\cdot t= 128-2-1= 125

38 \cdot t = 125

now it's easy to solve for t:

t=\frac{125}{38}

And thus we arrive to the solution.

5 0
3 years ago
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