What is the value of x?

Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the wat

nirvana33 [79]

Answer:

$V = \pi r^2 h$

For this case we know that $r=5m$ represent the radius, $h = 10m$ the height and the rate given is:

$\frac{dV}{dt}= \frac{100 L}{min}$

$Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}$

And replacing we got:

$\frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}$

And that represent $0.127 \frac{cm}{min}$

Step-by-step explanation:

For a tank similar to a cylinder the volume is given by:

$V = \pi r^2 h$

For this case we know that $r=5m$ represent the radius, $h = 10m$ the height and the rate given is:

$\frac{dV}{dt}= \frac{100 L}{min}$

For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:

$\frac{dV}{dt}= \pi r^2 \frac{dh}{dt}$

And solving for $\frac{dh}{dt}$ we got:

$\frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}$

We need to convert the rate given into m^3/min and we got:

$Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}$

And replacing we got:

$\frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}$

And that represent $0.127 \frac{cm}{min}$

5 0

3 years ago

NAND"" and ""NOR"" circuits are commonly used as a basis for flash memory chips. A NAND B is defined to be the negation of ""A a

Anit [1.1K]

Answer:

(i) A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

Since A ∧ B (the symbol ∧ means A and B) is true only when both A and B are true, its negation A NAND B is true as long as one of A or B is false.

Since A ∨ B (the symbol ∨ means A or B) is true when one of A or B is true, its negation A NOR B is only true when both A and B are false.

Below are the truth tables for NAND and NOR connectives.

(ii) To show that (A NAND B)∨(A NOR B) is equivalent to (A NAND B) we build the truth table.

Since the last column (A NAND B)∨(A NOR B) is equal to (A NAND B) it follows that the statements are equivalent.

(iii) To show that (A NAND B)∧(A NOR B) is equivalent to (A NOR B) we build the truth table.

Since the last column (A NAND B)∧(A NOR B) is equal to (A NOR B) it follows that the statements are equivalent.

6 0

3 years ago

Here's a linear equation. rewrite it in slope-intercept form -2-3y+15=0

irakobra [83]

-3y-2+15=0 would be the answer

3 0

3 years ago

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What is the sum of the first five terms of the geometric series 2 − 8 + 32 −

MrMuchimi

Answer:

∑ (n = 1 to 5) (2·(-4)^(n - 1))

S5 = 2·((-4)^5 - 1)/((-4) - 1) = 410

5 0

3 years ago

One faucet fills up a bathtub in 15 minutes while the second fills it up in 10 minutes. If both faucets are turned on, what frac

yaroslaw [1]

Faucet one fills up $\frac{1}{15}$ of the bathtub in one minute and faucet two fills up $\frac{1}{10}$ of the bathtub in one minute. If both are one then they will fill up $\frac{1}{15}+ \frac{1}{10} = \frac{5}{30} = \frac{1}{6}$ So, 1/6 of the bathtub in one minute.

8 0

3 years ago

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