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2 years ago

I need help with this one

Mathematics

1 answer:

sashaice [31]2 years ago

5 0

Answer:

The height is 15 m.

Step-by-step explanation:

V = (pi)r^2h

375(pi) = (pi)(5^2)h

Divide both sides by 25pi.

15 = h

Answer: The height is 15 m.

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Write the equation for the following relation. Include all of your work in your final answer. \[R=\left\{(x,y):(4,5),\ (8,7),\ (

Alik [6]

Answer:12.9

Step-by-step explanation:

7 0

2 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

2 years ago

The length of one leg of a right triangle is 3 feet more than the other leg. If the hypotenuse is 15 feet, find the length of ea

jeyben [28]

Answer:

9 and 12

Step-by-step explanation:

Pythagorean Theorem. One of the most common Pythagorean triples is 3, 4, 5 with 3 and 4 the legs and 5 the hypoenuse. That will make 9, 12, 15 anotther trible because you are tripling the side lengths. 12-9=3 so this triangle works.

8 0

2 years ago

Isolate the h in c=25h+350

Sati [7]

Subtract 350 from both sides then divide both sides by 25.

(c-350)/25 = h

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2 years ago

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soldier1979 [14.2K]

Answer:

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Step-by-step explanation:

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3 years ago

I need help with this one ​

I need help with this one