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jenyasd209 [6]
3 years ago
5

What is the volume of this rectangular prism 7/5 CM by 5 cm and 7/2 cm

Mathematics
1 answer:
Step2247 [10]3 years ago
7 0

Answer:

V=\frac{49}{2}\ cm^3

or

V=24.5\ cm^3

Step-by-step explanation:

we know that

The volume of the rectangular prism is

V=LWH

where

L is the length

W is the width

H is the height

substitute the given values in the formula

V=(\frac{7}{5})(5)(\frac{7}{2})

V=\frac{245}{10}\ cm^3

Simplify

V=\frac{49}{2}\ cm^3 ---> fraction form

or

V=24.5\ cm^3 ----> decimal form

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Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains liters of a dye solution with a
Alja [10]

Answer:

t = 460.52 min

Step-by-step explanation:

Here is the complete question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution

Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.

inflow = 0 (since the incoming water contains no dye)

outflow = concentration × rate of water inflow

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So, Q' = inflow - outflow = 0 - Q/100

Q' = -Q/100 This is our differential equation. We solve it as follows

Q'/Q = -1/100

∫Q'/Q = ∫-1/100

㏑Q  = -t/100 + c

Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c}  = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}

when t = 0, Q = 200 L × 1 g/L = 200 g

Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}

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2 = 200e^{(-t/100)}\\\frac{2}{200} =  e^{(-t/100)}

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

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