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2 years ago

Simplify the ratio 15/18

1 answer:

4 0

Very easy. 15 and 18 are the factors of 3 so divide the numerator and denominator by 18. So you will get 5/6 that is it.

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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

Concentration = Quantity/volume = Q/200

outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.

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

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

We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2

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

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

6 0

3 years ago

Quincy has saved $2500 so far to buy a new car in 4 years. He can put this amount into an account, that

devlian [24]

Answer:

he should chose compounded annually because he would have and extra 32.12 dollars at the end of the 4 years

Step-by-step explanation:

hope this helps

5 0

2 years ago

The function f(x) = -6x. The graph of g(x) is f(x)vertically stretched by a factor of 7 and reflected in the x-axis. What is the

Vera_Pavlovna [14]

we are given a function

$f(x)=-6x$

First translation:

The graph of function is vertically stretched by a factor of 7

Whenever we vertically stretch any function by 'a' units

so, we can write it as

$g(x)=a\times f(x)$

Here, it is vertically stretch by 7

so, we get

$g(x)=7\times -6x$

$g(x)=-42x$

Second translation:

Whenever we reflect any function about x-axis

we multiply y-value by -1

so, we can write it as

$g(x)=-f(x)$

Here , it is reflected in the x-axis

so, we can multiply by -1 to y-value

we get

$g(x)=-1\times -42x$

$g(x)=42x$ .............Answer

3 0

3 years ago

Read 2 more answers

If (2 − 3i) + (x + yi) = 6, what is x + yi?

Soloha48 [4]

(2 − 3i) + (x + yi) = 6

We add the left hand side

(2+x) + (-3+y)i = 6

6 can be written in a+ib

6 can be written as 6 + 0i

(2+x) + (-3+y)i = 6 +0i

Now we frame 2 equations

2 + x= 6

-3 + y =0

Solve the first equation

2 + x = 6

Subtract 2 from both sides

x = 4

solve the second equation

-3 + y =0

Add 3 on both sides

y= 3

So x+yi is 4+3i

7 0

2 years ago

Read 2 more answers

What are the first five multiples of 7

sukhopar [10]

Answer:

7, 14, 21, 28, 35

Step-by-step explanation:

brainliest is appreciated

6 0

2 years ago

Read 2 more answers