Mathematics: The average of two numbers is 20. if one of the numbers is doubled and the other is trebled the average increase to 52

The average of two numbers is 20. if one of the

krystinayagel013

09.01.2022

Let x and y be the two numbers. Their average is

$\dfrac{x+y}{2}=20 \iff x+y=40$

If we multiply x and y be 2 and 3, respectively, the average becomes

$\dfrac{2x+3y}{2}=52 \iff 2x+3y=104$

We can use the two equations to make a linear system:

$\begin{cases}x+y=40\\2x+3y=104\end{cases}$

From the first equation we can derive

x=40-y

Plug this value in the second equation and we have

$2(40-y)+3y=104 \iff 80-2y+3y=104 \iff y=24$

Now recall the relation between x and y to conclude

x=40-y=40-24=16

So, the two numbers are 16 and 24

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sameh0425

03.05.2023

The required value of c is -192.

Step-by-step explanation:

We are given the differential equation:

$xy'+2y=4x^2 \\(x0)$

The solution to the given differential equation is:

$y=x^2+\dfrac{c}{x^2}$

Initial condition:

y(4) = 4

Putting the values, in the solution, we get,

$4=(4)^2+\dfrac{c}{(4)^2}\\\\4 = 16+\dfrac{c}{(4)^2}\\\\\Rightarrow \dfrac{c}{(4)^2}=-12\\\Rightarrow c =-12(16)\\\Rightarrow c =-192$

Thus, the required value of c is -192.

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