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3 years ago

I need help can u help me please and thanks

Mathematics

1 answer:

son4ous [18]3 years ago

3 0

Answer:

17.74

Step-by-step explanation:

The fraction is easily converted to one with a denominator of 100 (a power of 10):

$\dfrac{37}{50}=\dfrac{37\cdot 2}{50\cdot 2}=\dfrac{74}{100}=0.74$

Then the number of interest is ...

17 37/50 = 17 74/100 = 17.74

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Solve the following equation for x. 7x^2-112=0

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x = 4 or x = -4

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2 years ago

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A tank initially contains 60 gallons of brine, with 30 pounds of salt in solution. Pure water runs into the tank at 3 gallons pe

adoni [48]

Answer:

the amount of time until 23 pounds of salt remain in the tank is 0.088 minutes.

Step-by-step explanation:

The variation of the concentration of salt can be expressed as:

$\frac{dC}{dt}=Ci*Qi-Co*Qo$

being

C1: the concentration of salt in the inflow

Qi: the flow entering the tank

C2: the concentration leaving the tank (the same concentration that is in every part of the tank at that moment)

Qo: the flow going out of the tank.

With no salt in the inflow (C1=0), the equation can be reduced to

$\frac{dC}{dt}=-Co*Qo$

Rearranging the equation, it becomes

$\frac{dC}{C}=-Qo*dt$

Integrating both sides

$\int\frac{dC}{C}=\int-Qo*dt\\ln(\abs{C})+x1=-Qo*t+x2\\ln(\abs{C})=-Qo*t+x\\C=exp^{-Qo*t+x}$

It is known that the concentration at t=0 is 30 pounds in 60 gallons, so C(0) is 0.5 pounds/gallon.

$C(0)=exp^{-Qo*0+x}=0.5\\exp^{x} =0.5\\x=ln(0.5)=-0.693\\$

The final equation for the concentration of salt at any given time is

$C=exp^{-3*t-0.693}$

To answer how long it will be until there are 23 pounds of salt in the tank, we can use the last equation:

$C=exp^{-3*t-0.693}\\(23/60)=exp^{-3*t-0.693}\\ln(23/60)=-3*t-0.693\\t=-\frac{ln(23/60)+0.693}{3}=-\frac{-0.959+0.693}{3}= -\frac{-0.266}{3}=0.088$

5 0

3 years ago

What is the solution of the system ? <br> 2x+3y=4 <br> x-y=-3

fgiga [73]

Change the equation, x - y = -3, to isolate x or y and plug that new equation into the equation 2x + 3y = 4

I changed it to: x = y - 3
so
2(y - 3) + 3y = 4
2y - 6 + 3y = 4
5y - 6 = 4
5y = 4 + 6
5y = 10
y = 10/5
y = 2

then you plug that 2 into the equation x = y - 3 to get the value of x

x = (2) - 3
x = -1

you can check this by plugging the x and y values into the equation 2x + 3y = 4

2(-1) + 3(2) = 4
-2 + 6 = 4
4 = 4

hope this helps :)

6 0

3 years ago