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3 years ago

Tell whether (3,5) is a solution of y = 5x – 10.

Mathematics

2 answers:

Ivanshal [37]3 years ago

6 0

Answer:

yes it is

Step-by-step explanation:

plug x and y in

3 * 5 - 10 = 5 <== And this is true

julsineya [31]3 years ago

3 0

Answer:

The answer would be yes.

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A principal of $3500 is invested at 5% interest, compounded annually. How much will the investment be worth after 10 years?

FinnZ [79.3K]

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3 years ago

Read 2 more answers

A 140 gallon tank initially contains 5 lbs salt dissolved in 40 gallons of water. Brine containing 1 lb salt per gallon begins t

laiz [17]

Answer:

96.46

Step-by-step explanation:

Volume of the Gallon =140 gallons

At time t=0, V(0)=40 gallons

$\frac{dV}{dt}=Rate \:In - Rate \:Out \\\frac{dV}{dt}=3\frac{gal}{min} - 1\frac{gal}{min} =2\frac{gal}{min}$

V(t)=2t+k, Where K is a constant.

Since V(0)=40

V(0)=2(0)+k=40

k=40

V(t)=40+2t

The Change in Salt Concentration

$\frac{dC}{dt}=Rate \:In - Rate \:Out \\\frac{dC}{dt}=1\frac{lb}{gallon}*3\frac{gallon}{minute}-1\frac{lb}{gallon}*\frac{C}{40+2t} \frac{gallon}{minute}\\\frac{dC}{dt}=3-\frac{C}{40+2t}$

Rearranging

$\frac{dC}{dt}+\frac{C}{40+2t}=3$

Using Integrating Factor: $e^{\int\frac{1}{40+2t} dt} =e^{ln|40+2t|}=40+2t$

$\frac{dC(40+2t)}{dt}=3(40+2t)$

$\int d[C(40+2t)]=\int(120+6t)dt\\C(40+2t)=120t+3t^2+k_0\\C(t)=\frac{120t+3t^2}{40+2t}+\frac{k_0}{40+2t}$

At t=0, C(0)=0.125, k_0=5

$C(t)=\frac{120t+3t^2}{40+2t}+\frac{5}{40+2t}\\C(t)=\frac{120t+3t^2+5}{40+2t}$

At V(t)=140

V(t)=40+2t=140

t=50

$C(50)=96.46$

Just the tank overflows, C(t)=96.46

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