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3 years ago

Answer for brainlist and extra points ☀️

Mathematics

1 answer:

tia_tia [17]3 years ago

8 0

Answer:x+2y-12=0

Step-by-step explanation:

3x+6y=36

-36. -36

3x+6y-36=0

Divide by 3 to get

X+2x-12=0

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A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th

Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let $S(t)$ be the amount of sugar in the tank at time $t$ . Then $S(0)=25$ .

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

$\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}$

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

$\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}$

Separate variables, integrate, and solve for S.

$\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt$

$\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt$

$-100\ln\left|P-\dfrac S{100}\right|=t+C$

$\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t$

$P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}$

$\dfrac S{100}=P-Ce^{-100t}$

$S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}$

Use the initial value to solve for C :

$S(0)=25\implies 25=100P-C\implies C=100P-25$

$\implies S(t)=100P-(100P-25)e^{-100t}$

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

$1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}$

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

$S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}$

5 0

3 years ago

suppose your parents are helping you invest money for the future. they open an account for you in January with an initial deposi

alex41 [277]

X=year
y=$

y=200(1.003)^12x

3.6%->.036/12 (compounded monthly)

=0.003+1

y=200(1.003)^12(1) (1 year)

=$207.31999

BUT

200•12 ($200 deposited every month)

=$2400

2400+207.3199=

$2607.32

6 0

3 years ago

Since 5² =25 and (-5)²=25, what are the values for the square root of 5.

snow_lady [41]

Square root 5 is 2. 34

3 0

3 years ago

Won has a container with the shape below.

blagie [28]

Answer:

B. The shape can be broken into a rectangular prism and a rectangular pyramid.

C. The formula for the volume of this figure is V = B h + one-third B h.

D. The volume of the container is 2,760 centimeters cubed.

Step-by-step explanation:

I did the edge test.

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3 years ago

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What is the slope of the line with equation 4x + 2y = 8?

Papessa [141]

Y=2x+4
Hope this helps :D

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3 years ago

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