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2 years ago

Please help i need it for tomorrow With explanation please

Mathematics

2 answers:

Gemiola [76]2 years ago

5 0

Answer:

pangalang ng pair angles figure

bazaltina [42]2 years ago

5 0

Answer:

I don't know answers sorry

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A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so

Debora [2.8K]

Let $A(t)$ = amount of salt (in pounds) in the tank at time $t$ (in minutes). Then $A(0) = 11$ .

Salt flows in at a rate

$\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}$

and flows out at a rate

$\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}$

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

$\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}$

which I'll solve with the integrating factor method.

$\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95$

$-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}$

$\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}$

Integrate both sides. By the fundamental theorem of calculus,

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}$

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)$

$\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}$

$\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}$

$\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}$

After 1 hour = 60 minutes, the tank will contain

$A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131$

pounds of salt.

7 0

1 year ago

Please help me on this ratio question I'm stuck

Pavlova-9 [17]

24/6=4
(6x4)+(2x4)+(3x4)=
24+8+12=44=answer!

5 0

3 years ago

5x-(x+1)=5-2x i dont understand what to do. Plz help

Vlada [557]

Answer:

x=1

Step-by-step explanation:

5x-(x+1)=5-2x

distribute

5x-x-1 = 5-2x

4x-1 = 5-2x

add 2x on each side

4x-1+2x = 5-2x+2x

6x -1 = 5

add 1 on each side

6x-1+2 = 5+1

6x = 6

divide by 6

6x/6 = 6/6

x = 1

6 0

2 years ago

What is the measure of ∠C in the figure below

sertanlavr [38]

Answer:

C. 56°

Step-by-step explanation:

An isosceles triangle has two sides that are equal. ∆ABC has two equal sides. Thus, the angles opposite the two sides of an isosceles triangle are also congruent to each other.

<C and <A are congruent to each other.

m<A = 56°, therefore,

m<C = 56°

4 0

2 years ago

-2(3x+5y)=10 in slope intercept form

lesantik [10]

Answer:

The equation in the slope-intercept form is:

y = -3/5x - 1

Step-by-step explanation:

Given the equation

$-2(3x+5y)=10$

We know that the slope-intercept form of a line equation is

$y = mx+b$

where

m is the slope

b is the y-intercept

Writing the equation in slope-intercept form

-2(3x+5y)=10

-6x -10y = 10

Add 6x to both sides

-6x -10y + 6x = 10 + 6x

-10y = 10 + 6x

Divide both sides by -10

-10y / -10 = (10 + 6x) / -10

y = -3/5x - 1

Thus, the equation in the slope-intercept form is:

y = -3/5x - 1

4 0

2 years ago