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emmainna [20.7K]

3 years ago

13

A rectangular box has a square base. The combined length of a side of the square base, and the height is 20 inches. Let X be the

length of a side of the base of the box

1 answer:

Brrunno [24]3 years ago

7 0

Answer:

V = (l)(w)(h)

V = (x)(x)(20-x)

V = x²(20-x)

V = -x³ + 20x²

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I need help. Only do number 34.

Svetach [21]

Answer:

Amplitude: 3

Period: 2π

Step-by-step explanation:

5 0

2 years ago

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

Evaluate the expression:<br><br> for y = 2 + 3x when x=4. What does y=?

lora16 [44]

Answer:

y = 14

Step-by-step explanation:

Plug in 4 as x into the equation:

y = 2 + 3x

y = 2 + 3(4)

Simplify:

y = 2 + 12

y = 14

So, when x = 4, y = 14.

4 0

2 years ago

The length of a rectangular deck is 4 times it’s width. If the deck’s perimeter is 30ft, what is the deck’s area?

ioda

Try this solution (note, this is not the shortest way):

1. if the given length is 'l' and the width is 'w', then according to the condition 4*l=w;

2. according to the condition the perimeter is 30 ft. Formula of the perimeter is P=2(l+w), then 2(l+w)=30;

3. if to substitute '4*l' instead of 'w', the formula of the perimeter (from item no. 2) will be as 2(4*l+l)=30 or 10*l=30 ⇒ l=3 ft. The length is 3 ft.!

4. if l=3 ft., then w=4*3=12 ft. The width is 12 ft.!

5. Area is

A=w*l; A=12*3=<u>36 ft²</u>

7 0

3 years ago

Can someone answer and do the working out please!

trasher [3.6K]

Answer:

y=−4

Step-by-step explanation:

Let's solve your equation step-by-step.

7y−4=−32

Step 1: Add 4 to both sides.

7y−4+4 =−32+4

7y =−28

Step 2: Divide both sides by 7.

7y/7 = −28/7

y=−4

(/:divide) Hope it helps!!

4 0

3 years ago