6(2x-3)-8=-2
Solve for x! Tyy

Answer:

x(t) = 581.66 lb

Step-by-step explanation:

From the given information:

Consider the salt quantity in the tank at time t be x(t) lb.

∴ the rate of change of salt content in the tank is [tex]\dfrac{dx}{dt}= Rate \ of \ \ inflow - rate \ of \ \ outflow[/tex]

where:

the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons

=21 lb/s

rate of outflow = salt conc. in the tank  × flow rate

= x/250 ×  9

= 9x/250  lb/s

∴

[tex]\dfrac{dx}{dt} = 21 - \dfrac{9x}{250}[/tex]

[tex]\dfrac{dx}{dt} + \dfrac{9x}{250}= 21[/tex]

This is a 1st order linear differentiation,

The integrating factor if [tex]e^{^{ \int \dfrac{9}{250}\ dt}} = e^{^{ \dfrac{9t}{250} }}[/tex]

∴

[tex]e^{^{ \dfrac{9t }{250}}} \ \ x(t) = \int 21 e^{\dfrac{9t}{250}} \ dt + C[/tex]

[tex]e^{^{ \dfrac{9t }{250}}} \ \ x(t) = 21 \times \dfrac{250}{9}e^{\dfrac{9t}{250}} + C[/tex]

[tex]x(t) = \dfrac{1750}{3}+Ce^{^{\dfrac{-9t}{250}}}[/tex]     at  t = (0) and x(0) = 100 lb

Hence;

[tex]100 = \dfrac{1750}{3}+C[/tex]

[tex]C = \dfrac{1750}{3} -100[/tex]

[tex]C = - \dfrac{1450}{3}[/tex]

∴[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9t}{250}}}[/tex]

after time t = 1 minute i.e 60 s

[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9 \times 60}{250}}}[/tex]

[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-540}{250}}}[/tex]

x(t) = 581.66 lb

Answer:

12 + (8k) = 48

k= 9/2

Step-by-step explanation:

Answer:

Ran: 2.5hr

Biked: 1.5hr

Step-by-step explanation:

x = total hrs ran

y = total hrs biked

4 = total hours ran + biked

soo.....

x + y = 4hr

then you can convert that for solving y or x

Ex. x = 4-y or y = 4-x

Then just plug in either x or y

EQUATION: 5x + 13y = 32

Dont plug in both x or y at the same time. Pick one and solve

Answer:

Step-by-step explanation:

Jessica: 5 miles

Taylor: 5/7 = .7143 miles

Answer:

17 inches.

Step-by-step explanation:

Answer:

answer is 17 inches

Step-by-step explanation:

Answer: d s 5\ answer

Step-by-step explanation:

Answer:

r≤5

Step-by-step explanation:

Steps are in the photo. Hope this helps.

Answer:

[tex]x^{20}[/tex]

Step-by-step explanation:

[tex](x^{2} )^{5}[/tex]·[tex](x^{5})^{2}[/tex]

[tex](x^{10} )[/tex] · [tex](x^{10})[/tex]

[tex]x^{20}[/tex]

Answer:

dhsfhb

Step-by-step explanation:

top secret

Answer:

Have a good day, dont see a picture?

Step-by-step explanation:

Answer:

40 percent

Step-by-step explanation:

Use of proportion

50 (2) = 100%

20 (2) = 40%

      do the same thing; what you do on the bottom you do on the top too

Answer:

I believe it is 40%.

Step-by-step explanation:

Answer:

12 miles

Step-by-step explanation:

60 min in 1 hr and 10 min = 1 mile..... so 6, 10 min intervals..... and so 6 time 2 is 12

Answer:

[tex]g'(x) = \dfrac{5 *(25x^2-1)}{(25x^2+1)}- \dfrac{4 * (16x^2-1)}{(16x^2+1)}[/tex]

Step-by-step explanation:

Given that:

[tex]g(x) = \int^{5x}_{4x} \dfrac{u^2-1}{u^2+1} \ \ du[/tex]

Then: the derivative of the function is as follows:

[tex]g'(x) = \dfrac{(5x)^2-1}{(5x)^2+1} \ \ \dfrac{d}{dx}(5x) -\dfrac{(4x)^2-1}{(4x)^2+1} \ \ \dfrac{d}{dx}(4x)[/tex]

[tex]g'(x) = \dfrac{5 *(25x^2-1)}{(25x^2+1)}- \dfrac{4 * (16x^2-1)}{(16x^2+1)}[/tex]

Area of a rectangle = w*l

w = width

l = length

In our problem,

Area = 105mi^2

l = x

w = x - 8

Let's plug our values into the formula above.

105mi^2 = x(x - 8)

Distribute the x

105mi^2 = x^2 - 8x

Subtract 105mi^2 from both sides.

0 = x^2 - 8x - 105

Let's factor the right side.

0 = (x - 15)(x + 7)

Set both terms equal to 0

x - 15 = 0

Add 15 to both sides.

x = 15

x + 7 = 0

Subtract 7 from both sides.

x = -7

Since the length cant be a negative number, 15 is the correct answer.

Length = x = 15 mi

Width = x - 8 = 15 - 8 = 7 mi

The length of the rectangle is 15 miles while the width is 7 miles.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

The perimeter of rectangle = 2( length + width).

Suppose the length is L while the width is W.

Area of rectangle = length × width.

L x W = 105

W = L - 8

By substitution,

L x (L - 8) = 105

L² - 8L - 105 = 0

L² - 15L + 7L - 105 = 0

L(L - 15) + 7(L - 15) = 0

(L + 7)(L - 15) = 0

L = -7, L = 15

Since length will not be negative thus L = 15 miles.

W = 15 - 8 = 7 miles

Hence "The length of the rectangle is 15 miles while the width is 7 miles."

For more about rectangles,

https://brainly.com/question/15019502

#SPJ2

Answer:

the answer is c for the second one and the first one is A

Answer:

The correct option is;

Reflection over the y-axis

Step-by-step explanation:

An even function is a function that satisfies the following function equation;

f(x) = f(-x)

Therefore, for an even function, we have;

f(x) - f(-x) = 0

Which gives that the values of f(x) of the even function is the same upon reflection about the y-axis whereby the values of x changes from x to -x

Therefore, the symmetry of an even function is about the y-axis

However, an odd function is a function that satisfies the following function equation;

f(-x) = -f(x)

Therefore, reflection across the y-axis will result in an inversion of the odd function such that the odd function is not symmetrical about the y-axis as we have;

f(-x) = -f(x) ≠ f(x) which simplifies to f(x) ≠ f(-x).

Answer:

1)[tex]h = \frac{3V}{\pi {r}^{2} }[/tex]

2)[tex]b = \frac{a}{2} + 2[/tex]

3)[tex]y = \frac{w - 3x}{7} [/tex]

Step-by-step explanation:

1)[tex]V= \frac{1}{3} \pi {r}^{2} h[/tex]

[tex] = > V = \frac{ \pi {r}^{2} h}{3} [/tex]

[tex] = > 3V = \pi {r}^{2} h[/tex]

[tex] = > h = \frac{3V}{\pi {r}^{2} } [/tex]

2)[tex]a=2(b-c)[/tex]

[tex] = > \frac{a}{2} = b - c[/tex]

[tex] = > b = \frac{a}{2} + c[/tex]

3)[tex]w=3x+7y[/tex]

[tex] = > w - 3x = 7y[/tex]

[tex] = > y = \frac{w - 3x}{7} [/tex]

Answer:

(18+2)x($1.35+$3.45)= $96

Could I please have BRAINLIEST.

Answer:

-6/11 =x

Step-by-step explanation:

We can use cross products to solve

(5x+2)/8=x/6

6 ( 5x+2) = 8x

Distribute

30x + 12 = 8x

Subtract 30x from each side

30x -30x +12 = 8x - 30x

12 = -22x

Divide each side by -22

12/-22 = -22x/-22

-6/11 =x

Answer:

The probability of getting a black pen from the bag is 13.5%.

Step-by-step explanation:

To determine the percentage probability that a black pen will be obtained from the bag, the following calculation must be performed:

12 + 20 + 5 = 37

37 = 100%

5 = X

(5 x 100) / 37 = X

500/37 = X

13.5 = X

Thus, it is determined that the totality of pens is 100%, and through a cross multiplication the percentage of the 5 black pens with respect to the total of pens is obtained.

Therefore, the probability of getting a black pen from the bag is 13.5%.

6/31. There are 6 black pens left and the red pen was removed, so the original sample size of 32 is reduced to 31.

Answer:

here's your answer

hope this helped you

please mark as the brainliest (ㆁωㆁ)

Answer: 7/2x + 2

Step-by-step explanation:

Answer:

what is the Question

Step-by-step explanation:

Answer:

Harry is 2, Jim is 6

Step-by-step explanation:

The first statement tells us they are 4 years part. Then you need to find two numbers that are 4 apart and that has one that is half the other, like 4 and 8. Finally, subtract two because this will happen in two years and you need their ages now.

Sorry if this was confusing.

Answer:

The area of Chen's office (if that's what you're looking for) is 120.9 feet

Step-by-step explanation:

All I did was a = lw, the formula for finding the area of something using length and width

a = lw

a = 15.5 × 7.8

a = 120.9

Hope this helped.

Answer:

the answer is A

Step-by-step explanation:

Answer:

Idl but I believe its 2340

Step-by-step explanation:

but I could be wrong

Answer:

D

Step-by-step explanation:

Because 12 is greater than -5 and when you divide a postive and a negative you get a negative number. And negative numbers are less than 0 .

Answer:

east-56 a=+b 2squared

Step-by-step explanation: