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3 years ago

Model the pair of situations

Mathematics

1 answer:

Nookie1986 [14]3 years ago

5 0

Answer:

Step-by-step explanation:

Chungus

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Any help with this greatly appreciated.

Anestetic [448]

Put the equation in standard linear form.

$x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}$

Find the integrating factor.

$\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5$

Multiply both sides by $\mu$ .

$(t+5) x'(t) + x(t) = 5(t+5)e^{5t}$

Now the left side the derivative of a product,

$\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}$

Integrate both sides.

$(t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt$

On the right side, integrate by parts.

$(t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C$

Solve for $x(t)$ .

$\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}$

3 0

2 years ago

Eleven less than three times a number

Zina [86]

If you are looking for how to turn that worded problem into an equation...
Heres the answer you're looking for

3x-11

5 0

3 years ago

Answer this question for brainliest and 20 points

Naddik [55]

Answer:

Least to greatest: 2, 3, 1

Step-by-step explanation:

Square root of 8 over 2 is about 1.41 which makes it the least value

2 is obviously equal to 2 which puts it in the middle

Square root of 7 is about 2.64 which makes it the greatest value

3 0

2 years ago

What is the remainder of (3-6×2-9xl+3)?

Naddik [55]

9lx−6x^2+6
It not 91 it the letter L just lower case

3 0

3 years ago

The length of a swimming pool is 10 ft shorter than twice the width. the length is 35 ft. what is the width

Hatshy [7]

Okay so we need to figure out the width of the swimming pool using the length, and we know the width is 10 ft shorter than twice the width. I believe the easiest way to do this would be to first do 35-10, and then divide it in half. That gives us 12.5. To check our work I'll do the problem 12.5+12.5+10=35.

The width of the swimming pool is 12.5 ft.

8 0

2 years ago