Which of the following inequalities is represented by the following graph?

Pumping stations deliver oil at the rate modeled by the function D, given by d of t equals the quotient of 5 times t and the qua

goblinko [34]

<h2>Hello!</h2>

The answer is: There is a total of 5.797 gallons pumped during the given period.

To solve this equation, we need to integrate the function at the given period (from t=0 to t=4)

The given function is:

$D(t)=\frac{5t}{1+3t}$

So, the integral will be:

$\int\limits^4_0 {\frac{5t}{1+3t}} \ dx$

So, integrating we have:

$\int\limits^4_0 {\frac{5t}{1+3t}} \ dt=5\int\limits^4_0 {\frac{t}{1+3t}} \ dx$

Performing a change of variable, we have:

$1+t=u\\du=1+3t=3dt\\x=\frac{u-1}{3}$

Then, substituting, we have:

$\frac{5}{3}*\frac{1}{3}\int\limits^4_0 {\frac{u-1}{u}} \ du=\frac{5}{9} \int\limits^4_0 {\frac{u-1}{u}} \ du\\\\\frac{5}{9} \int\limits^4_0 {\frac{u-1}{u}} \ du=\frac{5}{9} \int\limits^4_0 {\frac{u}{u} -\frac{1}{u } \ du$

$\frac{5}{9} \int\limits^4_0 {(\frac{u}{u} -\frac{1}{u } )\ du=\frac{5}{9} \int\limits^4_0 {(1 -\frac{1}{u } )$

$\frac{5}{9} \int\limits^4_0 {(1 -\frac{1}{u })\ du=\frac{5}{9} \int\limits^4_0 {(1 )\ du- \frac{5}{9} \int\limits^4_0 {(\frac{1}{u })\ du$

$\frac{5}{9} \int\limits^4_0 {(1 )\ du- \frac{5}{9} \int\limits^4_0 {(\frac{1}{u })\ du=\frac{5}{9} (u-lnu)/[0,4]$

Reverting the change of variable, we have:

$\frac{5}{9} (u-lnu)/[0,4]=\frac{5}{9}((1+3t)-ln(1+3t))/[0,4]$

Then, evaluating we have:

$\frac{5}{9}((1+3t)-ln(1+3t))[0,4]=(\frac{5}{9}((1+3(4)-ln(1+3(4)))-(\frac{5}{9}((1+3(0)-ln(1+3(0)))=\frac{5}{9}(10.435)-\frac{5}{9}(1)=5.797$

So, there is a total of 5.797 gallons pumped during the given period.

Have a nice day!

4 0

4 years ago

Zoe's pizza cost $12.99. She gave a tip of $2.00. What percent did Zoe leave as a tip?

krok68 [10]

She left a 15 percent tip.

6 0

3 years ago

Read 2 more answers

Selim is ordering concrete spheres to place as barriers in the city park. The spheres cost $2 per square foot, and Selim can spe

vlada-n [284]

Answer:

1.78 feet.

Step-by-step explanation:

If they cost $20 each and its $2 per square foot, the area of the spheres

is 20 / 2 = 10 ft^2.

Area of sphere = 4 π r^2 = 10 (where r = the radius)

---> r^2 = 10 / 4π

= 0.796

---> r = 0.892 ft

So the diameter = 2 * r

= 1.78 feet to nearest hundredth.

4 0

2 years ago

Find the x-intercept of the following equation. Simplify your answer.

TiliK225 [7]

The X- intercept is (2,0) if you’re looking for one number then it would just be 2

4 0

3 years ago

You have a 12 inch by 14 inch picture that you frame. When you hung the picture, you found that the entire area is 261.44 in. Wh

erastova [34]

Answer: c) 3.2 inches

<u>Step-by-step explanation:</u>

Let x represent the width of the frame

Then the area of the frame is:

(x + 12)(x + 14) = 261.44

Rewrite it in Standard form of a quadratic equation:

x² + 26x + 168 = 261.44

x² + 26x - 93.44 = 0

Use Quadratic Formula to solve for x:

$x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-26+\sqrt{26^2-4(1)(-93.44)}}{2(1)}\\\\\\x=\dfrac{-26+\sqrt{1049.76}}{2}\\\\\\x=\dfrac{-26+32.4}{2}\\\\\\x=\dfrac{6.4}{2}\\\\\\x=\large\boxed{3.2}$

4 0

3 years ago