9.07x 6.5 show work

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

Please help! I don’t know what I did wrong. Thank you!

egoroff_w [7]

Answer:

C

Step-by-step explanation:

They are both acute angles so the measurement cannot be above 90 degrees (right angle).

m<ADC is clearly smaller than m<AEC therefore m<AEC must be bigger than 28 degrees. C is the only option that fits

5 0

3 years ago

Shawna needs a new bed pillow. One store

Jobisdone [24]

Answer:

$9.5

Step-by-step explanation:

All you have to do is divide 19 by 2 to get the cost of one pillow. I hope this helps :)

8 0

3 years ago

Read 2 more answers

Can u plz help me !!!

kakasveta [241]

From what I see, I believe the answer is [A] about 65 degrees

[B] would be too low

[C] would be close but no right

[D] would just be flat out straight

:)

5 0

3 years ago

Read 2 more answers

What value represents the vertical translation from the graph of the<br> (x+5)2+3?<br> 0 -5<br> O-3

neonofarm [45]

Answer:

The value 3 represents the vertical translation upwards of $f(x)$ to $g(x)$

Step-by-step explanation:

The question is incomplete or missing data.

The correct question

What value represents the vertical translation from the graph of the parent function $f(x) = x^2$ to the graph of the function

$g(x) = (x + 5)^2 + 3$ ?

Given functions:

Parent function

$f(x) = x^2$

Translated function

$g(x) = (x + 5)^2 + 3$

Translation rules

For horizontal shift

$f(x)\rightarrow f(x+c)$

If $c>0$ the function shifts $c$ units to the left.

If $c$ the function shifts $c$ units to the right.

For vertical shift

$f(x)\rightarrow f(x)+c$

If $c>0$ the function shifts $c$ units to the up.

If $c$ the function shifts $c$ units to the down.

From the functions given the translation rule can be given as:

$f(x)\rightarrow f(x+5)+3$

$g(x)=f(x+5)+3$

This shows the graph is shifted left by 5 units and upwards by 3 units.

Thus the value 3 represents the vertical translation of $f(x)$ to $g(x)$

5 0

4 years ago