The Product of 4 and z is the same as 16

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

3 years ago

Help help math math math

Anarel [89]

Answer:

i think this is right i hope it helped :)

Step-by-step explanation:

5m - 8 = 2m + 1

5m + 2m - 8 = 1

7m - 8 = 1

7m = 7

m = 1

6 0

2 years ago

Read 2 more answers

Which decimal is less than 0.8 and greater than 0.02

nikklg [1K]

Answer:

0.02<x<0.80

0.4

Step-by-step explanation:

0.02 is equal to 2/100 and 0.8 is equal to 80/100

so you could really choose any number between 0.03 and 0.79

4 0

4 years ago

Read 2 more answers

I have a question!!! HELP!!!

marta [7]

Answer:

Susie made the error when she subtracted 2.

3 0

3 years ago

Read 2 more answers

Luis has a bag that contains strawberry chews, apple chews, and peach chews. He performs an experiment. Luis randomly removes a

Blizzard [7]

The probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is (29/37).

<h3>What is Probability?</h3>

The probability helps us to know the chances of an event occurring.

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

The number of times the experiment was done is 37 (15+14+8). The number of times apple chew came as a result of the experiment is 14, while the number of times peach chew came as a result of the experiment is 15. Therefore, the probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is

$\rm Probability = \dfrac{\text{Number of times apple chew or peach chew was selected}}{\text{Total number of times experiment was performed}}\\\\\\Probability = \dfrac{14+15}{37} = \dfrac{29}{37}$

Hence, the probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is (29/37).

Learn more about Probability:

brainly.com/question/795909

#SPJ1

7 0

2 years ago