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3 years ago

Will give brainliest if it's correct!!

Mathematics

2 answers:

a_sh-v [17]3 years ago

6 0

The answer is b i think

kap26 [50]3 years ago

3 0

C. 2y=5
standard form is Ax+By=C

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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

There are 20 packages of beef in a restaurant freezer. The average weight of 14 of the packages is 2 lb. The remaining packages

Shtirlitz [24]

I belive that the answer is about 180 lb.

3 0

3 years ago

Read 2 more answers

What is 3/8 inch converted to a decimal.

USPshnik [31]

0.375 is 3/8 converted into a decimal, to get that you just divide 8 by 3.

7 0

3 years ago

Read 2 more answers

8 cm<br> 20 cm<br> 0 80<br> O 160<br> 0 28<br> O 40

Bond [772]

8x20=160
So your answer would be 160

6 0

3 years ago

James bought 5 1/6pounds of grapes for $7.75. At theunit rate, how much would 3.4 pounds of grapes cost?

frutty [35]

Answer:

Explanation:

5 1/6 pounds of graphs are bought for $7.75, meaning 1 pound costs

$\frac{7.75\text{ dollars}}{5\frac{1}{6}lb}$

And we need to compute the division above.

The first step is to convert the mixed number 5 1/6 into an improper fraction.

Now, it is true that

$5\frac{1}{6}=5+\frac{1}{6}$

multiplying 5 by 6/6 gives

$5\cdot\frac{6}{6}+\frac{1}{6}$ $\frac{30}{6}+\frac{1}{6}$

7 0

1 year ago