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3 years ago

What is the area of the parallelogram ?

Mathematics

2 answers:

Mazyrski [523]3 years ago

8 0

Answer:

40m2

Step-by-step explanation:

a = base by height

= 10 by 4

UNO [17]3 years ago

5 0

Answer:

Area =40m2

Step-by-step explanation:

A=bh

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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

Which integers are between 16/3 and -9/2

Lunna [17]

Convert both to mixed numbers:

16/3 = 5 1/3

-9/2 = -4 1/2

Which integers are between -4 1/2 and 5 1/3?

The solution set is -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

I hope I helped you with your solution! If you could give me brainliest, I would be very thankful!

5 0

4 years ago

A-b

Lynna [10]

Answer:

$\boxed{\sf d. \ \frac{a}{b} = \frac{10}{7}}$

Step-by-step explanation:

$\sf \implies \dfrac{a - b}{b} = \dfrac{3}{7} \\ \\ \sf \implies \frac{a}{b} - \frac{b}{b} = \frac{3}{7} \\ \\ \sf \implies \frac{a}{b} - 1 = \frac{3}{7} \\ \\ \sf \implies \frac{a}{b} - 1 + 1 = \frac{3}{7} + 1 \\ \\ \sf \implies \frac{a}{b} = \frac{3}{7} + 1 \\ \\ \sf \implies \frac{a}{b} = \frac{3}{7} + \frac{7}{7} \\ \\ \sf \implies \frac{a}{b} = \frac{3 + 7}{7} \\ \\ \sf \implies \frac{a}{b} = \frac{10}{7}$