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Dmitrij [34]
2 years ago
14

What is the volume of the following rectangular prism? 3 1/3 units^2 1 2/5 units

Mathematics
2 answers:
nlexa [21]2 years ago
6 0
The Answer : 23.6 units
MArishka [77]2 years ago
3 0

Answer:

23.6

Step-by-step explanation:

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3(2x+1)=7-2(x+5)<br> Can you please show me how to solve this step by step please
Talja [164]
3(2x+1) = 7-2(x+5)
    6x+3 = 7-2x-10
         -3             -3
         6x = 7-2x-10-3
       +2x     +2x
         8x = -6
        ----    -----
          8        8
           x = -3/4 

8 0
3 years ago
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.

<h2>Why?</h2>

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
What is 0.0162 as a fraction
CaHeK987 [17]
You have to ask yourself how would you read that decimal?  It is 162 ten-thousandths because the last digit, which is 2 is in the ten-thousandths place. So the fraction would be 162/10000
5 0
3 years ago
Which function is represented by the graph?
Virty [35]
The correct answer is C.
7 0
3 years ago
Items 17-18: Use the diagram to the right. I just need 17-18 please and thank you!!!
mixer [17]

Answer:

17. (B)

18. both opposite sides are equal in length and height.

Step-by-step explanation:

5 0
2 years ago
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