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Debora [2.8K]
3 years ago
12

Find the average velocity of the function over the given interval.

Mathematics
1 answer:
snow_lady [41]3 years ago
6 0

Answer:

Average velocity of the function over the given interval

              =  log(\frac{7}{4} ) -2

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given function y = 3/x -2 ...(i)

The average velocity of the function over the given interval

             Average velocity  = \frac{1}{b-a} \int\limits^b_a {(\frac{3}{x} -2)} \, dx

                               =    \frac{1}{7-4} \int\limits^7_4 {(\frac{3}{x} -2)} \, dx

now integrating

                           =   \frac{1}{3}( \int\limits^7_4 {(\frac{3}{x} )} \, dx-2\int\limits^7_4 {1} \, dx )

                           = \frac{1}{3} (3 (log x) - 2 x )_{4} ^{7}

                        =   \frac{1}{3}( (3 (log 7) - 14 )-(3 log 4 -8))

by using formulas

                 log a-log b = log(a/b)

  on simplification , we get                  

                 = \frac{1}{3}( (3 (log 7) -3 log 4 ) - \frac{1}{3} (6)

                = log(\frac{7}{4} ) -2

Average velocity of the function over the given interval

              =  log(\frac{7}{4} ) -2

 

 

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$1500 is invested at a rate of 3% compounded monthly. Write a compound interest function to model this situation. Then find the
Marianna [84]

Answer:

<u>Equation</u>:  F=1500(1.0025)^{12t}

<u>The balance after 5 years is:  $1742.43</u>

<u></u>

Step-by-step explanation:

This is a compound growth problem . THe formula is:

F=P(1+\frac{r}{n})^{nt}

Where

F is future amount

P is present amount

r is rate of interest, annually

n is the number of compounding per year

t is the time in years

Given:

P = 1500

r = 0.03

n = 12 (compounded monthly means 12 times a year)

The compound interest formula modelled by the variables is:

F=1500(1+\frac{0.03}{12})^{12t}\\F=1500(1.0025)^{12t}

Now, we want balance after 5 years, so t = 5, substituting, we get:

F=1500(1.0025)^{12t}\\F=1500(1.0025)^{12*5}\\F=1500(1.0025)^{60}\\F=1742.43

<u>The balance after 5 years is:  $1742.43</u>

3 0
3 years ago
Which of the following options have the same value as 5\%5%5, percent of 353535?
professor190 [17]

Answer:

\frac{5}{100}\times35

0.05\times35

Step-by-step explanation:

<u><em>Given:</em></u>

Which of the following options have the same value as 5% 35, percent of 35?

<u><em>Following Options:</em></u>

5 \times 35

\frac{5}{100}\times35

0.5\times0.35

0.05\times35

\frac{5}{10}\times35

<u><em>Solve:</em></u>

5 % = 0.05=\frac{5}{100}

Thus the following options:

5 \times 35           [ False x ]

5 does not equal 5%

\frac{5}{100}\times35         [True √ ]

5% =\frac{5}{100}

0.5\times0.35      [ False x ]

0.5 = 0.50

0.05\times35       [True √ ]

5% = 0.05=\frac{5}{100}

\frac{5}{10}\times35          [ False x ]

\frac{5}{10}=0.50

Therefore, the options [B] \frac{5}{100}\times35 and [D] 0.05\times35 is True.

<em>Kavinsky</em>

3 0
1 year ago
I need help with this question
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Step-by-Step Explanation:

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Step-by-step explanation:

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