1 year ago

Katie spent m minutes practicing her trumpet on

Mathematics

1 answer:

fgiga [73]1 year ago

7 0

Answer:

7m minutes

Step-by-step explanation:

We know that:

3 days of practice = Monday + Tuesday + Wednesday
Monday = m
Tuesday = m + 6
Wednesday = 5m - 6

Solution:

3 days of practice = Monday + Tuesday + Wednesday
=> 3 days of practice = m + m + 6 + 5m - 6

[Simplifying]

=> 3 days of practice = 7m - 6 + 6

[Final Answer]

=> 3 days of practice = 7m

Hence, the total number of minutes she practiced over the course of the three days is 7m minutes.

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Find the following integral. Integrate x + 5/x^2 +10x +26 dx

sweet-ann [11.9K]

Given :

Polynomial , $f(x)=x+\dfrac{5}{x^2}+10x+26$ .

To Find :

Integration of f(x) .

Solution :

We know , integration of $x^n$ is :

$\int x^n \, dx = \dfrac{x^{n+1}}{n+1}+C$

( Here , is C is a constant )

Now ,

$\int f(x)\ dx=\int( x+\dfrac{5}{x^2}+10x+26)dx\\ \\ \int f(x)\ dx= \int x\ dx+\int 5x^{-2}\ dx+\int 10 x \ dx +26\ dx\\ \\ \int f(x)\ dx=\dfrac{x^2}{2}+\dfrac{5\times x^{-1}}{(-1)}+\dfrac{10x^2}{2}+26x+C\\\\ \int f(x)\ dx=\dfrac{11x^2}{2}+26x-5x^{-1}+C$