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jekas [21]
3 years ago
7

peter played his favorite video game for 10 hours last week. today, peters parents restricted him to 5 additional hours each wee

k for the next 8 weeks. create the function f(x) that models peters total video game time and explain what each number in the situation represents graphically, using complete sentances
Mathematics
1 answer:
never [62]3 years ago
7 0
<span>f(x) is the function that models Peters total video game time. 
</span><span>Peter played his favorite video game for 10 hours last week.
</span><span>Peters parents restricted him to 5 additional hours each week for the next 8 weeks.
After 8 weeks Peter will have played f(x) hours video game.
f(x)=10+8*x , where x is the number of hours Peter plays every week and this number is smaller than 5 (his parents restricted this number) , x<5

</span>
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Integrate 1 - x / x(x2 + 1) d x by partial fractions.
solniwko [45]

Answer:

log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x

Step-by-step explanation:

step 1:-   by using partial fractions

[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }......(1)

<u>step 2:-</u>

solving on both sides

1-x=A(x^{2} +1)+(Bx+C)x......(2)

substitute x =0 value in equation (2)

1=A(1)+0

<u>A=1</u>

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

<u>-</u>1  =  C

<u>step 3:-</u>

substitute A,B,C values in equation (1)

now  

\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 }  d x -\int\limits \frac{1}{x^{2}+1 }  d x

by using integration formulas

i)  by using \int\limits \frac{1}{x}   d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\.....(b)

\int\limits tan^{-1}x  dx =\frac{1}{1+x^{2} } +C.....(c)

<u>step 4:-</u>

by using above integration formulas (a,b,and c)

we get answer is

log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x

6 0
3 years ago
What are the zeros of this function? Circle them on the graph.
Rashid [163]

Given:

The graph of a function.

To find:

The zeros of this function on the graph.

Solution:

We know that, zeros are the values at which the values of the function is 0. It means, the points where the graph of function intersect the x-axis are know as zeros of the function.

From the given graph it is clear that, the graph intersect the x-axis at two points.

Therefore, the marked points on the below graph are the zeros of the function.

8 0
3 years ago
What is the missing operations to 4×9+7×9=(4+7)×
ICE Princess25 [194]

Answer:

9, if you're asking for only the number of it. But If it needs more then please elaborate.

Step-by-step explanation:

4×9+7×9=(4+7)×9

36+63=11*9

99=99

Order Of Operation Helps!

8 0
3 years ago
Read 2 more answers
Three times a number, x, increased by four is equal to five times the number, x. Which equation can be used to solve
ikadub [295]

Answer:

=5x⁴+3x

=-2x+4

=8x+4

=-2x-4

Step-by-step explanation:

hope it's help

7 0
3 years ago
Pls help...................
bearhunter [10]
First one b ≤ 9 good luck
5 0
3 years ago
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