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LuckyWell [14K]
3 years ago
11

The function m=30-3r represents the amount m (in dollars) of money you have after renting r video games.

Mathematics
1 answer:
san4es73 [151]3 years ago
5 0
The domain of the equation are all the possible values of the independent variables that would make the equation reasonable, possible or true. In this item, the independent variable is r. This could take a value of 0 up to the point when m is equal to zero.
        m = 30 - 3r = 0
              r = 10

The domain is therefore [0, 10]. 

The range is the value of the dependent variable which would be from 0 to the point when no video game is played. This is, [0, 30]. 

The function is discrete because r and m cannot take every value in the number line. 
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<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%7B%20%20%5Cpi%20%7D%20%5Ccos%28%20%5Ccot%28x%29%20%20%20%20-%20%2
Nikolay [14]

Replace x with π/2 - x to get the equivalent integral

\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx

but the integrand is even, so this is really just

\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx

Substitute x = 1/2 arccot(u/2), which transforms the integral to

\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du

There are lots of ways to compute this. What I did was to consider the complex contour integral

\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}

and it follows that

\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}

7 0
1 year ago
1. Find the domain and range of the relation and determine whether it is a function.
Katyanochek1 [597]
A. the relation is a function
8 0
3 years ago
How to divide 4.48 ÷7​
Rina8888 [55]

Answer:

<h2>0.64</h2>

Step-by-step explanation:

4.48/7

7 into 4 (0 times)

Bring next number down 4.48 ⬇️

7 into 44 (6 times, 2 left over)

Bring next number down 4.48 ⬇️

7 into 28 (4 times)

Answer 0.64

I'm always happy to help :)

5 0
3 years ago
Read 2 more answers
The mean of 5 numbers is 30. The median is 33. What might the numbers be?
tatiyna

Let a,b,c,d and e are five numbers

mean = (a +b+ c+ d+e)/5 = 30

⇒ (a +b+ c+ d+e) = 150_______(1)

now, Let the number excluded be a

then, new mean =  (b+ c+ d+e)/4 = 28

⇒ (b+ c+ d+e)= 112

putting this value in (1),

⇒a + 112 = 150

⇒a = 150 -112 = 38

excluded number = 38

4 0
2 years ago
10•f(7)+9•g(-1)? What’s the answerrr
Inessa [10]

Answer:

= 70f - 9g

Step-by-step explanation:

1. Remove parentheses

2. Multiply the numbers

3. Multiply the numbers

5 0
3 years ago
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