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sesenic [268]
2 years ago
14

Which number produces a rational number when multiplied by 0.5?

Mathematics
1 answer:
xxMikexx [17]2 years ago
4 0

If the number begins by being rational, multiplying by 0.5 will not change whether or not it is rational. It will remain rational.


That would include any even number 12 * 0.5 = 6

12 started out as rational, so the answer is rational (6)


Any odd number is also rational

23 * 0.5 = 11.5

23 and 11.5 are both rational.


3.636363636 ... is rational so when multiplied by 0.5 the result will be rational.

1.818181818....


So if we start with something irrational like pi

then pi * 0.5 is not rational.

If you have choices, please list them.
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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
So, the additive inverse of -7/8 is​
zlopas [31]

Answer:

Im prett sure its 7/8

Step-by-step explanation:

The additive inverse of a number is a number that, when added, goes to zero. For example, 7 is -7 because when added it equals 0 (or 7-7)

8 0
3 years ago
−7/8 −(−5/6) ​ in simplest form
svp [43]

Answer:

-1/24

Step-by-step explanation:

-7/8 - (-5/6)

Subtracting a negative is like adding

-7/8 + 5/6

Get a common denominator

-7/8 * 6/6    + 5/6 *8/8

-42/48 + 40/46

-2/48

-1/24

3 0
2 years ago
Plz help me with 30 a and b
Verdich [7]
A. Y=-0.2X+6.1.
B. It's wanting an X and Y table I guess. So week zero is 6.1. Week one is 5.9. Two is 5.7. Three is 5.5. Four is 5.3. Five is 5.1. Hope that's far enough.
8 0
2 years ago
Ten less than twice a number is the same as 7 times the number. find the number
Dafna11 [192]
The number is -2 // Math [n is equivalent to number]: 2n -10 = 7n
                                                                                    2n = 7n + 10
                                                                                    -5n = 10
                                                                                    -n = 2
                                                                                    n = -2
// Hope this helped, please give me brainliest, thanks!! //
6 0
3 years ago
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