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3 years ago

What is the range of the function f(x)=3x−1f(x)=3x-1 when the domain is {-1, 0, 1}?

Mathematics

1 answer:

Triss [41]3 years ago

4 0

<span>f(x)=3x−1

</span><span>domain is {-1, 0, 1}

3(-1) -1 = -4
3(0) - 1 = -1
3(1) - 1 = 2

Range { -4, -1, 2}</span>

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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

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

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2 years ago

Which statement best describes the area of the triangle shown below?

wel

Answer:

It is twice the area of a rectangle of length 4 units and width 2 units.

Step-by-step explanation:

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2 years ago

If 2x + 5y = 21 and x + y = 3, then what is the solution

Viefleur [7K]

2x+5y=21, x+y=3
y=3-x
2x+5y=21
2x+5(3-x) =21
2x+15-5x=21
2x-5x+15=21
-3x+15=21
-3x=21-15
-x=6/3
-x=2
x=-2

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3 years ago

Researchers collected data from 100 randomly chosen counties in Texas on pollution levels and asthma rates. Pollution levels wer

lesya692 [45]

Answer:

The answer is "3.14".

Step-by-step explanation:

The coefficient of pollution level is "b" and "a" intercept

$\to y=a+bx\\\\$

We must verify it.

$H_0 :\beta = 0\\\\H_a : \beta \neq 0\\\\$

$Beta \to b=1.76, SE=0.56 \ Estimate$

The statistics on tets are now provided

$\to t=\frac{b}{SE}=\frac{1.76}{0.56}=3.14$

Because statistics will be more than critical $(1.984)$ values, we thus reject $H_0$

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3 years ago

HELP! WILL GIVE BRAINLEST!The graph below shows an angle in standard position. What is the degree measure of the angle depicted?

Tanya [424]

Answer:

45 degree angle

Step-by-step explanation:

Let's say that the line crossing the middle of quadrant four was on the y-axis, that would be known as a 90 degree angle. Since it was cut in half, that would become a 45 degree angle.

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2 years ago

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