What is the equation of the line that passes through the given points in slope-intercept form? (-2,3) and (-3,-4)

Mathematics

1 answer:

Orlov [11]2 years ago

6 0

Step-by-step explanation:

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the equation of the line.

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A cyclist travels 5.8 km in 30 minutes. What is his average speed in km/h?

Mila [183]

Answer:

11.6km/hr

Step-by-step explanation:

You need to double 30 minutes to get an hour, so do the same with the distance.

5.8*2=11.6 km

11.6km/hr

6 0

2 years ago

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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

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