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2 years ago

Identify the value of a if y= ax+ 7x + 2 and the point (2, 12) is on the graph.

Mathematics

1 answer:

alexandr1967 [171]2 years ago

6 0

Answer:

a=-2

So yep. ;)

Step-by-step explanation:

Alright, so, (2,12), 2 is the x and 12 is the y.

Stick them into the equation: $12=a*2+(7*2)+2$

Then, solve:

$12=a*2+14+2$

a = -2

So yes, they're on the graph.

Hope this helped! :)

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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

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

7 0

1 year ago

Destiny is planning a ice cream social. I local park right outside shelter for $40 in charges nine dollars per gas for ice cream

zysi [14]

Answer:

Step-by-step explanation:

8 0

2 years ago

5/8 -0.5 evaluate each expression. Write answer as a decimal

gregori [183]

Answer:

0.125

Step-by-step explanation:

0.5 =1/2

Now

5/8 - 1/2

5/8 - 1*4/2*4

5/8-4/8

(5-4)/8

1/8

0.125

6 0

2 years ago

The hour hand on a clock is 4 cm long, and the minute hand is 10 cm long. What is the exact distance between the tips of the han

Allushta [10]

Answer:

2 sqrt(19)

Step-by-step explanation:

We know that the angle between the two hands

360 /12 *2 = 60 degrees

We divide by 12 because there are 12 number and multiply by 2 because there are 2 number between 10 and 12

This is a triangle where we know 2 sides and the angle between them.

We can use the law of cosines to determine the third side

c^2 = a^2 + b^2 -2abcosC

Where C is the angle between sides a and b

a =4 and b = 10 C = 60 and we are looking for side c

c^2 = 4^2 + 10^2 -2*4*10 cos60

c^2 =16+100 - 80cos 60

c^2 = 76

Take the square root of each side

sqrt(c^2) = sqrt(76)

c = sqrt(76)

c =sqrt(4) sqrt(19)

c =2 sqrt(19)

4 0

2 years ago

What is the solution set of -11 > 1 + a?<br>a > -10<br>a -12

Luda [366]

Answer is 10 because I just took the test

5 0

3 years ago

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