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3 years ago

The coordinate pairs (-5, -11), (0, -1), and (5, 9) are solutions to which function?

1 answer:

5 0

So, the slope is 2 for each of the points. Now, you plug it into y=mx+bSo, you get, y=2x+b
To find b, you choose any pair of x and y values.-5=-22+bb=17

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Identify the least common multiple that would eliminate the y variable in the system of equations 6x-5y=-4 4x+2y=28

nikdorinn [45]

The coefficient for y is -5 in the first equation, +2 in the second equation, so the least common multiple is -10

8 0

3 years ago

Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5 0

3 years ago

Pls help! I need help with a and c I did b already!

laila [671]

Answer:

A= y= -2x+7.

B= y= - $\frac{3}{2}$ x+ 6

Step-by-step explanation:

The linear equation is y=mx+b

A= y= -2x+7.

-2 represents he slope and 7 represents the y intercept.

B= y= - $\frac{3}{2}$ x+ 6

- $\frac{3}{2}$ is the slop and 6 is the y intercept.

Hope this helps :)

8 0

3 years ago

If the die were to be rolled 6000 times, would we expect to obtain exactly 1000 '2's? explain your answer.

ludmilkaskok [199]

The probability of that occurring is 0%. There are 6 sides in a typical dice, which means the probability of rolling a 2 is 1/6th. (1/6)^1000 will give you the probability of rolling a 2 exactly 1000 times. (1/6)^1000 equates to 0%.

7 0

2 years ago

Find the mean of the data. give your answer in decimal form

aleksandr82 [10.1K]

Mean = (1+1+2+3+3+3+4+5)/8 = 22/8 = 2.75

answer
mean = 2.75

8 0

3 years ago