On analyzing a function, John finds that f(a) = b. This means that the graph of f passes through the point

At which one of the following times is the angle between the hands of a clock exactly one straight angle? a)12:00 b)12:30 b)3:45

Marta_Voda [28]

12:00 will have both hands pointing up
12:30 will have the straight line at the half past part but it will not be exactly on the 12
3:45 it will be past the 3 and exactly on 45 so it will not work
And 6:00 will be a straight line as one hand will be at the 12 and and it will be straight on the 6 as it is on the hour so the answer is d

6 0

3 years ago

Khloe has 28 coins in her collection. That is five more than kourntey has. How many does kourtney have?

AnnyKZ [126]

28 is five more than 23

7 0

3 years ago

Read 2 more answers

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,

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

(c) The series

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

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

Write the following equation in standard form: y + 4 = -3(x + 2)

Irina18 [472]

Answer:

-3x-y=10

Step-by-step explanation:

y+4=-3(x+2)

y+4=-3x-6

y=-3x-6-4

y=-3x-10

-3x-y=10

5 0

3 years ago

You are at a concert and the seating area is shown below. Suppose you think each person takes up 2 square feet, estimate the att

Nataliya [291]

Answer:

I think its 183.750

Step-by-step explanation:

(700 multiplied by 525) divided by 2 equals 183.750

5 0

3 years ago