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3 years ago

the space club is having so posters printed the printer charges $250 plus $2 per poster how many posters van be printed for $100

1 answer:

5 0

You can solve this by saying $1000 is equal to 250 + $2 * the amount of posters (x)
1000=250+2x
1000-250=2x
750=2x
x= (750/2)
x =375 posters

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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

3x^2+5x+2 help me solve this

katovenus [111]

Answer:

(3x +2)(x +1)

Step-by-step explanation:

A number of different ways are suggested for doing this. One that seems straightforward is this.

For ax^2 +bx +c, look for factors of ac that total b. Here we have ...

ac = 3·2 = 6

b = 5

It is easy to see that the factors we just multiplied to get 6 are ones that total 5: 3+2 = 5.

Now, rewrite the "bx" term using this sum.

3x^2 +3x +2x +2

Factor each pair of terms.

3x(x +1) +2(x +1)

And factor out the common factor:

(3x +2)(x +1)

6 0

3 years ago

Billy has 2 cats and one of them ate 3 oatmeal bowls. If they both eat 3 oatmeal bowls how much sugar should they all together h

9966 [12]

3 x (2/3) = 2

2 x 2 = 4

If both cats eat 3 oatmeal bowls, they should have 4 cups altogether.

2 x 23.8888 = 47.7776

4 x 23.8888 = 95.5552

47.7776 + 95.5552 = 143.3328

If one cat eats 2 fish plates and the other cat eats 4 fish plates, they use 143.3328 pounds altogether.

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3 years ago

I need help with my math!!!

Aleonysh [2.5K]

Answer:

The correct answer is y = | x + 6 |

6 0

3 years ago

Twice a number subtracted from four times a number added to 15

katrin2010 [14]

Answer:15=4x=2x 6x=15x=5/2x=2.5

Step-by-step explanation:

4 0

3 years ago