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3 years ago

What is the average value of y=cosx/x^2+x+2 on the closed interval "[-1, 3]"?

1 answer:

5 0

We have
y=cos x/(x²+x+2) on the closed interval [-1, 3]

we know that
The average value of f(x) on the interval [a, b] is given by:
F(avg) = 1/(b - a) ∫ f(x) dx (from x=a to b).
(b-a)=(3+1)------> 4
= 1/4 ∫ cos(x)/(x² + x + 2) dx (from x=-1 to 3).

Note that [cos(x)/(x² + x + 2)] does not have an elementary anti-derivative.
By approximating techniques:
1/4 ∫ cos(x)/(x^2 + x + 2) dx (from x=-1 to 3) ≈ 0.182951

the answer is
the average value of y = cos(x)/(x² + x + 2) on [-1, 3] is approximately 0.182951

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Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?

grandymaker [24]

-2m - 5m = -7m
-7m - 8 = 3 -7 + m
3 - 7 = -4
-7m - 8 = m - 4
-7m - 8 + 8 = m - 4 + 8
-7m = m + 4
-7m - m = m + 4 - m
-8m = 4
-8m/-8 = 4/ -8
FINAL = m= -1/2 = -0.5

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3 years ago

When playing the roulette at a casino, you have exactly 1/35 chance of winning in each round if you play a single number. Your f

Vikentia [17]

Answer:

0.2275 = 22.75% probability that you actually won that round

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Fireworks going off

Event B: You won

Probability of fireworks going off.

100% of 1/35 = 0.0286(when you win)

10% of 34/35 = 0.9714(you lost). So

$P(A) = 0.0286 + 0.1*0.9714 = 0.12574$

Probability of you winning and fireworks going off:

100% of 1/35, so $P(A \cap B) = 0.0286$

If you failed to see the outcome of a round, but you see the fireworks going off, then what is the probability that you actually won that round?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0286}{0.12574} = 0.2275$

0.2275 = 22.75% probability that you actually won that round

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3 years ago

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Lubov Fominskaja [6]

Answer:

Step-by-step explanation:

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1 year ago

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Leya [2.2K]

$25000 _____$12,000x2 + $1000
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3 years ago

Answer fast! I don't understand how to do this. I have a test going on about exponent properties.

qwelly [4]

Answer:

$x^4yz$

Step-by-step explanation:

$\frac{(x^6y^3z^2)}{(x^2y^2z)}$ (This can be simplified, because when you divide expressions with exponents that have the same bases, you can subtract the exponents from the one with the corresponding base)

$\frac{(x^6y^3z^2)}{(x^2y^2z)}$

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2 years ago