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4 years ago

I need help solving this whole thing

Mathematics

1 answer:

xz_007 [3.2K]4 years ago

5 0

Use pemdas to answer this question.

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Find f. f ″(x) = x^−2, x > 0, f(1) = 0, f(6) = 0

marin [14]

If you do in fact mean $f(1)=f(6)=0$ (as opposed to one of these being the derivative of $f$ at some point), then integrating twice gives

$f''(x) = -\dfrac1{x^2}$

$f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1$

$f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2$

From the initial conditions, we find

$f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0$

$f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)$

Eliminating $C_2$ , we get

$(C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))$

$-5C_1 = \ln(6)$

$C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)$

Then

$\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}$

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2 years ago

Domain and range of g(x)= 5x-3/2x+1 Solve for domain and range?

alukav5142 [94]

The domain and the range

3 0

3 years ago

Calculate the probability that a life aged 0 will die between ages 19 and 36, given the survival function

Papessa [141]

Answer:

Question: **Actuarial Mathematics, Survival Models** Calculate The Probability That A Life Aged 0 Will Die Between Ages 19 And 36, Given The Survival Function S0(x) = (1/10), 0 X 100 Answer: 0.1.

Step-by-step explanation:

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3 years ago

Need Help please i will mark brainliest when it lets me

timurjin [86]

Answer:it’s the second one

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A random number is selected from the interval [6.35, 10]. Find the probability that the number is within a distance of 0.25 from

exis [7]

Let X be a random number selected from the interval. Then the probability density for the random variable X is

$f_X(x)=\begin{cases}\dfrac1{10-6.35}=\dfrac1{3.65}\approx0.2740&\text{if }6.35\le x\le 10\\0&\text{otherwise}\end{cases}$

8 and 10 are the only even integers that fit the given criterion (6 is more than 0.25 away from 6.35), so that we're looking to compute

P(|X - 8| < 0.25) + P(|X - 10| < 0.25)

… = P(7.75 < X < 8.25) + P(9.75 < X < 10.25)

… = P(7.75 < X < 8.25) + P(9.75 < X < 10)

(since P(X > 10) = 0)

… = 0.2740 (8.25 - 7.75) + 0.2740 (10 - 9.75)

… = 0.2055

6 0

3 years ago