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3 years ago

F(x) = x − 8, g(x) = |x + 8| Find (f ∘ g)(x).

Mathematics

1 answer:

miskamm [114]3 years ago

5 0

Answer:

Step-by-step explanation:

$f(x) = x - 8 \\ \\ g(x) = |x + 8|$

To find (f ∘ g)(x) , substitute g(x) into f(x). That is for every x in f (x) replace it with g (x)

That's

Hope this helps you

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

2 years ago

Do number 2 please. Please bots don’t answer! I just trying to get help :(

zavuch27 [327]

Answer:

no 2. cube a' will be smaller because it was multiplied by a fraction

no 3. c

8 0

1 year ago

If a=3 what does 3(6-)=

natita [175]

Answer: -18

Step-by-step explanation:

3 x -6 = 18

5 0

2 years ago

Read 2 more answers

Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation o

Hitman42 [59]

Answer:

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet.

This means that $\mu = 2.5, \sigma = 0.4$

Find the probability that an individual man’s step length is less than 1.9 feet.

This is the p-value of Z when X = 1.9. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1.9 - 2.5}{0.4}$

$Z = -1.5$

$Z = -1.5$ has a p-value of 0.0668

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

3 0

2 years ago

Help! This is due today!

bulgar [2K]

Answer:

27π

Step-by-step explanation:

area of circle = πr^2

= π × 6^2

= 36π

36/4

= 9

36 - 9

= 27π units squared

4 0

2 years ago