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Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = ta

Irina-Kira [14]

Answer:

The inner function is $u = \pi x$ .

The outer function is $f(u) = \tan{u}$ .

$\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}$

Step-by-step explanation:

The inner function is the one we apply the outer function to.

So

$y = \tan{\pi x}$

We apply the outer function tangent to $\pi x$ .

So, the inner function is $u = \pi x$ .

The outer function is $f(u) = \tan{u}$ .

The derivative of a compositve function

$y = f(u)$ in which $u = g(x)$ is given by the following function.

$y^{\prime} = f^{\prime}(u)*g^{\prime}(x)$

So

$f(u) = \tan{u}$

$f^{\prime}(u) = \sec^{2}{u}$

$u = g(x) = \pi x$

$g^{\prime}(x) = \pi$

So

$y^{\prime} = f^{\prime}(u)*g^{\prime}(x)$

$\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}$

7 0

3 years ago

4. Match these equation balancing steps with the description of what was done in each step.

Archy [21]

Answer:

step 1 - C.

step 2 - A.

step 3 - B.

6 0

3 years ago

Slope intercept form for 1/-2

boyakko [2]

y= 1/-2x + b

The standard slope intercept form would be y =mx+b

"m" would be the increase/decrease or what makes the line go up or down,

and the "b" would be the height in which it starts at

Hope this helped.

7 0

3 years ago

he end of a baseball game, the players were given the choice of having a bottle of water or a box of juice. Of all of the player

Mnenie [13.5K]

Answer:

12 is 3/4 of what number? You need to divide by the top and multiply by the bottom. 12 divided by 3 is 4, and 4 times 4 is 16.

6 0

3 years ago

Read 2 more answers

Assume that adults were randomly selected for a poll. They were asked if they "favor or oppose using federal tax dollars to fund

ser-zykov [4K]

Testing the hypothesis, it is found that since the p-value of the test is 0.0042 < 0.01, it can be concluded that the proportion of subjects who respond in favor is different of 0.5.

At the null hypothesis, it is tested if the proportion is of 0.5, that is:

$H_0: p = 0.5$

At the alternative hypothesis, it is tested if the proportion is different of 0.5, that is:

$H_1: p \neq 0.5$

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.
p is the value tested at the null hypothesis.
n is the sample size.

In this problem, the parameters are given by:

$p = 0.5, n = 483 + 398 = 881, \overline{p} = \frac{483}{881} = 0.5482$

The value of the test statistic is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}$

$z = \frac{0.5482 - 0.5}{\sqrt{\frac{0.5(0.5)}{881}}}$

$z = 2.86$

Since we have a two-tailed test(test if the proportion is different of a value), the p-value of the test is P(|z| > 2.86), which is 2 multiplied by the p-value of z = -2.86.

Looking at the z-table, z = -2.86 has a p-value of 0.0021.

2(0.0021) = 0.0042

Since the p-value of the test is 0.0042 < 0.01, it can be concluded that the proportion of subjects who respond in favor is different of 0.5.

A similar problem is given at brainly.com/question/24330815

3 0

3 years ago