Let y=(3x + f(4 − x^2))^3. Find dy/dx for x=1, given that f(3)= -6 and f'(3)= 4

Consider the graph above. Write about a situation that could be modeled using this graph. In your response, use the prompts belo

Vikentia [17]

Answer:

See Explanation

Step-by-step explanation:

Given

See attachment for graph

Required

A situation that can be modeled by the graph.

The prompt and the response are as follows:

<u>The type of function:</u>

It is a linear function

<u>The variables modeled in the function</u>

The variables are x and y

<u>The domain and the range</u>

From the graph, we can see that x and y values are not limited to any constraints.

So, the domain and the range are:

$Domain: \{-\infty \le x \le \infty \}$

$Range: \{-\infty \le y \le \infty \}$

<u>Question that could be </u> $answered$ <u></u>

The graph could be used to predict y value, given the x value.

Take for instance, find y when x = 10

The answer can be handpicked directly from the graph. However, the best way is to calculate the graph equation, first.

So, we have:

Pick any two points on the line of the graph

$(x_1,y_1) = (-2,0)$

$(x_2,y_2) = (0,4)$

Calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{4 - 0}{0 - -2}$

$m = \frac{4}{2}$

$m =2$

The equation of the graph is:

$y = m(x - x_1) + y_1\\$

So, we have:

$y = 2(x - -2) + 0$

$y = 2(x +2)$

Expand

$y = 2x +4$

To solve for y when x = 10;

$y = 2 * 10 +4$

$y = 20 +4$

$y = 24$

5 0

3 years ago

2.) debt ratio is calculated by____.

Nonamiya [84]

2)Since the score is 750, then the annual rate is 9.25% (see the table)
Then monthly rate:9.25/12=0.77%.
Then compute 0.77% from <span> $2,375.00 like this:
</span> $0.0077\times2375=\$18.30$
Answer: interest to pay: $18.30.

3)Compute monthly rate for first account:
9.75/12=0.81%
Compute 0.81% of $<span>1,675.00 like this:</span> $0.0081\times1675=13.5$
Second account:
compute monthly rate: 12.5/12=1.04%.
Then compute $0.0104\times1,675.00=17.4$
Conclusion:
Monthly interest is $13.5+$17.4=$30.9

4 0

3 years ago

Read 2 more answers

Dagney read 120 pages in three hours. Write two rates implied by the statement. How long would it take Dagney to read a 560 page

vitfil [10]

Dagney reads at 40 pages an hour, or .75 pages a minute.

it would take 4.5 hours to read the novel

3 0

3 years ago

Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.173, n = 120$ . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

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

$Z = \frac{34 - 20.76}{4.14}$