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3 years ago

This is a CALCULUS question, "Derivatives As A function"

Mathematics

1 answer:

irina1246 [14]3 years ago

4 0

Derivative Functions

The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. We can formally define a derivative function as follows.

Definition:

let f be a function. The derivative function, denoted by f', is the function whose domain consists of those values of x such that the following limit exists:

$f'(x)= \lim_\\ \ \\ \frac{f(x+h)-f(x)}{h} {h \to 0}$

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sertanlavr [38]

Answer: The system consists of parallel lines

Step-by-step explanation:

Given system of lines :

$y=\dfrac13x-4$

$3y-x=-7$

Substitute $y=\dfrac13x-4$ in $3y-x=-7$ , we get

$3(\dfrac13x-4)-x=-7\\\\\Rightarrow\ x-12-x=-7\\\\\Rightarrow\ -12=-7$ , which is not true.

That means , system has no solution.

i.e. they are representing parallel lines. [Parallel lines do not intersect and hence they do not have solution.]

6 0

3 years ago

within a kiambu county,students were randomly assigned to one of two mathematics teachers.Mrs.Elite and Mrs. Bright. After the a

DerKrebs [107]

Using the t-distribution, as we have the standard deviation for the samples, it is found that since the absolute value of the test statistic is greater than the critical value, we reject the claim that Mrs.Elite and Mrs. Bright are equally effective teachers.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, we test if they are equally effective teachers, that is, the subtraction of their means is 0, hence:

$H_0: \mu_1 - \mu_2 = 0$

At the alternative hypothesis, we test if they are not equally effective teachers, that is, the subtraction of their means is not 0, hence:

$H_1: \mu_1 - \mu_2 \neq 0$

<h3>What is the distribution of the differences?</h3>

For Mrs. Elite, we have that:

$\mu_1 = 78, \sigma_1 = 10, n_1 = 30, s_1 = \frac{10}{\sqrt{30}} = 1.82574$

For Mrs. Bright, we have that:

$\mu_2 = 85, \sigma_2 = 15, n_2 = 25, s_2 = \frac{15}{\sqrt{25}} = 3$

For the distribution of differences, we have that:

$\overline{x} = \mu_1 - \mu_2 = 78 - 85 = -7$

$s = \sqrt{s_1^2 + s_2^2} = \sqrt{1.82574^2 + 3^2} = 3.5119$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{-7 - 0}{3.5119}$

$t = -1.99$

Considering a<em> two-tailed test</em>, as we are testing if the mean is different of a value, with 30 + 25 - 2 = <em>53 df and a significance level of 0.1</em>, the critical value is of $|t^{\ast}| = 1.6741$ .

Since the absolute value of the test statistic is greater than the critical value, we reject the claim that Mrs.Elite and Mrs. Bright are equally effective teachers.

To learn more about the t-distribution, you can take a look at brainly.com/question/13873630

3 0

3 years ago

Malloy solved the equation −5x − 16 = 8; his work is shown below. Identify the error and where it was made. −5x − 16 = 8 Step 1:

xxTIMURxx [149]

Answer is

<span>d. Step 3: He should have divided both sides by −5.</span>

5 0

4 years ago

Read 2 more answers

a commercial jet has been instructed to climb from its present altitude pf 9000 feet to a cruising altitude of 44000 feet, if th

zzz [600]

Firstly we need to count what is the difference between both altitudes:

44,000 - 9,000 = 35,000

If a plane descends at a rate of 2,500 feet per minute, then we have to count how many 2,500s fit in 35,000:

35,000 / 2,500 = 14

It means that the jet will reach its cruising altitude in 14 minutes.

5 0

4 years ago

The explicit formula for an arithmetic sequence is an = 20 + (n − 1)(2). What is the 200th term?

Andrews [41]

Answer:

$a_{200}=418$