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3 years ago

Given the piecewise function. Shown below

Mathematics

1 answer:

creativ13 [48]3 years ago

5 0

Answer:

(x, g(x)) = {(-2, -2), (0, 0), (2, 2), (4, -3), (6, -3)}

Step-by-step explanation:

The first three values of x in the table are all less than or equal to 2, so the first part of the function definition applies. The y-value is equal to the x-value. The ordered pairs are ...

(-2, -2), (0, 0), (2, 2)

The last two values of x in the table are more than 2, so the last part of the function definition applies. For those values of x, the y-value is -3. The ordered pairs are ...

(4, -3), (6, -3)

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Answer:

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Step-by-step explanation:

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2 years ago

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Find dy/dx for y= x^3 ln (cot x)

ICE Princess25 [194]

<h3>Answer</h3>

$\dfrac{dy}{dx} = 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)$

<h3>Explanation</h3>

By the product rule $(d/dx)(f(x)g(x)) = f(x)g'(x) + g(x)f'(x)$ , we have

$\begin{aligned}\frac{dy}{dx} &= \left(x^3 \ln (\cot x) \right)' \\&= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \end{aligned}$

By the chain rule:

$\begin{aligned}\big(\ln (\cot x)\big)' &= \dfrac{1}{\cot x} \cdot (\cot x)' \\ &= \dfrac{1}{\cot x} \cdot -\csc^2 x\\&= -\tan (x) \csc^2(x) \\&= - \frac{\sin x}{\cos x} \cdot \frac{1}{\sin^2 x} = - \frac{1}{\cos x} \cdot \frac{1}{\sin x} \\&= -\csc(x)\sec(x)\end{aligned}$

By the power rule:

$(x^3)' = 3x^2$

thus

$\begin{aligned}\frac{dy}{dx} &= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \\&= x^3\big( -\csc(x)\sec(x) \big) + \ln(\cot x) \cdot (3x^2) \\&= -x^3 \csc(x)\sec(x) + 3x^2 \ln(\cot x) \\&= 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)\end{aligned}$

Nothing to do to simplify any further, other than factoring out $x^2$ .

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3 years ago

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pshichka [43]

Answer:

They studied for a little more than an our. A

Step-by-step explanation:

Because if you multiply 4 on 2/3 you get 8/12, then add 8/12 and 7/12 together to get 15/12 simplified 1 3/12.

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2 years ago

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In the year 2008, a person bought a new car for $26500. For each consecutive year

DanielleElmas [232]

Answer:

$20500

Step-by-step explanation:

26500-(.12*26500)=23320 For 1 year

23320-(.12*23320)=$20521.60 For 2 years

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2 years ago

A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain us

Zanzabum

Answer:

Step-by-step explanation:

Hello!

The objective of the study is to determine whether the magnets are effective in treating pain. For these two independent groups of individuals with equal affections were randomly sampled, one was treated with magnets and the other group of individuals, call it control group, was treated with a placebo treatment.

The information for both samples is:

X₁: pain measurement using a visual analog scale after the individual received magnet treatments.

X₁~N(μ₁;σ₁²)

n₁= 20

X[bar]₁= 0.46

S₁= 0.93

X₂: pain measurement using a visual analog scale of an individual of the control groups.

X₂~N(μ₂;σ₂²)

n₂= 20

X[bar]₂= 0.41

S₂= 1.26

The claim is that the pain reductions of the control group have more variation than the pain reductions of the target group. If it's so then we could suspect that the population variance of the control group, σ₂², will be greater than the population variance of the magnet group, σ₁².

To test the relationship between these two population variances you have to conduct a variance ratio test using the Snedecors F statistic.

The hypotheses are:

H₀: σ₂² ≤ σ₁²

H₁: σ₂² > σ₁²

α: 0.05

$F= (\frac{S_2^2}{S_1^2}) * (\frac{Sigma_2^2}{Sigma_1^2} )~~ F_{(n_2-1);(n_1-1)}$

This hypothesis test is one-tailed to the right, there is only one critical value:

$F_{(n_2-1);(n_1-1); 1 - \alpha } = F_{19;19; 0.95}= 2.17$

The decision rule for the test is:

If $F_{H_0}$ ≥ 2.17, then the decision is to reject the null hypothesis.

If $F_{H_0}$ < 2.17, then the decision is to not reject the null hypothesis.

$F_{H_0}= \frac{S_2^2}{S_1^2}*\frac{Sigma_2^2}{Sigma_1^2} = \frac{(1.26)^2}{(0.93)^2} * 1$

$F_{H_0} = 1.835 = 1.84$

Since the calculated value of F is less than the critical value, the decision is to reject the null hypothesis. So using a 5% significance level the decision is to not reject the null hypothesis, you can conclude that the population variance of the pain reduction of the control group is less or equal than the population variance of the pain reduction on individuals treated with magnets.

I hope it helps!

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3 years ago