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3 years ago

For what values of x∈[0,2π] does the graph of y=x+2cosx have a horizontal tangent?

Mathematics

1 answer:

Katen [24]3 years ago

3 0

Answer: x = pi/6 and x = pi/3.

Step-by-step explanation:

We have the function:

y = x + 2*cos(x)

It will have a horizontal tangent at the point where it's derivate is equal to zero.

Then first let's differentiate y.

y' = dy/dx = 1 - 2*sin(x).

Then we must find the value of x between 0 and 2*pi (or 0° and 360°)

y'(x) = 1 - 2*sin(x) = 0.

Let's solve that:

2*sin(x) = 1

sin(x) = 1/2.

We know that:

sin(30°) = 1/2.

and

Sin(120°) = 1/2

Then let's convert 30° into radians.

We know that:

pi = 180°.

Then:

pi/180° = 1.

30° = 30°*(pi/180°) = (30°/180°)*pi = (3/18)*pi = pi/6

120° = (120°/180°)*pi = (12/18)*pi = (1/3)*pi = pi/3.

Then the two values of x are: pi/6 and pi/3.

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Find the p-value: An independent random sample is selected from an approximately normal population with an unknown standard devi

vladimir1956 [14]

Answer:

(a) p-value = 0.043. Null hypothesis is rejected.

(b) p-value = 0.001. Null hypothesis is rejected.

(d) p-value = 0.022. Null hypothesis is rejected.

Step-by-step explanation:

To test for the significance of the population mean from a Normal population with unknown population standard deviation a t-test for single mean is used.

The significance level for the test is α = 0.05.

The decision rule is:

If the p - value is less than the significance level then the null hypothesis will be rejected. And if the p-value is more than the value of α then the null hypothesis will not be rejected.

(a)

The alternate hypothesis is:

Hₐ: μ > μ₀

The sample size is, n = 11.

The test statistic value is, t = 1.91 ≈ 1.90.

The degrees of freedom is, (n - 1) = 11 - 1 = 10.

Use a t-table t compute the p-value.

For the test statistic value of 1.90 and degrees of freedom 10 the p-value is:

The p-value is:

P (t₁₀ > 1.91) = 0.043.

The p-value = 0.043 < α = 0.05.

The null hypothesis is rejected at 5% level of significance.

(b)

The alternate hypothesis is:

Hₐ: μ < μ₀

The sample size is, n = 17.

The test statistic value is, t = -3.45 ≈ 3.50.

The degrees of freedom is, (n - 1) = 17 - 1 = 16.

Use a t-table t compute the p-value.

For the test statistic value of -3.50 and degrees of freedom 16 the p-value is:

The p-value is:

P (t₁₆ < -3.50) = P (t₁₆ > 3.50) = 0.001.

The p-value = 0.001 < α = 0.05.

The null hypothesis is rejected at 5% level of significance.

(c)

The alternate hypothesis is:

Hₐ: μ ≠ μ₀

The sample size is, n = 7.

The test statistic value is, t = 0.83 ≈ 0.82.

The degrees of freedom is, (n - 1) = 7 - 1 = 6.

Use a t-table t compute the p-value.

For the test statistic value of 0.82 and degrees of freedom 6 the p-value is:

The p-value is:

P (t₆ < -0.82) + P (t₆ > 0.82) = 2 P (t₆ > 0.82) = 0.444.

The p-value = 0.444 > α = 0.05.

The null hypothesis is not rejected at 5% level of significance.

(d)

The alternate hypothesis is:

Hₐ: μ > μ₀

The sample size is, n = 28.

The test statistic value is, t = 2.13 ≈ 2.12.

The degrees of freedom is, (n - 1) = 28 - 1 = 27.

Use a t-table t compute the p-value.

For the test statistic value of 0.82 and degrees of freedom 6 the p-value is:

The p-value is:

P (t₂₇ > 2.12) = 0.022.

The p-value = 0.444 > α = 0.05.

The null hypothesis is rejected at 5% level of significance.

5 0

3 years ago

Try This question solve using elimination I’ll give you brainliest

koban [17]

Answer:

(7, 1/2)

Step-by-step explanation:

Multiply second equation by 2 and subtract.

3x - 4y = 19

- (4x - 4y = 26)

You get -x = -7

x = 7

Substitute x into any equation.

3(7) - 4y = 19

21 - 4y = 19

-4y = -2

y = 1/2

4 0

3 years ago

the area of a parallelogram is 36x^6y^5. if the base of the parallelogram is 3xy^2,what is the height of the parallelogram asap

trapecia [35]

Answer:

h = 12x^5y^3

Step-by-step explanation:

The area of a parallelogram is found using A = b*h. Substitute the values given and solve for h.

A = b*h

36x^6 y^5 = 3xy^2 * h

36x^6 y^5 ÷ 3xy^2 = h

12x^5y^3 = h

4 0

3 years ago

Prove that

Dovator [93]

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

secx = $\frac{1}{cosx}$ , cosecx = $\frac{1}{sinx}$

cotx = $\frac{cosx}{sinx}$ , tanx = $\frac{sinx}{cosx}$

Consider the left side

secA cosecA - cotA

= $\frac{1}{cosA}$ × $\frac{1}{sinA}$ - $\frac{cosA}{sinA}$

= $\frac{1}{cosAsinA}$ - $\frac{cosA}{sinA}$

= $\frac{1-cos^2A}{cosAsinA}$

= $\frac{sin^2A}{cosAsinA}$ ( cancel sinA on numerator/ denominator )

= $\frac{sinA}{cosA}$

= tanA = right side ⇒ proven

5 0

3 years ago

How can you actually divide numbers without subtraction?

Tamiku [17]

#include <stdio.h> #include <stdlib.h>

// Function to perform division (x / y) of two numbers x and y. // without using division operator in the code. int divide(int x, int y)

{ // handle divisibility by 0. if (y == 0)

{ printf("Error!! Divisible by 0"); exit(1);

} // store sign of the result.

int sign = 1; if (x * y < 0)

7 0

3 years ago