Find the Area of the Shaded Region.

Let tk(x)tk(x): be the taylor polynomial of degree k of the function f(x)=sin(x)f(x)=sin⁡(x) at a=0a=0.suppose you approximate f

Aloiza [94]

Ans : Note that: sin(x) = sum(n=0 to infinity) [(-1)^n * x^(2n + 1)]/(2n + 1)!. Then, since the series is alternating, the error in the approximation found by taking the first n terms of the series is no bigger than the n+1'th term. In other words: E â‰¤ a_n+1 = x^(2n + 3)/(2n + 3)!. (Note that a_n does not include (-1)^n, the alternating part) We need that 1/6 â‰¤ x^(2n + 3)/(2n + 3)!. Given |x| < 1, n = 2 will be the least integer solution. Thus, we need 2 + 1 = 3 terms.

4 0

3 years ago

A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is

arlik [135]

Answer:

(a) H₀: μ = 5 vs. Hₐ: μ ≠ 5.

(b) The test statistic value is -3.67.

(c) The p-value of the test is 0.0025.

(d) The mean amount of time spent in the shower by an adult is different from 5 minutes.

Step-by-step explanation:

In this case we need to test whether the mean amount of time that college students spend in the shower is significantly different from 5 minutes.

The information provided is:

$n=15\\\bar x=4.29\\s=0.75\\\alpha =0.01$

(a)

The hypothesis for the test can be defined as follows:

H₀: The mean amount of time spent in the shower by an adult is 5 minutes, i.e. μ = 5.

Hₐ: The mean amount of time spent in the shower by an adult is different from 5 minutes, i.e. μ ≠ 5.

(b)

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}\\\\=\frac{4.29-5}{0.75/\sqrt{15}}\\\\=-3.67$

Thus, the test statistic value is -3.67.

(c)

Compute the p-value of the test as follows:

$p-value=2\times P(t_{\alpha/2, (n-1)}$

*Use a t-table.

Thus, the p-value of the test is 0.0025.

(d)

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.0025 < α = 0.01

The null hypothesis will be rejected at 1% level of significance.

Thus, concluding that the mean amount of time spent in the shower by an adult is different from 5 minutes.

7 0

3 years ago

Y=4x-3 as a ordered pair is your sloution of

Effectus [21]

Answer:

(1,1)

(0,-3)

(2,5)

Step-by-step explanation:

Hope it helps you

5 0

3 years ago

Q1: How are rational exponents and radicals related? Q2: How can the average rate of change be identified for a function? Q3: Ho

masha68 [24]

Answer:

The answer is given below

Step-by-step explanation:

Q1: How are rational exponents and radicals related?

Rational exponents are exponents in fraction form. Radicals are roots (square root, cube root and so on).

The denominator of the rational exponent is the root which is the same as the radical.

Q2: How can the average rate of change be identified for a function?

The average rate of change is ratio of the change in output to the change in input values. The average rate of change for a function is the slope of the function.

It can be gotten by finding the first derivative of he function.

Q3: How do linear and exponential functions compare as the domain increases?

For linear functions as x increases, y also increases by the same amount (i.e rate of change is constant). For exponential function the rate of change increases by a factor known as the multiplier.

8 0

4 years ago

What is 7/6-6/7 i need to know pls

madam [21]

Answer:

13/42

Step-by-step explanation:

7 0

3 years ago