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2 years ago

[Calc 1] An explanation on how to best solve this. I've been stuck trying to use chain rule

Mathematics

1 answer:

aev [14]2 years ago

4 0

Answer:

G'(y) = 4y^7(y+4)/(y+2)^5

Step-by-step explanation:

Work it a piece at a time.

Define z = y^2/(y+2). Then your derivative is found from the power rule as ...

G = z^4

G' = 4z^3·z'

Now, define z = u/v. Then your derivative is found using the quotient rule:

z' = (vu' -uv')/v^2 = ((y+2)(2y) -(y^2)(1))/(y+2)^2

Putting this together we have ...

$G'(y)=4\left(\dfrac{y^2}{y+2}\right)^3\cdot\dfrac{y^2+4y}{(y+2)^2}\\\\\boxed{G'(y)=\dfrac{4y^8+16y^7}{(y+2)^5}}$

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ducational Television In a random sample of people, said that they watched educational television. Find the confidence interval

SIZIF [17.4K]

Complete Question

Educational Television In a random sample of 200 people, 159 said that they watched educational television. Find the 90% confidence interval of the true proportion of people who watched educational television. Round the answers to at least three decimal places.

Answer:

The 90% confidence interval is $0.748 < p < 0.842$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of people that watched the educational television is $k = 159$

Generally the sample proportion is mathematically represented as

$\^ p = \frac{159}{200}$

=> $\^ p = 0.795$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.645 * \sqrt{\frac{0.795 (1- 0.795)}{200} }$

=> $E = 0.04696$

Generally 95% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.795 -0.04696 < p < 0.795 + 0.04696$

=> $0.748 < p < 0.842$

3 0

2 years ago

north high school has 5,000 students. south high school has 1/10 as many students as North high school. how many students are th

olga2289 [7]

5000(1/10)=500 students

6 0

3 years ago

Read 2 more answers

Please I need help on Fundametal Trigonometric Identities?

svp [43]

Fundamental Trigonometric Identities are listed below:

$sin^{2}$ Θ + $cos^{2}$ Θ = 1
$sec^{2}$ Θ - $tan^{2}$ Θ = 1
$cosec^{2}$ Θ - $cot^{2}$ Θ = 1
sinΘ = 1 / cosec Θ
cos Θ = 1 / sec Θ
tan Θ = 1 / cot Θ
tan Θ = sinΘ / cosΘ
cotΘ = cosΘ / sinΘ

<h3>Meaning of Fundamental Trigonometric Identities</h3>

Fundamental Trigonometric Identities can be defined as the basic identities or variables that can be used to proffer solutions to any problem relating to angles and trigonometry.

In conclusion, A few Fundamental Trigonometric Identities are listed above.

Learn more about Fundamental Trigonometric Identities: brainly.com/question/7331447

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1 year ago

Please help and i apreciate it

LuckyWell [14K]

I think the answer is letter c

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2 years ago

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Show that the two triangles given beside are similar and calculate the lengths of sides PQ and PR.

Rina8888 [55]

9514 1404 393

Answer:

ΔABC ~ ΔPQR
PQ = 8
PR = 14

Step-by-step explanation:

Angles A and P are marked congruent; angles B and Q are marked congruent, so the triangles are similar by the AA similarity postulate. The similarity statement can be written ...

ΔABC ~ ΔPQR by AA similarity

The ratio of sides of PQR to ABC is the ratio QR/BC = 12/6 = 2. That is, each side in the larger triangle is 2 times the length of the corresponding smaller side.

PQ = 2·AB = 2·4 = 8

PR = 2·AC = 2·7 = 14

The side lengths of interest are ...

PQ = 8, PR = 14

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2 years ago