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3 years ago

Find the derivative of y=cos^2(5x^3-2x)

Mathematics

1 answer:

DENIUS [597]3 years ago

7 0

Step-by-step explanation:

Use power rule and chain rule.

y = cos²(5x³ − 2x)

dy/dx = 2 cos(5x³ − 2x) (-sin(5x³ − 2x)) (15x² − 2)

dy/dx = 2 cos(5x³ − 2x) sin(5x³ − 2x) (2 − 15x²)

Use double angle formula to simplify:

dy/dx = sin(10x³ − 4x) (2 − 15x²)

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What will be the area of the enlarged picture on the wall?

fgiga [73]

224 I think yea it’s probably it

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3 years ago

Read 2 more answers

Two dice are thrown simultaneously find

STALIN [3.7K]

Answer:

13.89%

Step-by-step explanation:

First lets find all possibilities of two dice being thrown, we can do this by finding a simple dice chart online (I attached an image of one to help.)

There are 36 possibilities, and we need to find how often the two dice add together to equal eight. 6+2=8, 5+3=8, etc.

There are five 5 total times that two dice can equal eight. so 5 out of 36 times we roll two dice we'll get eight.

$\frac{5}{36}$

Type that into the ol' handy dandy calculator and we've got 0.1388888889. So... a lot of 8's, we don't need that many and we just can't have an answer with that many.

To make that number into a percentage we have to move the dot two spaces over, and round to the thousandths place (two numbers).

This would give us 13.89%, our final answer.

Hope this helped!

4 0

3 years ago

7. Approximately 9 out of 100 people are left handed. Out of a population of 1740 people. How man are likely o be left

True [87]

Answer:

Hello There.The correct answer is 157

Because All you need to do is is Multiply 1740 x 9 then you need to add to 100 to get 15760 And that how you get the answer 1740 x 9 + 100 =15760.

3 0

3 years ago

PLEASE HELP! What is the ratio of the volumes of two spheres, if the ratio of their radii is 13: 9

DiKsa [7]

Answer:

$V_1 : V_2= 2197 : 729$

Step-by-step explanation:

Let the volumes of both the spheres be $V_1, \:V_2$ and their radii be $r_1, \:r_2$ respectively.

$\huge r_1 : r_2= 13 : 9$ (given)

$\implies\huge \frac{r_1}{r_2}= \frac{13}{9}.....(1)$

$\huge \frac{V_1}{V_2}=\frac{\cancel {\frac{4}{3} \pi} r_1^3}{\cancel {\frac{4}{3} \pi} r_2^3}$

$\huge \frac{V_1}{V_2}=\frac{ r_1^3}{r_2^3}$

$\huge \frac{V_1}{V_2}=\bigg(\frac{ r_1}{r_2}\bigg) ^3..... (2)$

From equations (1) & (2), we have:

$\huge \frac{V_1}{V_2}=\bigg(\frac{13}{9}\bigg) ^3$

$\huge \frac{V_1}{V_2}=\frac{2197}{729}$

$\huge \therefore V_1 : V_2= 2197 : 729$

Thus, the ratio of the volumes of two spheres would be 2197 : 729.

7 0

3 years ago

Read 2 more answers

In the United States, 35% of households own a 4K television. Suppose we take a random sample of 150 households. (a) Describe the

sattari [20]

Answer:

(a) The distribution of the sample proportion is Normal distribution.

(b) The probability that in this sample of 150 households that more than 50% own a 4K television is 0.00012.

Step-by-step explanation:

We are given that in the United States, 35% of households own a 4K television.

Suppose we take a random sample of 150 households.

Let $\hat p$ = sample proportion of households who own a 4K television.

The z-score probability distribution for sample proportion is given by;

Z = $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion

p = population proportion of households own a 4K television = 35%

n = sample of households = 150

(a) The distribution of the sample proportion is related to the Normal distribution.

(b) Probability that in this sample of 150 households more than 50% own a 4K television is given by = P( $\hat p$ > 0.50)

P( $\hat p$ > 0.50) = P( $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ > $\frac{ 0.50-0.35}{\sqrt{\frac{0.50(1-0.50)}{150} } }$ ) = P(Z > 3.67) = 1 - P(Z $\leq$ 3.67)

= 1 - 0.99988 = 0.00012

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.67 in the z table which has an area of 0.99988.

Therefore, probability that in this sample of 150 households more than 50% own a 4K television is 0.00012.

8 0

3 years ago