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3 years ago

Differentiate x+sinx/x+cosx with respect to x

Mathematics

1 answer:

givi [52]3 years ago

5 0

Step-by-step explanation:

content://com.cryptotab.android.FileProvider/images/screenshot/1615820475640483392397139554304.jp

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If someone could help!

ad-work [718]

Step-by-step explanation:

This time round, use SOH method (Sin angle = Opposite/Hypotenuse)

given Opposite = 7

Hypotenuse = 10

$\sin(x) = \frac{opposite}{hypotenuse} \\ \sin(x) = \frac{7}{10} \\ x = {sin}^{ - 1} ( \frac{7}{10} ) \\ = 44.4deg(nearest \: tenth)$

4 0

3 years ago

Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many h

Elden [556K]

Let

x-----> the number of hours that Candice spent doing her homework

y-----> the number of hours that Ronald spent doing his homework

we know that

$x=5\frac{1}{4}\ hours$

convert mixed number to an improper fraction

$5\frac{1}{4}\ hours=\frac{5*4+1}{4}= \frac{21}{4}\ hours$

$x=\frac{21}{4}\ hours$ -------> equation A

$y=\frac{1}{2}x$ ------> equation B

Substitute equation A in equation B

$y=\frac{1}{2}*\frac{21}{4}=\frac{21}{8}\ hours$

convert an improper fraction to a mixed number

$\frac{21}{8}\ hours=2.625=2+0.625=2+\frac{5}{8}=2\frac{5}{8}\ hours$

therefore

<u>the answer is the option B</u>

$2\frac{5}{8}\ hours$

5 0

3 years ago

Read 2 more answers

Geometry help! Picture included :)

AURORKA [14]

Set up a proprtion and cross multiply.

18/7.5=22/4x+1

7.5×22=18 (4x+1)
165=72x+18
147=72x
x=2.04

8 0

3 years ago

Paul currently has $300 to spend on a data plan. He found a phone for $100 and a $50 a month charge.

zvonat [6]

Let x= months
So 50x is the total amount he pays after x months. You went to add 100 to this because there's a fixed cost of 100 for the phone
So you have the expression 100+50x which is the amount he pays after x months
Since he has a limit of 300,
100+50x < 300

3 0

3 years ago

The following data were collected from 12 rain gauges in a park. Build a 95% CI for the mean rainfall at the park.

dybincka [34]

Answer:

Critical values: $t_{\alpha/2}=-2.201$ $t_{1-\alpha/2}=2.201$

95% confidence interval would be given by (3.646;4.472)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The data is:

4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87

2) Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$

=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

On this case the average is $\bar X= 4.059$

=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

The sample standard deviation obtained was s=0.6503

3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . The degrees of freedom are given by: