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2 years ago

Find the derivative using the first principles.

Mathematics

1 answer:

lubasha [3.4K]2 years ago

3 0

$~~~~\dfrac{d}{dx} \left( \sqrt[5]{1+x} \right)\\\\\\=\dfrac{d}{dx} (1+x)^{\tfrac 15}\\\\\\=\dfrac 15 \left(1 + x\right)^{\tfrac 15 -1} \cdot \dfrac{d}{dx}(1+x)\\\\\\=\dfrac 15 (1+x)^{-\tfrac 45} \cdot(0+1)\\\\\\=\dfrac{1}{5(1+x)^{\tfrac 45}}$

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13x+5y=90 what is x? what is y?

Leona [35]

Answer:

X=-5y/13+90/13, Y=-13x/5+18

Step-by-step explanation:

You need to solve the equation for X and Y.

Solving for X:

13x+5y=90

Subtract 5y: 13x=-5y+90

Divide by 13: x=-5y/13+90/13

For Y:

13x+5y=90

Subtract 13x: 5y=-13x+90

Divide by 5: y=-13x/5+90/5

(Simplifies to -13x/5+18)

3 0

3 years ago

Write the sentence as a proportion: $3.50 for 9 bottles is equivalent to $31.50 for 81 bottles.

melamori03 [73]

Answer:

$0.39:1

Step-by-step explanation:

$0.39:1

Dividing the amount by the cost of the bottles.

8 0

3 years ago

The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $3

DerKrebs [107]

Using the normal distribution, it is found that the probabilities are given as follows:

a) 0.8871 = 88.71%.

b) 0.0778 = 7.78%.

c) 0.8485 = 84.85%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

The parameters in this problem are given as follows:

$\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5$

Item a:

The probability is the <u>p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000</u>, hence:

X = 1250:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{1250 - 1140}{77.5}$

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

X = 1000:

$Z = \frac{X - \mu}{s}$

$Z = \frac{1000 - 1140}{77.5}$

Z = -1.81

Z = -1.81 has a p-value of 0.0351.

0.9222 - 0.0351 = 0.8871 = 88.71% probability.

Item b:

The probability is <u>one subtracted by the p-value of Z when X = 1250</u>, hence:

1 - 0.9222 = 0.0778 = 7.78%.

Item c:

The probability is the <u>p-value of Z when X = 1220</u>, hence:

$Z = \frac{X - \mu}{s}$

$Z = \frac{1220 - 1140}{77.5}$

Z = 1.03

Z = 1.03 has a p-value of 0.8485.

0.8485 = 84.85% probability.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

3 0

2 years ago

Pls help meee and thank you

Dmitry [639]

Answer:

i can help u

Step-by-step explanation:

tell me what it is

8 0

3 years ago

Read 2 more answers

Four tenths plus four ninths

olga2289 [7]

Answer:

38/45

Step-by-step explanation:

4/10+4/9 Simplify.

2/5*4/9 Find a common denominator (45).

2/5*9/9=18/45

4/9*5/5=20/45

18/45+20/45=38/45

Hope this helps and have a great day C:

8 0

3 years ago

Find the derivative using the first principles. ​

Find the derivative using the first principles.