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3 years ago

What is the derivative of arcsin(6x)

1 answer:

8 0

$\bf sin^{-1}(6x)\\\\
-----------------------------\\\\
\textit{using the chain-rule}\implies \cfrac{d}{dx}\left[ sin^{-1}(6x) \right]\implies \cfrac{1}{\sqrt{1-(6x)^2}}\cdot 6\\\\ \cfrac{6}{\sqrt{1-36x^2}}$

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What is 96-8c=20-12

galben [10]

Answer:

c = 11

Step-by-step explanation:

96 - 8c = 20 - 12 , that is

96 - 8c = 8 ( subtract 96 from both sides )

- 8c = - 88 ( divide both sides by - 8 )

c = 11

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2 years ago

All 3,000 seats in a theater are being replaced. So far, 5 sections 136 seats and a sixth section containing 348 seats have been

Ostrovityanka [42]

1,124 seats still need to be replaced.

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3 years ago

Read 2 more answers

The table below represents a function. Which of the following equations could be its function rule?

worty [1.4K]

Answer:

$y=2x-2$ is the required equation.

Therefore, the second option is true.

Step-by-step explanation:

We know that the slope-intercept form of the line equation of a linear function is given by

$y=mx+b$

where m is the slope and b is the y-intercept

Taking two points (0, -2) and (1, 0) from the table to determine the slope using the formula

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:-2\right),\:\left(x_2,\:y_2\right)=\left(1,\:0\right)$

$m=\frac{0-\left(-2\right)}{1-0}$

$m=2$

substituting the point (0, -2) and the slope m=2 in the slope-intercept form to determine the y-intercept i.e. 'b'.

$y=mx+b$

$-2 = 2(0)+b$

$-2=0+b$

$b=-2$

Now, substituting the values of m=2 and b=-2 in the slope-intercept form to determine the equation of a linear function

$y=mx+b$

$y=2x+(-2)$

$y=2x-2$

Thus, $y=2x-2$ is the required equation.

Therefore, the second option is true.

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2 years ago

For women aged 19-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation

Mrac [35]

Answer: p = 0.00714

Step-by-step explanation:

Since the population standard deviation of the distribution is known, the z test ( which produces the z score) is the perfect test for finding the probability of the data set in the question.

From the question,

Population mean (u) = 114.8

Sample mean (x) = 121.5

Population standard deviation (σ) = 13.1

Sample size (n) = 23

The z score formulae is given below as

Z = x - u/σ/√n

Z = 121.5 - 114.8/(13.1/√23)

Z = 6.7/(13.1/√23)

Z = 6.7/2.731

Z = 2.45.

The question is interested in knowing the probability of mean systolic blood pressure greater than 121.5.

This implies that we are looking for the probability at which our z score is greater than 2.45: P(z>2.45)

The z score (z=2.45) has divided the distribution into two regions, z< 2.45 ( area to the left of the distribution) and z>2.45 ( area to the right of distribution).

Hence, p(z>2.45) + p(z<2.45) = 1

To get a the probability, we have to use a standard normal distribution table.

The table we have here gives probability of the distribution to the left ( that's area towards the left), hence we need to find p(z<2.45) first

From the table p(z<2.45) = 0.99286

But p(z>2.45) = 1 - p(z<2.45)

p(z>2.45) = 1 - 0.99286

p(z>2.45) = 0.00714

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3 years ago

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2 years ago