All categories

4 years ago

Find the equation of the tangent line to the curve y=6sinx at the point (π/6,3

1 answer:

6 0

Hello:
f(x) =6sin(x)
f'(x) = 6 cos(x)

the equation of the tangent line is : y=f'(π/6)(x-π/6)+f(π/6)
f'(π/6)=6cos(π/6)=6×(√3/2)=3√3
f(π/6) =3
the equation is : y = 3√3(x-π/6)+3

You might be interested in

A recipe uses 8 cups of milk for every 3 cups of oatmeal.

vampirchik [111]

If you divide 8 by three and you'd get 26 but the 6 keep reapeting

5 0

3 years ago

Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F. Sally's temperature can be described by z =

irina1246 [14]

Answer:

Sally's temperature is 97.27 °F.

Step-by-step explanation:

All the information given in the question tells us that the human body temperatures are normally distributed with a population's mean = 98.20°F and a standard deviation = 0.62°F.

The question gives us Sally's temperature in a z-score. We have to remember that the standard normal distribution is a particular case of a normal distribution where the mean = 0 and the standard deviation = 1.

Using the standard normal distribution, we can determine every probability associated with a normal distribution "transforming" the raw scores, coming from normally distributed data, into z-scores.

A z-score gives us the distance from the population's mean and is in standard deviation units. So, a z = 1.5 tells us that the value is 1.5 standard deviations above the mean. Conversely, a z = -1.5 tells us that the raw score is also 1.5 standard deviation from the mean, but in the opposite direction, that is, below the mean.

The formula for a z-score is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ (1)

Where

$\\ x\;is\;the\;raw\;score$ .

$\\ \mu\;is\;the\;population\;mean$ .

$\\ \sigma\;is\;the\;population\;standard\;deviation$ .

Then to find x (or the raw score, that is, Sally's temperature), we need to solve the formula (1) for it to finally solve the question.

Then

$\\ \mu = 98.20^\circF$ °F

$\\ \sigma = 0.62^\circF$ °F

$\\ z = -1.5$

Thus (with no units)

$\\ -1.5 = \frac{x - 98.20}{0.62}$

$\\ (-1.5*0.62) = x - 98.20$

$\\ (-1.5*0.62) + 98.20 = x$

$\\ x = (-1.5*0.62) + 98.20$

$\\ -0.93 + 98.20$

$\\ x = 97.27$ °F

Thus, Sally's temperature is $\\ x = 97.27$ °F (rounding the answer to the nearest hundredth).

8 0

3 years ago

Read 2 more answers

I need help in this question that is in the photo

mihalych1998 [28]

The answer is A, 1. In the statement x^2 >x, if we try 4, 5 and 8 for x, we get 16, 25 and 64 for x^2. The statement is true. But if we try x = 1, when we square it we still have 1. Therefore for x=1, x^2>x is false.

7 0

3 years ago

What is the LCM of 24a^3 b and 36ab^2? 12ab 24a 3b^2 36ab 72a 3b^2

Finger [1]

I hope this helps you

4 0

3 years ago

If a video game was 10% off and the amount of the discount was $6 what was the original price?

Alenkinab [10]

Answer: the original price was $60! <3

Step-by-step explanation:

4 0

3 years ago