1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
castortr0y [4]
3 years ago
12

College calculus: volume of a solid

Mathematics
1 answer:
Oliga [24]3 years ago
3 0
First, start by graphing the given region.
You should get a parabolic shape with min at (0,6) and end points intersecting with y=7.
When you rotate this around y=5, it will look like a vertical doughnut.
The cross-section of a doughnut is circular and looks like a washer.

Hence, we will use the 'washer method'
V = \pi  \int\limits^a_b {R^2 - r^2} \, dx
R is radius of outer ring from center which is y=5. The max value of region is y=7, giving a distance of 2 for our radius.
R = 2
'r' is radius of inner ring, this is point along curve f(x)=5+sec(x).
The distance from y=5 would be f(x) - 5.
r = sec(x)

V = \pi  \int\limits^{\pi/3}_{-\pi/3} {4 - sec^2 (x)} \, dx  \\  \\  \\ V = \pi |_{-\pi/3}^{\pi/3}(4x - tan x) \\  \\  \\ V = \frac{8\pi^2}{3} - 2\sqrt{3} \pi
You might be interested in
Define intersecting lines
kakasveta [241]

Answer:

lines that meet at a point

4 0
3 years ago
CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars
velikii [3]

Answer:

P(939.6 < X < 972.5) = 0.6469

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that \mu = 965, \sigma = 113

Sample of 57:

This means that n = 57, s = \frac{113}{\sqrt{57}} = 14.97

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

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

By the Central Limit Theorem

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

Z = \frac{972.5 - 965}{14.97}

Z = 0.5

Z = 0.5 has a pvalue of 0.6915

X = 939.6

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

Z = \frac{939.6 - 965}{14.97}

Z = -1.7

Z = -1.7 has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

So

P(939.6 < X < 972.5) = 0.6469

3 0
2 years ago
HELP WILL MARK BRAINLIEST TO BEST ANSWER!!!!!!!!<br> I NEED ASAP
Bond [772]
Answer is B

Find perimeter then divide by 3 (because price is per 3 meters) then times by 500 to get the answer
4 0
3 years ago
Which pairs of variables would most likely have a positive association? Choose all that apply.
alex41 [277]

Answer:

The age of a kitten and it’s weight

Temperature and sales of Ice Cream

The number of notebooks bought and the total cost

Step-by-step explanation:

8 0
3 years ago
the hight, the feet, of a javelin t seconds afther it is moldeled by the function (t) =4t^2 + 24t + 6. Afther how many seconds d
ruslelena [56]
The max height will be reached after 3 seconds.

You have a typo in your equation. For this type of quadratic equation, it always starts out with a negative coefficient of the t squared term.

To find the x-coordinate of the vertex, we just need to use the expression: -b/2a.

Then, we have:

-24 / (2(-4))

-24 / -8

3
8 0
3 years ago
Other questions:
  • A bird feeder is in the shape of a cylinder. It has a volume of about 100 cubic inches. It has a radius of 2 inches. What is the
    14·2 answers
  • Jared is using a 100 ft rope to set up a kite-shaped area for food vendors. He has started roping off the area as shown below, a
    5·2 answers
  • Mary and her dad shared one dozen brownies 2/6 of them have nuts which dad doesn't eat how many brownies did dad not eat because
    7·2 answers
  • POINTS GIVE AWAYY !!!!!!! FOLLOW ME FOR MOREEEEEEE YEEEE​
    11·1 answer
  • Can anybody help me solve for surface area?<br><br><br> (Formula=add all the areas of the faces)
    13·1 answer
  • Volume of cylinder, write the term in pie
    12·1 answer
  • WILL GIVE BRAINLIEST!! Priscilla received 240 votes in the election for student council president. That was 60% of the students
    10·2 answers
  • HELP
    10·2 answers
  • LOOK AT PICTURE BELOW
    12·1 answer
  • Find the locus of a point P which moves so that the sum of squares of squares of its distance A(3,0)and B(-3,0) is 4 times the d
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!