Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = 6 sin x, y = 6 cos x, 0 ≤ x ≤ π/4; about y = −1

Answers

Answer 1

Answer: hmm well, here an example y=3 ,

y=3 , rather than the x− x− axis.) Your integrand looks fine and reduces to

(9−18sinx+9sin2x) − (9−18cosx+9cos2x) (9−18sin⁡x+9sin2⁡x) − (9−18cos⁡x+9cos2⁡x)

= 18 (cosx−sinx) + 9 (sin2x−cos2x) = 18 (cosx−sinx) − 9 cos2x .= 18 (cos⁡x−sin⁡x) + 9 (sin2⁡x−cos2⁡x) = 18 (cos⁡x−sin⁡x) − 9 cos⁡2x .

The evaluation of the volume is then

π [ 18 (sinx+cosx) − 92sin2x ]π/40π [ 18 (sin⁡x+cos⁡x) − 92sin⁡2x ]0π/4

= π ( [ 18 ( 2–√2+2–√2) − 92⋅1 ] − [ 18 (0+1) − 92⋅0 ] ) = π ( [ 18 ( 22+22) − 92⋅1 ] − [ 18 (0+1) − 92⋅0 ] )

= π ( 182–√ − 92 − 18 ) = π ( 182–√ − 452 ) or 9π2 ( 42–√ − 5 ) ,

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The average starting salary of this year's vocational school graduates is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Answers

Answer:

Minimum: $25,200

Maximum: $44,800

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

$Z = (X - \mu)/(\sigma)$

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.

In this question:

$\mu = 35000, \sigma = 5000$

What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Minimum: 50 - (95/2) = 2.5th percentile.

Maximum: 50 + (95/2) = 97.5th percentile

2.5th percentile:

X when Z has a pvalue of 0.025. So X when Z = -1.96.

$Z = (X - \mu)/(\sigma)$

$-1.96 = (X - 35000)/(5000)$

$X - 35000 = -1.96*5000$

$X = 25200$

The minimum is $25,200

97.5th percentile:

X when Z has a pvalue of 0.975. So X when Z = 1.96.

$Z = (X - \mu)/(\sigma)$

$1.96 = (X - 35000)/(5000)$

$X - 35000 = 1.96*5000$

$X = 44800$

The maximum is $44,800

2Viviana is ordering carpet

for 16 square rooms in a

hotel. Each room will need

100 square feet of

carpet. What is the

length of 1 room?

Answers

Answer:

Length of a room is 10ft

Step-by-step explanation:

Given

$Rooms = 16$

$Carpet\ Area = 100ft^2$

Required

Determine the length of each room

Here, we'll assume that the carpet will cover each room completely.

If so:

$Carpet\ Area = Length * Length$

$100ft^2 = Length * Length$

$100ft^2 = Length^2$

Take square root of both sides

$√(100ft^2) = √(Length^2)$

$√(100ft^2) = Length$

Take positive square root

$10ft = Length$

$Length = 10ft$

Hence, the length of a room is 10ft

Three teams, A, B and C, play in a competition.games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 8 games.
In total, how many games have the three teams won?

Answers

Answer:

A = 24

B = 8

C = 6

Step-by-step explanation:

4:3 from B:C

8:6

8 games won by B and 6 games won by C.

3:1 from A:B

24:8

24 by A and 8 by B

Final answer:

Team A won 24 games, Team B won 8 games and Team C won 6 games. So, the total games won by all three teams is 38.

Explanation:

From the problem, we know that the ratio of games won by Team A to Team B is 3:1, and the ratio of games won by Team B to Team C is 4:3. We also know that Team B has won 8 games.

Since the ratio of Team B to Team A is 1:3, Team A must have won 3 times as many games as Team B. Therefore, Team A has won 3 * 8 = 24 games.

The ratio of games won by Team B to Team C is 4:3. This means Team B won 4 games for every 3 games Team C won. Since Team B won 8 games, Team C must have won 3/4 as many games as Team B. Therefore, Team C won 3/4 * 8 = 6 games.

So, in total, the three teams won 24 + 8 + 6 = 38 games.

Learn more about Ratio here:

brainly.com/question/32531170

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Four friends want to share two largepizzas equally. Each pizza is cut into
ten slices. How many slices will each
person get?

Answers

Answer: 5

Step-by-step explanation:

2 pizzas ten slices eatch, so 20 slices. 20 slices devided by 4 is five. :)

More on the Leaning Tower of Pisa. Refer to the previous exercise. (a) In 1918 the lean was 2.9071 meters. (The coded value is 71.) Using the least-squares equation for the years 1975 to 1987, calculate a predicted value for the lean in 1918. (Note that you must use the coded value 18 for year.)