Consider the following. x = 6 sin y , 0 ≤ y ≤ π, x = 0; about y = 4
(a) Set up an integral for the volume V of the solid obtained by rotating the region bounded by the given curve about the specified axis.
(b) Use your calculator to evaluate the integral correct to four decimal places.

Answer:

i think this person answered but idrk perseusharrison79

Step-by-step explanation:

For 2 parallelograms, the corresponding side lengths are 1 inch and x inches, and 2 inches and 6 inches.

Not drawn to scale

StartFraction 1 over x EndFraction = StartFraction 2 over 6 EndFraction

StartFraction 1 over x EndFraction = StartFraction 6 over 2 EndFraction

StartFraction 1 over 6 EndFraction = StartFraction 2 over x EndFraction

One-half = StartFraction 6 over x EndFraction

Step-by-step explanation:

Answer:

The common difference is 1/2

Step-by-step explanation:

Data obtained from the question include:

3rd term (a3) = 0

Common difference (d) =.?

From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:

a7 – 2a4 = 1

Recall:

a7 = a + 6d

a4 = a + 3d

a3 = a + 2d

Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.

But, a3 = 0

a3 = a + 2d

0 = a + 2d

Rearrange

a = – 2d

Now:

a7 – 2a4 = 1

Substituting the value of a7 and a4, we have

a + 6d – 2(a + 3d) = 1

Sustitute the value of 'a' i.e –2d into the above equation, we have:

–2d + 6d – 2(–2d + 3d) = 1

4d –2(d) = 1

4d –2d = 1

2d = 1

Divide both side by 2

d = 1/2

Therefore, the common difference is 1/2

***Check:

d = 1/2

a = –2d = –2 x 1/2 = –1

a3 = 0

a3 = a + 2d

0 = –1 + 2(1/2)

0 = –1 + 1

0 = 0

a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2

a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2

= (–2 + 3)/2 = 1/2

a7 – 2a4 = 1

2 – 2(1/2 = 1

2 – 1 = 1

1 = 1

Answer:

The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm

The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm

The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm

Answer:

1/3 feet.

Step-by-step explanation:

The length = area / width

= 7/9 / 2 1/3

= 7/9 / 7/3

= 7/9 * 3/7

= 3/9

= 1/3 feet,

Answer:

√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.

Answer:

[tex] 7\sqrt{3} [/tex]

Step-by-step explanation:

[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]

the answer is the bottom left option

Correct question:

The vector matrix [ [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex] is dilated by a factor of 1.5 and then reflected across the x axis. If the resulting matrix is [a/b] then a=??? and b=???

Answer:

a = 3

b = 10.5

Step-by-step explanation:

Given:

Vector matrix = [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex]

Dilation factor = 1.5

Since the vector matrix is dilated by 1.5, we have:

[tex] \left[\begin{array}{ccc}1.5 * 2\\1.5 * 7\end{array}\right] [/tex]

= [tex] \left[\begin{array}{ccc}3\\10.5\end{array}\right] [/tex]

Here, we are told the vector is reflected on the x axis.

Therefore,

a = 3

b = 10.5

Answer:

a = 3

b = -10.5

Step-by-step explanation:

got a 100% on PLATO

Answer:

Answer:

Do you have an image because I'm a bit confused with you just asking the measure of PSQ.

Step-by-step explanation:

Answer:

  5 feet

Step-by-step explanation:

"Twice as tall" means "2 times as tall".

  2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft

The child's mother is 5 feet tall.

Answer:

The mother is 5ft tall

Step-by-step explanation:

2 1/2 + 2 1/2 = 5ft

2ft+2ft = 4ft

1/2+1/2= 1ft

4ft+1ft = 5ft

Answer:

1,050 workers

Step-by-step explanation:

25% = 0.25

0.25 × 1400 = 350

1400 - 350 = 1050

Hope this helps.

Answer:

a) 16xy³

Step-by-step explanation:

For a binomial expansion (a + b)ⁿ, the r+1 term is:

nCr aⁿ⁻ʳ bʳ

Here, a = 4x, b = y, and n = 4.

For the fourth term, r = 3.

₄C₃ (4x)⁴⁻³ (y)³

4 (4x) (y)³

16xy³

I'm not sure what exactly you did wrong, but I agree with you that the sample size is too small, so the correct answer will probably be the fourth options. Hope that this gives you some confidence, and 'm sorry not to be able to help you any further...

Answer: a) additive inverse (addition)

              b) multiplicative inverse (division)

Step-by-step explanation:

Step 2: 6 is being added to both sides

Step 4: (3/4) is being divided from both sides

It is difficult to know what options are provided in the drop-down menu without seeing them. If I was to complete a proof and justify each step, then the following justifications would be used:

Step 2: Addition Property of Equality

Step 4: Division Property of Equality

Hey there! I'm happy to help!

We see that if the river isn't moving at all the boat can move at 18 mph (most likely because it has an engine propelling it.)

We want to set up a proportion where our 21 miles downstream time is equal to our 15 miles upstream time so we can find the speed. A proportion is basically showing that two ratios are equal. Since our downstream distance and upstream distance can be done in the same amount of time, we will write it as a proportion.

We want to find the speed of the river. We will use r to represent the speed of the river. When going downstream, the boat will go faster, so it will have a higher mph. So, our speed going down is 18+r. When you are going upstream, it's the opposite, so it will be 18-r.

[tex]\frac{distance}{speed} =\frac{21}{18+r} = \frac{15}{18-r}[/tex]

So, how do we figure out what r is now? Well, one nice thing to know about proportions is that the product of the items diagonal from each other equals the product of the other items. Basically, that means that 15(18+r) is equal to 21(18-r). This is a very nice trick to solve proportions quickly. We see that we have made an equation and now we can solve it!

15(18+r)=21(18-r)

We use the distributive property to undo the parentheses.

270+15r=378-21r

We subtract 270 from both sides.

15r=108-21

We add 21 to both sides.

36r=108

We divide both sides by 36.

r=3

Therefore, the speed of the river is 3 mph.

You also could have noticed that 18mph to 21 mph is +3, and 18mph to 15 mph -3 in -3 mph, so the speed of the river is 3 mph. That would have been a quicker way to solve it XD!

Have a wonderful day!

Answer:

(190-5a)°

Step-by-step explanation:

Sum of internal angles of a triangle equals to 180°

If the third angle is x, then we have:

The third angle is: (190-5a)°

Answer:

n = 5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 30 = n/ 5 sqrt(3)

5 sqrt(3) tan 30 = n

5 sqrt(3) * 1/ sqrt(3) = n

5 = n

Answer:

[tex] \frac{1}{6} [/tex]

Step-by-step explanation:

the ways of choosing 2 cards out of 4, is calculator by

[tex] \binom{4}{2} = 6[/tex]

so, 6 ways to select 2 cards.

but in only one way we can have 2 even cards. thus, the answer is

[tex] \frac{1}{6} [/tex]

Answer:

The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].

Step-by-step explanation:

The equation of the curvature is:

[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]

The parametric componentes of the curve are:

[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]

The first and second derivative associated to each component are determined by differentiation rules:

First derivative

[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]

[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]

Second derivative

[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]

[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]

[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]

[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]

Now, each term is replaced in the the curvature equation:

[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]

And the resulting expression is simplified by algebraic and trigonometric means:

[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]

[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]

[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]

[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]

[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]

The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].

Answer:

The original digit is 62

Step-by-step explanation:

Let the Tens be represented with T

Let the Units be represented with U

Given:

Unknown Two digit number

Required:

Determine the number

Since, it's a two digit number, then the number can be represented as;

[tex]T * 10 + U[/tex]

From the first sentence, we have that;

[tex]T = 4 + U[/tex]

[tex]T = 4+U[/tex]

Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]

So;

[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]

[tex]10U + T + 10T + U= 88[/tex]

Collect Like Terms

[tex]10U + U + T + 10T = 88[/tex]

[tex]11U + 11T = 88[/tex]

Divide through by 11

[tex]U + T = 8[/tex]

Recall that [tex]T = 4+U[/tex]

[tex]U + T = 8[/tex] becomes

[tex]U + 4 + U = 8[/tex]

Collect like terms

[tex]U + U = 8 - 4[/tex]

[tex]2U = 4[/tex]

Divide both sides by 2

[tex]U = 2[/tex]

Substitute 2 for U in [tex]T = 4+U[/tex]

[tex]T = 4 + 2[/tex]

[tex]T = 6[/tex]

Recall that the original digit is [tex]T * 10 + U[/tex]

Substitute 6 for T and 2 for U

[tex]T * 10 + U[/tex]

[tex]6 * 10 + 2[/tex]

[tex]60 + 2[/tex]

[tex]62[/tex]

Hence, the original digit is 62

Step-by-step explanation:

pnotgrt8rthan4 = 3 ÷ 7 × 100

= 42.8571428571 / 43%

Answer:

Each table is $6 and each chair is $2.50

Step-by-step explanation:

Answer:

Factoring is a useful skill in real life. Common applications include: dividing something into equal pieces, exchanging money, comparing prices, understanding time, and making calculations during travel.

Sorry if this is a little wordy, I can get carried away with this sort of thing

anyway, hope this helped and answered your question :)

Answer:

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Step-by-step explanation:

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

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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, we have that:

[tex]\mu = 13, \sigma = 0.2[/tex]

What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster

We have to find the pvalue of Z when X = 13.36.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13.36 - 13}{0.2}[/tex]

[tex]Z = 1.8[/tex]

[tex]Z = 1.8[/tex] has a pvalue of 0.9641

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Answer:

Step-by-step explanation:

k = 3 ; 2k + 2 = 2*3 + 2 = 6 + 2 = 8

k = 4;  2k + 2 = 2*4 + 2 = 8 +2 = 10

k =5; 2k + 2 = 2*5 +2 = 10+2 = 12

k=6;  2k +2 = 2*6 + 2 = 12+2 = 14

k = 7 ; 2k + 2 = 2*7 +2 = 14 +2 = 16

k = 8 ; 2k + 2 = 2*8 + 2 = 16 +2 = 18

∑ (2k + 2) = 8 + 10 + 12 + 14 + 16 + 18 = 78

Answer:

12am

Step-by-step explanation:

Answer:

12:00 am or midnight

Step-by-step explanation:

00 00 hrs in 12-hours clock is 12:00 am or 12:00 o'clock midnight.

Answer:

[tex]153.86 \: {units}^{2} [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]

Answer:

153.86 [tex]units^{2}[/tex]

Step-by-step explanation:

Areaof a circle = πr^2

[tex]\pi = 3.14[/tex](in this case)

[tex]r^{2} =7[/tex]

A = πr^2

= 49(3.14)

= 153.86

Answer:

B. [tex]4^2[/tex]

Step-by-step explanation:

[tex]4^7 \times 4^{-5}[/tex]

Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]

[tex]4^{7 + -5}[/tex]

Add exponents.

[tex]=4^2[/tex]

Answer:

Step by step explanation

[tex] {4}^{7} \times {4}^{ - 5} [/tex]

Use product law of indices

i.e

[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]

( powers are added in multiplication of same base)

[tex] = {4}^{7 + ( - 5)} [/tex]

[tex] = {4}^{7 - 5} [/tex]

[tex] = {4}^{2} [/tex]

Hope this helps...

Best regards!

Answer:

1/5

Step-by-step explanation:

The number 5 or greater than 4 is 5.

1 number out of 5 total parts.

= 1/5

P(5 or greater than 4) = 1/5

Answer:

Option (c).

Step-by-step explanation:

It is given that, I paid twice as much by not waiting for a sale and not ordering online.

Let the cost of items ordering online be x.

So, now i am paying twice of x = 2x

Now, we have find 2x is what percent of x.

[tex]Percent =\dfrac{2x}{x}\times 100=200\%[/tex]

It means, I paid 200% of what I could have online and on sale.

Therefore, the correct option is (c).