Will mark brainliest! Determine whether the rectangles are similar. If so, write the similarity
ratio and a similarity statement.

The work done by vector field F on the particle moving along curve C is 11.

To compute the work done by vector field F on a particle moving along curve C, we can use the line integral. The line integral of a vector field F along a curve C is given by:

∫ F · dr

where F is the vector field and dr is the differential displacement along the curve.

Given:

Curve C: r(t) = (1 + 3sin(t))i + (1 + 4sin²(t))j + (1 + 4sin³(t))k, 0 ≤ t ≤ π/2

Vector Field F: F(x, y, z) = xi + yj + zk

To compute the line integral, we need to parameterize the curve C. We can use the given parameterization r(t) to obtain the differential displacement vector field dr.

dr = (dx/dt)dt i + (dy/dt)dt j + (dz/dt)dt k

Let's calculate the line integral step-by-step:

Calculate the differential displacement vector dr:

dx/dt = 3cos(t)

dy/dt = 8sin(t)cos(t)

dz/dt = 12sin²(t)cos(t)

dr = (3cos(t))dt i + (8sin(t)cos(t))dt j + (12sin²(t)cos(t))dt k

Compute F · dr:

F · dr = (xi + yj + zk) · ((3cos(t))dt i + (8sin(t)cos(t))dt j + (12sin²(t)cos(t))dt k)

= 3cos(t)dt + 8sin(t)cos(t)dt + 12sin²(t)cos(t)dt

= (3cos(t) + 8sin(t)cos(t) + 12sin²(t)cos(t))dt

Integrate F · dr along the curve C with respect to t from 0 to π/2:

∫ F · dr = ∫[0 to π/2] (3cos(t) + 8sin(t)cos(t) + 12sin²(t)cos(t))dt

To evaluate this integral, we can split it into three separate integrals:

I₁ = ∫[0 to π/2] 3cos(t) dt

I₂ = ∫[0 to π/2] 8sin(t)cos(t) dt

I₃ = ∫[0 to π/2] 12sin²(t)cos(t) dt

Let's calculate each integral:

I₁ = ∫[0 to π/2] 3cos(t) dt

= [3sin(t)] from 0 to π/2

= 3sin(π/2) - 3sin(0)

= 3 - 0 = 3

I₂ = ∫[0 to π/2] 8sin(t)cos(t) dt

= [4sin²(t)] from 0 to π/2

= 4sin²(π/2) - 4sin²(0)

= 4 - 0

= 4

I₃ = ∫[0 to π/2] 12sin²(t)cos(t) dt

= [4sin³(t)] from 0 to π/2

= 4sin³(π/2) - 4sin³(0)

= 4 - 0

= 4

Now, we can find the total line integral:

∫ F · dr = I₁ + I₂ + I₃

= 3 + 4 + 4

= 11

Therefore, the work done by vector field F on the particle moving along curve C is 11.

To know more about vector field check the below link:

https://brainly.com/question/31400700

#SPJ4

Incomplete question:

If C is the curve given by r (t) = (1 + 3 sin t) i + (1+4 sin² t) j + (1+4 sin³ t) k, 0 ≤t ≤ π/2 and F is the radial vector field F(x, y, z) = xi+yj+zk, compute the work done by F on a particle moving along C.

Answer:

The answer is $82.46 sales tax

$1,260.46 Total

Step-by-step explanation:

Since the price before the Sales tax is $1,178.00 and if you add the 7% Sales tax the total is $1,260.46 and the price of the Sales tax is $82.46

The "integers"— , positive, negative, NOT zero. The "rational numbers"— , or fractions, like 355/113.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Read more about area here:https://brainly.com/question/27440983

#SPJ1

the greatest common factor of the given expressions is -5xy.

To find the greatest common factor of the given expressions, we need to factor them first.

\(-15x^2y - 10xy^3 + 5xy^4 = -5xy(3x^2 + 2y^2 - y^3)\\5xy = 5xy(1)\\5x^2y^4 = 5xy^4(x^2)\\5xy^2 = 5xy^2(1)\)

xy = xy(1)

Now, we can find the common factors by taking the minimum exponent of each variable in the factors:

The common factors are:5xy

Therefore, the greatest common factor of the given expressions is -5xy.

Learn more about factor here

https://brainly.com/question/29128446

#SPJ1

Answer:

I think it's 10-x because that would give you a negative number

Answer:

2

Step-by-step explanation:

The equation is equal to 6-3x=8x-16. This gives 11x=22. x=2

It would take approximately 6 minutes to travel through the thickest oceanic crust at a speed of 100 km/hr.

To determine the time it would take to travel through the thickest oceanic crust at a speed of 100 km/hr, we need to know the thickness of the oceanic crust.

The oceanic crust is the outermost layer of the ocean floor and is generally thinner than the continental crust. On average, the thickness of the oceanic crust ranges from 5 to 10 kilometers (km). However, the thickness can vary depending on the specific location and geological factors.

Assuming we consider the thickest part of the oceanic crust, which could be up to 10 km thick, we can calculate the time it would take to travel through it at a speed of 100 km/hr.

Using the formula Time = Distance / Speed, we can determine the time as follows:

Time = (Thickness of Oceanic Crust) / (Speed)

Time = 10 km / 100 km/hr = 0.1 hr

Converting 0.1 hour to minutes, we have:

Time = 0.1 hr * 60 min/hr = 6 minutes

The correct answer is D. 6 minutes. This calculation is based on the assumption that we are considering the thickest part of the oceanic crust, which is approximately 10 km thick. It's important to note that the actual thickness of the oceanic crust can vary, and the time required would depend on the specific thickness encountered during the journey.

Learn more about approximately here:

https://brainly.com/question/31695967

#SPJ11

Answer:

29 is the answer

Step-by-step explanation:

the answer is 29

Answer:

the anwser is gonna be 29 blood

Using the combination, 1716 are 7 digit phone numbers in which the digits are non-increasing and every digit is less than or equal to the previous one.

In the given question,

We have to find how many 7 digit phone numbers are there in which the digits are non-increasing and that is, every digit is less than or equal to the previous one.

We have to write 7 digit phone number.

Let the 7 digit are

A, B, C, D, E, F, G

Every digit is less than or equal to the previous one.

A ≥ B ≥ C ≥ D ≥ E ≥ F ≥ G

The sum of these number is 7.

So |A| + |B| + |C| + |D| + |E| + |F| + |G| = 10

We always have precisely one non-increasing digit for any given set of seven digits. Therefore, the solution to our problem is to make it simpler to calculate the total number of combinations where 7 digits must be chosen from a set of 7 digits where each digit is repeatable.

So the solution should be

= \(^{7+7-1}C_{7}\)

= \(^{13}C_{7}\)

We know that \(^nC_{r}=\frac{n!}{r!(n-r)!}\)

= \(\frac{13!}{7!(13-7)!}\)

= \(\frac{13!}{7!6!}\)

Simplifying

= \(\frac{13\times12\times11\times10\times9\times8\times7!}{7!\times6\times5\times4\times3\times2\times1}\)

Simplifying

= 13×11×2×3×2

= 1716

Hence, 1716 are 7 digit phone numbers in which the digits are non-increasing and every digit is less than or equal to the previous one.

To learn more about combination link is here

https://brainly.com/question/14685054

#SPJ4

Answer:

So if James has 30 candy it would be best to do it in multiple ways in my opinion, so basically you can divide it among 3 kids including James where the kids get 10 each or you can divide it among 6 kids (still including James) and they all get 5 pieces of candy! Hope this helps and stay safe :)

Step-by-step explanation:

Possible Answers:

14 kids and james- 2 candies each

9 kids and james- 3 candies each

1 kid and james -  15 candies each

4 kids and james - 6 candies each

2 kids and james - 10 candies each

There might be more, but those are the ones at the top of my head

I hope this helped, please mark Brainliest, thank you!! :)

Answer:

$288.43

Step-by-step explanation:

$347.14 - $58.71 = $288.43

Hope this helped! Good luck in Math! Also, I also have a question that someone needs to answer to lol. Have a good day!

The steps that are possible when solving the equation are as follows:

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Therefore, let's solve the equation step by step.

\(5\frac{1}{2}x+ \frac{2}{3}x = 37\)

let's convert the mixed fraction to improper fractions.

\(\frac{11}{2}x+\frac{2}{3}x = 37\)

Let's take the next step by adding the like terms on the left side of the equation.

\(\frac{3(11)x+2(2)x}{6}=37\)

\(\frac{33x+4x}{6}=37\)

\(\frac{37x}{6} = 37\)

The next step is to cross multiply the equation.

37x = 37 × 6

37x = 222

divide both sides by 37

x = 222 / 37

x = 6

learn more on equation here: https://brainly.com/question/29198159

#SPJ1

Answer:

2+2 = 4

Step-by-step explanation:

ADD DOS PLUS DOS

Answer:

10/2=15/?

Step-by-step explanation:

I can help you to your all question but it need time. I have to write short.

?=3

Answer:

C

Step-by-step explanation:

This is called the hinge theorem, where you find out if an angle is small or big. first, you draw a triangle out and label it. when you finish this you can go and find the smallest side. The angle across from the side will be the smallest. In this problem, the smallest is <H, but that answer is not on there. So you can go and find the largest side and then the angle across from it will be the biggest, which is <G. Since the only thing, the question is asking for is "which statement is true", you can put C because <G is the biggest.

Answer:

£56

Step-by-step explanation:

We know

The ratio Zoe and Hannah hare tip is

3:7

last week Zoe received £24

To find out how much did Hannah receive last week, we first take

24 / 3 = 8

Then we take

8 times 7 = £56

So, last wee Hannah receive £56

Answer:

both of the triangels  have an area of 400

If the price of the dream car will increase at an annual rate of 1.7 percent, it will cost about $62,232.25 after 7 years.

To find the future cost of the dream car in 7 years, we can use the formula for compound interest.

The formula for compound interest is given:

A = P (1 + r/n)^nt

Where:

A = amount of money after n years

P = principal (initial) amount of money

r = annual interest rate

t = number of years

n = number of times interest is compounded per year

Given that the dream car costs $52,300 today and it will increase at an annual rate of 1.7%, we can find the future cost of the car in 7 years as follows:

P = $52,300r = 1.7% = 0.017t = 7 years

n = 1 (annual compounding)

Using these values in the formula

A = $52,300 (1 + 0.017/1)^(1*7)

A = $52,300 (1.017)^7A ≈ $62,232.25

Therefore, the dream car will cost about $62,232.25 after 7 years.

To know more about compound interest click here:

https://brainly.com/question/29335425

#SPJ11

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

hope this helps lovely! <3

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

Learn more about acceleration

brainly.com/question/12550364

#SPJ11

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

21 times 5 = 105

3 times 4 = 12

105/12= 8.75

Answer:

8.75

Step-by-step explanation:

21 x 5 = 105 (21 +21 + 21 + 21 +21)

3 x 4 = 12 (3 + 3 + 3 + 3)

105 / 12 = 8.75 (/ symbol is divide)

The absolute error is 2 ounces, and the relative error is approximately 11.76%.

The absolute error is the difference between the claimed weight and the true weight of the steak, which is:

Absolute error = |15 - 17| = 2 ounces

The relative error is the absolute error divided by the true weight of the steak, which is:

Relative error = (2/17) x 100% = 11.76%

So, the absolute error of the claimed weight is 2 ounces, and the relative error is 11.76%.

To find the absolute error, you'll need to subtract the true value (17 ounces) from the claimed value (15 ounces):

Absolute error = |True value - Claimed value| = |17 - 15| = 2 ounces

Now, to find the relative error, you'll divide the absolute error by the true value, and then multiply by 100 to get a percentage:

Relative error = (Absolute error / True value) x 100 = (2 / 17) x 100 ≈ 11.76%

So, the absolute error is 2 ounces, and the relative error is approximately 11.76%.

Learn more about absolute error at: brainly.com/question/30759250

#SPJ11

Answer: $650 + $450 divide it and then subtract it then it should be the answer X

Step-by-step explanation: answer

The sum of 7 terms of the sequence in terms of m is S=7m.

The given sequence is an arithmetic sequence, which is a sequence of numbers in which each term after the first is formed by adding a constant, d, to the preceding term. This constant, d, is referred to as the common difference.

Let the first term of the sequence be a and the common difference be d. Then the sequence of numbers can be expressed as a, a + d, a + 2d, a + 3d, a + 4d, a + 5d, a + 6d.

The sum of the seven numbers can be expressed as:

S = a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) + (a + 5d) + (a + 6d)

S = 7a + 21d

Since m is the middle term of the sequence, we know that the general form for m is a + 3d.

Substituting a + 3d for m, we get:

S = 7a + 21d

S = 7(a + 3d)

S = 7m

Therefore, the sum of 7 terms of the sequence in terms of m is S=7m.

To learn more about an arithmetic sequence visit:

https://brainly.com/question/10396151.

#SPJ1

Answer:

any number equal to or less than -4

Step-by-step explanation:

x - 1 < -4

< represents that -4 is a larger number than x - 1. we know that -4 is a negative number, so anything below -4 would be less. x = -4 would be a good solution, but the reality is that any number equal to or less than -4 is the correct answer. I hope this helps!

Answer:

slope = \(\frac{4}{5}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (3, 4) ← 2 points on the line

m = \(\frac{4-0}{3-(-2)}\) = \(\frac{4}{3+2}\) = \(\frac{4}{5}\)

Answer:

(a) The approximate distribution of the proportion pf of women who worked = 0.82, the standard distribution = 0.00738

The approximate distribution of the proportion pM of men who worked = 0.88, the standard distribution ≈ 0.01625

(b)  pM - pF =  0.06

While pF - pM = -0.06

The difference in the standard deviation ≈ 0.01025

(c) The probability that a higher proportion of women than men worked last year is 0

Step-by-step explanation:

(a) The given information are;

The percentage of college men that were employed last summer = 88%

The percentage of college women that were employed last summer = 82%

The number of college men interviewed in the survey = 400

The number of college women interviewed in the survey = 400

Therefore, given that the proportion of women that worked = 0.82, we have for the binomial distribution;

p = 0.82

q = 1 - 0.82 = 0.18

n = 400

Therefore;

p × n = 0.82 × 400 = 328 > 10

q × n = 0.18 × 400 = 72 > 10

Therefore, the binomial distribution is approximately normal

We have;

\(The \ mean = p = 0.82\\\\The \ standard \ deviation, \sigma = \sqrt{ \dfrac{p \times q}{{n} } }= \sqrt{ \dfrac{0.82 \times 0.18}{{400} }} \approx 0.01921\\\)

Therefore, the approximate distribution of the proportion pf of women who worked = 0.82, the standard distribution ≈ 0.01921

Similarly, given that the proportion of male that worked = 0.88, we have for the binomial distribution;

p = 0.88

q = 1 - 0.88 = 0.12

n = 400

Therefore;

p × n = 0.88 × 400 = 352 > 10

q × n = 0.12 × 400 = 42 > 10

Therefore, the binomial distribution is approximately normal

We have;

\(The \ mean = p = 0.88\\\\The \ standard \ deviation, \sigma = \sqrt{ \dfrac{p \times q}{{n} } }= \sqrt{ \dfrac{0.88 \times 0.12}{{400} }} \approx 0.01625\\\)

Therefore, the approximate distribution of the proportion pM of men who worked = 0.88, the standard distribution ≈ 0.01625

(b) Given two normal random variables, we have

The distribution of the difference the two normal random variable = A normal random variable

The mean of the difference = The difference of the two means = pM - pF = 0.88 - 0.82 = 0.06

While pF - pM = -0.06

The difference in the standard deviation, giving only the real values, is given as follows;

\(The \ difference \ in \ standard \ deviation = \sqrt{ \dfrac{p_1 \times q_1}{{n_1} } -\dfrac{p_2 \times q_2}{{n_2} } }\\\\= \sqrt{\dfrac{0.82 \times 0.18}{{400} }-\dfrac{0.88 \times 0.12}{{400} }} \approx 0.01025\\\)

(c) When there is no difference between the the proportion of men and women that worked last summer, the probability that there is a difference = 0

Therefore, taking 0 as the standard score, we have;

\(z = \dfrac{0 - (-0.06)}{0.01025} \approx 5.86\)

Given that the maximum values for a cumulative distribution table is approximately 4, we have that the probability that a higher proportion of women than men worked last year is 0.