Evaluate R C F · dr, where F(x, y, z) = 5xi − 5yj − 3zk and C is given by the vector function r(t) = hsin t, cost, ti, where 0 ≤ t ≤ π.

Answers

Answer 1

Answer:

[tex]\mathbf{ - \dfrac{3 \pi^2}{2}}[/tex]

Step-by-step explanation:

Given that:

F(x, y, z) = 5xi - 5yj - 3zk

The objective is to evaluate the [tex]\int _c F \ dr .C[/tex]

and C is given by the vector function  r(t) = (sin t, cost, t) where  0 ≤ t ≤ π

[tex]F(r(t)) = 5 \ sint \ i - 5 \ cost \ j - 3t \ k[/tex]

[tex]\int_c F . \ dr = \int ^{\pi}_{0} ( 5 \ sint \ i - 5 cos t \ j - 3 t \ k ) ( cos \ t , - sin \ t , 1 ) \ dt[/tex]

[tex]=\int ^{\pi}_{0} ( 5 \ sint \ cost+ 5 cos t \ sin t - 3 t) dt[/tex]

[tex]=\int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt -3 \int ^{\pi}_{0} \ dt[/tex]

[tex]= \int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt - 3 [\dfrac {t^2}{2}]^{\pi}_{0} \ \ dt[/tex]

[tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0} - \dfrac{3}{2}(\pi)^2[/tex]

By dividing 2 with 10 and integrating [tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0}[/tex]; we have:

[tex]=5(sin^2t -sin^2 0) -\dfrac{3 \pi^2}{2}[/tex]

[tex]=5(0) -\dfrac{3 \pi^2}{2}[/tex]

[tex]= 0 - \dfrac{3 \pi^2}{2}[/tex]

[tex]\mathbf{= - \dfrac{3 \pi^2}{2}}[/tex]


Related Questions

write and expression for
five times a number decreased by eight​

Answers

Answer:

5 x 10 - 8 = ?

Step-by-step explanation:

Brainliest please!

Answer:

5×17-8

Step-by-step explanation:

First you multiply 5 by 17 and then you subtract 8


A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?

Answers

Answer:

0.6955x

Step-by-step explanation:

Given the following :

Promotional discount on items = 35%

Sales tax on items = 7%

Original cost of items = x

First we obtain the cost of item after the promotional discount is applied

Cost of item :

Original price - (original price * promotional discount)

x - (x * 0.35) = x - 0.35x

Cost of item = 0.65x

Then the sales tax is added :

Total amount after tax:

Cost of item + (cost of item × sales tax rate)

0.65x + (0.65x * 0.07)

0.65x + 0.0455x

= 0.6955x

Answer:

0.6955x

edge 2020 .

In a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 75º more than the measure of the second
angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle.

The measure of the first angle is°?
The measure of the second angle is º?
The measure of the third angle is °?​

Answers

Answer:

Angle 1= 63°

Angle 2 = 21°

Angle 3 = 96°

If AABC = APQR, then
AB =

Answers

Answer:

AB = PQ

Step-by-step explanation:

ABC = PQR

The angles are equal and the segments are equal

for the angles

A = P

B = Q

C = R

For the segments

AB = PQ

BC = QR

AC = PR

Answer:

Line AB is approximately equal to Line PQ

In the diagram above <1=135 find the measure of <2

Answers

Answer:

∠ 2 = 45°

Step-by-step explanation:

∠ 1 and ∠ 2 are same- side interior angles and are supplementary, thus

∠ 2 = 180° - ∠ 1 = 180° - 135° = 45°

Answer: 45

Step-by-step explanation:

A statistical study reported that a drug was effective with a p-value of .042.
a. An effective or ineffective sample may be found about 42 times in 1000 samples. (effective or ineffective)
b. The drug is evidently effective at alpha ? = 0.05. (Yes or No)
c. How would that compare to a drug that had a p-value of .087? (More Effective or Less Effective)

Answers

Answer:

(a) An ineffective sample may be found about 42 times in 1000 samples.

(b) Yes, the drug is evidently effective at alpha = 0.05.

(c) A drug that had a p-value of 0.042 is more effective in comparison to a drug that had a p-value of 0.087.

Step-by-step explanation:

We are given that a statistical study reported that a drug was effective with a p-value of 0.042.

Let the Null Hypothesis, [tex]H_0[/tex] : The drug was ineffective.

Alternate Hypothesis, [tex]H_A[/tex] : The drug was effective.

(a) An ineffective sample may be found about 42 times in 1000 samples.

(b) As we know that, if the P-value is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.

SO, here also; the P-value is less than the level of significance as 0.042 < 0.05, so we reject our null hypothesis and conclude that the drug is evidently effective.

(c) The drug that had a p-value of 0.087 would be ineffective as in this case the P-value is more than the level of significance as 0.087 > 0.05, so we do not reject our null hypothesis and conclude that the drug is evidently ineffective.

This means that a drug that had a p-value of 0.042 is more effective in comparison to a drug that had a p-value of 0.087.

PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)

Can someone only help with b and c thanks ​

Answers

Answer:

b. 8.91,8.9,8.19,8.1,8.098

c. 20.005,20,19.06,2.05,1.905

Answer:

b.  8.91,  8.9, 8.19,  8.1, 8.098.

c. 20.005, 20, 19.06, 2.05, 1.905.

Step-by-step explanation:

An ice cream shop offers three flavors of ice cream (vanilla, chocolate, and strawberry), and four toppings (caramel, chocolate sauce, nuts, and sprinkles). If a small sundae includes one scoop of ice cream and two different toppings, how many possible sundaes are there?

Answers

Hey there! I'm happy to help!

Let's pretend that we are building a small sundae. We have 3 choices of ice cream flavors.

Now, we want to pick a topping. We have 4 choices here.

After we choose a topping, we can pick another. We only have 3 choices now because we need different toppings, and we already used one.

We want to find how many possible combos we can make. What we do is multiply all of these numbers of choices, and this will show us how many possible sundaes there are.

3×4×3=36

Therefore, there are 36 different sundaes that can be made.

Have a wonderful day! :D

Water covers about 1.385 x 108 square miles of Earth's surface. How is this number written in standard notation?

Answers

Answer:

1.4958 x 10^2

Step-by-step explanation:

The product of the multiplication is 149.58. The formula for standard notation is: A x 10^n, where 1<=A<10.

Scientific notations are the way through which a very small or a very large number can be written in shorthand. Water covers about 138,500,000 square miles of Earth's surface.

What are Scientific notations?

Scientific notations are the way through which a very small or a very large number can be written in shorthand.  In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5e+12.

Given that the Water covers about 1.385 x 10⁸ square miles of Earth's surface. The area is given in scientific notations, this can be written in the standard form as shown below,

1.385 x 10⁸ square miles = 138,500,000 square miles

Hence, Water covers about 138,500,000 square miles of Earth's surface.

Learn more about Scientific notation here:

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how do i solve this absolute value equation |3x-2|+4=7?

Answers

Answer:

{3x-2}+4=10

Step-by-step explanation:

The answer to |3x-2|+4=7 is x=3/5 and x=-1/3

Round to the nearest whole number 90.05

Answers

Answer:

90

Step-by-step explanation:

Identify the one's place:

90.05

2 . Check the number to the right of it:

90.05

If the number is greater than or equal to 5, we round up. If it's less than or equal to four, we round down.

Zero is less than four. This means we round down.

90.05 ≈ 90

Hope this helps.

trig: Solve Quadratic Equations by Factoring help with 2b and 2c

Answers

Answer:

2b)x=1/3 or x= -4

2c) x= 0 or x= -2/3

Step-by-step explanation:

To factor ax² + bx + c, use the AC method.

Multiply a and cFind factors of ac that add up to bDivide those two factors by a.  Reduce the fractions.The numerators are the constants, and the denominators are the coefficients.

(b) 3x² + 11x − 4 = 0

a = 3, b = 11, c = -4ac = (3)(-4) = -12Factors of -12 that add up to 11 are 12 and -1.Divide by 3: -1/3 and 12/3 = 4/1The factors are 3x − 1 and x + 4.

(3x − 1) (x + 4) = 0

3x − 1 = 0, or x + 4 = 0

x = 1/3, or x = -4

(c) 12x² + 8x = 0

Here, you can simply factor the greatest common factor, 4x.

4x (3x + 2) = 0

4x = 0, or 3x + 2 = 0

x = 0, or x = -2/3

Does this graph show a function? Explain how you know.
5
O A. Yes; the graph passes the vertical line test.
O
B. No; there are y-values that have more than one x-value.
C. Yes; there are no y-values that have more than one x-value.
O
D. No; the graph fails the vertical line test.

Answers

Answer: D. No; the graph fails the vertical line test.

The vertical line test is a tool used to determine if we have a function. If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test. Consequently, this leads to the relation not being a function.

For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.

Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.

The graph shows a function The graph fails the vertical line test.

A vertical line test is a tool used to determine if we have a function.

What is the vertical line test?

The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple.

If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test.

Consequently, this leads to the relation not being a function.

For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.

Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.

To learn more about the vertical line test visit:

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Which could describr the motion of an object in distance and displacement

Answers

Answer:

Hope this will help you :)

Step-by-step explanation:

ABCD has a perimeter of 27 units and is dilated by a scale factor of 1/3. What is the perimeter of A¹B¹C¹D¹?

Answers

Answer:

9 units

Step-by-step explanation:

First of all, let us understand the meaning of dilation.

Dilation means to change the size of any image or line or a figure.

Dilation can be used to enlarge (dilation by a factor greater than 1) the original figure.

OR

Dilation can be used to make the image smaller (dilation by a factor lesser than 1) the original figure.

Here, we are given that an image with 4 points ABCD is dilated by a scale factor of [tex]\frac{1}{3}[/tex].

Its sides will be AB, BC, CD and DA.

Perimeter is equal to the sum of all the sides of a closed figure.

So, perimeter of ABCD = AB + BC + CD + DA = 27 units ...... (1)

Now, it is dilated by a scale factor of [tex]\frac{1}{3}[/tex].

So, all the sides will become smaller i.e.

A'B' = [tex]\frac{1}{3}[/tex] AB

B'C' = [tex]\frac{1}{3}[/tex] BC

C'D' = [tex]\frac{1}{3}[/tex] CD

D'A' = [tex]\frac{1}{3}[/tex] DA

Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A' = [tex]\frac{1}{3}[/tex]AB + [tex]\frac{1}{3}[/tex]BC + [tex]\frac{1}{3}[/tex]CD + [tex]\frac{1}{3}[/tex]DA

[tex]\frac{1}{3}[/tex] (AB + BC + CD + DA ) = [tex]\frac{1}{3} \times 27[/tex](By equation (1))

Perimeter of A'B'C'D' = 9 units

You roll a die. If it comes up a 1 or 2​, you win ​$200. If​ not, you get to roll again. If you get a 1 or 2 the second​ time, you win ​$100. If​ not, you lose. ​a) Create a probability model for the amount you win. ​b) Find the expected amount​ you'll win.

Answers

On the first roll, you have a 1/3 probability of rolling a 1 or 2 and thus winning $200.

There's a 2/3 probability of not rolling a 1 or 2 on the first roll. On the second roll, there is again a 1/3 probability of rolling a 1 or 2, and 2/3 probability otherwise, so that there is a 1/3*2/3 = 2/9 probability of getting a 1 or 2 and thus winning $100, and 2/3*2/3 = 4/9 probability of losing.

(a) Let [tex]W[/tex] be a random variable representing the winnings from playing the game. It has the probability mass function

[tex]P(W=w)=\begin{cases}\frac13&\text{for }w=\$200\\\frac29&\text{for }w=\$100\\\frac49&\text{otherwise}\end{cases}[/tex]

(b) Compute the expected value of [tex]W[/tex]:

[tex]E[W]=\displaystyle\sum_w w\,P(W=w)=\$200\cdot\frac13+\$100\cdot\frac29+\$0\cdot\frac49\approx\$88.89[/tex]

Precision can be evaluated by which of the followings
Mean
Median
O RSD
O Mode
iniling in ODS columns are

Answers

RSD = Highest - Lowest
Mode= the middle number
Mean = add all, then divide by how many #s

Help meeeee time card. Weekly time card $11hr

Answers

$88.24 is the answer

Answer: it would be $96.25

Step-by-step explanation:

In the am, it’s 4 hours. 4x11= $44

In the pm it’s 4 hours and 45mins. 4x11=44

The for the 45 mins. Multiply 45x11= 495 then divide by 60. That gives you $8.25. When you add them all together, you get 96.25

Find the solution of the system of equations
shown on the graph.

Answers

Answer:

(-4, 3)

Step-by-step explanation:

From the graph, it looks like the two lines intersect at pint (-4, 3).

What is the common ratio between successive terms in the sequence?
2, 4, 8, -16, 32, 64, ...

Answers

goes by 2 then turns to a negative every 3 numbers

Step-by-step explanation:

Negative ever my other the number it skips 32 2 4 8

Solve −2x − 15 = 6x + 9. (1 point) 3 −3 −1 6

Answers

Answer:

-2x-15=6x+9

-2x-6x=9+15

-8x=24

x=-24/8

x=-3

Consider the ratio of 153 per 108. Write this ratio in different forms below.
A ratio written as a reduced fraction -
A ratio written as a decimal rounded to the hundredths -
What is the answer to this?

Answers

Answer:

i) [tex]\frac{17}{12}[/tex], ii) Approximately 1.42, iii) The answer to this is given by the reduced fraction, as decimal form has an infninite periodic component.

Step-by-step explanation:

(i) A ratio written as a reduced fraction:

Given ratio is now simplified to its reduce form:

1) [tex]\frac{153}{108}[/tex] Given

2) [tex]\frac{51}{36}[/tex] Modulative property/Existence of multiplicative inverse/Definition of division/[tex]\frac{\frac{x}{y}}{\frac{w}{z}} = \frac{x\cdot z}{y\cdot w}[/tex]

3) [tex]\frac{17}{12}[/tex] Modulative property/Existence of multiplicative inverse/Definition of division/[tex]\frac{\frac{x}{y}}{\frac{w}{z}} = \frac{x\cdot z}{y\cdot w}[/tex]/Result

(ii) A ratio written as a decimal rounded to hundredths:

[tex]\frac{17}{12} \approx 1.42[/tex]

(iii) What is the answer to this?

The answer to this is given by the reduced fraction, as decimal form has an infninite periodic component.

Tell whether x and y show direct variation. Explain your reasoning. x=y+2

Answers

Answer:

x and y do not show direct variation

Step-by-step explanation:

Two quantities x and y show direct variation when

y = kx

and k ≠ 0

Given x = y + 2

Making y the subject of the formula:

y = x - 2

The equation above cannot be written in the form y = kx

This means that x and y are not in a proportional relationship

For instance, let's say when x = 4

y = (4) - 2 = 2

Now, if x is doubled, x = 8

y = (8) - 2 = 6

Therefore, doubling x does not necessarily double y, hence they are not in a direct variation.

7. x – a is the factor of a polynomial P(x) if P(a) is equal to

options:
A) 2
B) 1
C) 3
D) 0

Answers

Answer:

[tex]\huge \boxed{\mathrm{D) \ 0}}[/tex]

Step-by-step explanation:

x - a is a factor of the polynomial P(x).

P(a) means the input for the polynomial is a.

a - a = 0

Anything multiplied by 0 is 0. If the factor is equal to 0 then the whole polynomial will be equal to 0.

Answer:

D) 0

Step-by-step explanation:

Which of the following is the midpoint of a line segment with endpoints -4 and 7?
A. 1.5
B. 0
C. -3
D. 5.5

Answers

Answer:

A.1.5 is the correct answer.

Answer:

A. 1.5

Step-by-step explanation:

End points of the line segment:

- 4 and 7

Length of line segment:

7 - (-4) = 11

Half length of the line segment:

11/2 = 5.5

Midpoint is at same distance from either end:

7 - 5.5 = -4 + 5.5 = 1.5

Midpoint is 1.5

I NEED HELP PLEASE ​

Answers

Answer:

m= 0

y^m = x ^8m over z ^5m

x^ 8m = y^m z5^m

z^ 5m = x^8m over y^m

Step-by-step explanation:

i will give you brainliest if you right down the answer and explain it

Answers

Answer:

[tex]\sqrt{113\\[/tex]

Step-by-step explanation:

set the problem up like this:

[tex]\sqrt{(x2-x1)^{2} +(y2-y1)^2[/tex]

(x1,y1) (x2,y2)

x1=-3

y1+3

x2=5

y2=-4

The equation should look like this:

[tex]\sqrt{(5-(-3))^2 + (-4-3)^2[/tex]

Then you solve it and 113 is the square root in between.

Hope it helps...

(-2÷3)^-3 ÷ x = (9÷8)^-2​

Answers

Answer:

- 3⁷/2⁹

Step-by-step explanation:

(-2÷3)⁻³ ÷ x = (9÷8)⁻²-(2⁻³)×3⁽⁻¹⁾ˣ⁽⁻³⁾ ÷ x = (3²)⁻²×(2⁻³)⁻²-2⁻³×3³÷x = 3⁻⁴×2⁶x = -2⁻³×3³ ÷ (3⁻⁴×2⁶)x = - 2⁻³⁻⁶×3³⁻⁽⁻⁴⁾x = -2⁻⁹×3⁷x = - 3⁷/2⁹

Need help with this one ....

Answers

Answer:

$110,759.36

Step-by-step explanation:

136645-89188=47457

47457/11=4314.272727

4314.272727x6=25885.636363

136645-25885.64=110.759.36

what is the image point of ( 1,2) after a translated right 5 units and up 3 units​

Answers

Answer:

(6,5)

Step-by-step explanation:

In (1,2), 1 is is x so any number added to it goes to the right or left.  2 is y so any number added to it goes up or down.  It says translate right 5 units so that will be for x, a.k.a 1.  

1+5= 6 (new x)

Same with y, a.k.a 2.  It says up 3 units, so it must mean add on to y.

2+3= 5 (new y)

We now take our new values and put them back in the parentheses:

(6,5)

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