Answer:
[tex]$ \frac{2187 \pi}{4}$[/tex]
Step-by-step explanation:
Using Stoke's theorem, we get
[tex]$ \int \int_S curl F.dS = \int_C F.dr$[/tex]
Now parametrize C
r(t) = ( 3 cos t, 3 - 3 sin t ) where, t in [0 2π]
[tex]$ \int_C F. dr= \int_0 ^{2 \pi}F ( 3 \cos t, 3 - 3 \sin t). r'(t)dt$[/tex]
[tex]$= \int_0^{2 \pi}(( 9 \cos^2 t)(27)(-3\sin t), \sin t \times (-27 \cos t \sin t)) . (-3 \sin t, 0 - 3 \cos t) dt $[/tex]
[tex]$ = 27 \int_0^{2 \pi} 81 \cos ^2 t \sin ^2 t + 3 \cos ^2 t \sin tdt $[/tex]
[tex]$ = 27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2t+27 [ - \cos^3 t]_0^{2 \pi}$[/tex]
[tex]$ = 27 \times \frac{81}{4} \int_0^{2 \pi} \frac{(1- \cos 4t)}{2} $[/tex]
[tex]$= \frac{2187}{8}[t-\frac{1}{4} \sin 4t]_0^{2 \pi} $[/tex]
[tex]$= \frac{2187 \pi}{4}$[/tex]
By using Stokes Theorem the required S curl F.ds is [tex]\dfrac{2187\pi }{4}[/tex].
Given that,
Function F(x, y, z) = (x^2y^3z)i + sin(xyz)j + xyzk,
S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y =3, oriented in the direction of the positive y-axis.
We have to determine,
Use Stokes' Theorem to evaluate S curl F·dS.
According to the question,
By using Stokes Theorem to evaluate S curl F .dS.
[tex]\int\ \int _s curlF.ds = \int _c F.dr\\\\[/tex]
Now parametrize C
r(t) = ( 3 cos t, 3 - 3 sin t ) ,
Where, t in [0 2π]
Then,
[tex]\int_c F.dr = \int^{2\pi }_0 F(3cost, 3-3sint).r'(t)dt\\\\[/tex]
[tex]= \int^{2\pi }_0 ((9cos^2t)(27)(-3sint),(sint) \times (-27cost.sint). (-3sint,0-3cost)dt\\\\= 27 \int^{2\pi }_0 81cos^2t .\ tsin^2t + 3 cos^2t. t sintdt\\\\= 27 \int^{2\pi }_0 \dfrac{81}{4}sin^22t+ 27[-cos^3t]^{2\pi }_0\\\\= 27 \times \dfrac{81}{4} \int^{2\pi }_{0} (\dfrac{1-cos4t}{2})\\\\= \dfrac{2187}{8}[t-\dfrac{1}{4}sin4t]^{2\pi }_0\\\\= \dfrac{2187}{8}[2\pi -\dfrac{1}{4}sin4(2\pi )- 0-\dfrac{1}{4}sin4(0 )]\\\\= \dfrac{2187\pi }{4}[/tex]
Hence, By using Stokes Theorem the required S curl F.ds is [tex]\dfrac{2187\pi }{4}[/tex].
To know more about Integration click the link given below.
https://brainly.com/question/17207150
Find the percent of increase to the nearest whole from 12 to 20
Answer:
The answer is
[tex]67\%[/tex]Step-by-step explanation:
To find the percentage increase we use the formula
[tex]Percentage \: change = \frac{change}{original \: \: quantity} \times 100\%[/tex]From the question
The original value = 12
To find the change we subtract the smaller value from the larger one
That's
Change = 20 - 12 = 8
So the percentage increase is
[tex] \frac{8}{12} \times 100 \%\\ = \frac{2}{3} \times 100\% \\ = 66.67\%[/tex]We have the final answer as
[tex]67\%[/tex] to the nearest whole number
Hope this helps you
When two lines cross itis found that the angles opposite each other are the same size. They are known as
Answer:
"vertical angles"
Step-by-step explanation:
Those are "vertical angles."
Which simplified fraction is equal to 0.1ModifyingAbove 7 with bar? StartFraction 9 Over 17 EndFraction StartFraction 8 Over 45 EndFraction StartFraction 17 Over 9 EndFraction StartFraction 16 Over 90 EndFraction Please help i will give you brainliest
Answer:
8/45
Step-by-step explanation:
Define x to be the value of your fraction:
[tex]x=0.1\overline{7}\\\\10x=1.7\overline{7}\qquad\text{multiply by 10}\\\\10x-x=1.7\overline{7}-0.1\overline{7}=1.6\\\\x=\dfrac{1.6}{9}=\dfrac{8}{45}\qquad\text{divide by 9; put in lowest terms}[/tex]
____
When in doubt, you can use your calculator to see which fraction gives you 0.1777777778.
_____
We multiplied by 10^1 above, because there is 1 repeating digit. The power of 10 we use matches the number of repeating digits.
Answer:
8/45
Step-by-step explanation:
and have a good day
I need help please for the answer and how to solve it
Answer:
32) a) x = 3/19 ounces
33) d) 0,2 meter per minute
Step-by-step explanation:
32)
7 1/2 = 15/2
47 1/2 = 95/2
95/2 dough 15/2 sugar
1 dough x = (15/2*1) / 95/2
x = (15/2)(95/2)
x = 15/95
x = 3/19 ounces
33)
Distance 16 | 18 | 20 | 22
Time 80 | 90 | 100 | 110
Time 90 - 80 = 10
Distance 18 - 16 = 2
Each 10 minutes go 10 meters
2 / 10 = 0,2 meter per minute
Does the point (–3, 2) lie inside, outside, or on a circle with center (4, 0) and radius 5 units?
Answer:
The point (-3, 2) lies outside of the circle centered at (4, 0) with radius 5.
Step-by-step explanation:
The distance between two points (x₁, y₁) and (x₂, y₂) on the x-y plane can be calculated with:
√((x₁ - x₂)² + (y₁ - y₂)²)
So in this case, with the points (-3, 2) and (4, 0), the distance is:
√((-3 - 4)² + (2 - 0)²)
√(49 + 4)
√(53) ≈ 7.28
Since 7.28 > 5, the point (-3, 2) lies outside of the circle centered at (4, 0) with radius 5.
If two lines intersect , then they intersect in exactly one
Answer:
point?
Step-by-step explanation:
is this a question or a statement
Answer:
Point
Step-by-step explanation:
once two line intersect the area where they intersected becomes a point
Could the given matrix be the transition matrix of a regular Markov chain?
[Start 2/2 Matrix 1st Row 1st Column 0.3 2nd Column 0.7 2nd Row 1st Column 0 2nd Column 1 EndMatrix ]
Answer:
Following are the answer to this question:
Step-by-step explanation:
Matrix:
[tex]A=\left[\begin{array}{cc}0.3&0.7\\1&0\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{cc}0.79&0.21\\0.3&0.7\end{array}\right][/tex]
In the above-given matrix, all entries of the matrix A² will be positive and the matrix A will be the transition of the matrix A, that regulates the Markov chain.
How to Write the numbers 0.253 in two other forms
Answer:
253/1000, 23.5%
Step-by-step explanation:
Kadir, Chandran and Ping Wei participated in a Science quiz. The number of questions they had answered was in the ratio 4:6:3. Chandran had answered 30 questions. Calculate the total number of questions Kadir amd Ping Wei had answered.
Answer:
35
Step-by-step explanation:
We can call the amount of questions they answered as 4x, 6x and 3x respectively. Since Chandran answered 30 questions, we know that 6x = 30 so x = 5. The total number of questions Kadir and Ping Wei answered was 4x + 3x = 7x and since we know that x = 5, the answer is 7 * 5 = 35 questions.
what is refraction
Answer:
I hope this will be the answer... ✌️
[tex]\large{\pmb{\underline{\underline{\sf{Refraction:-}}}}}[/tex]
Refraction is the bending of a light or sound wave, or the way the light bends when entering the eye to form an image on the retina.
[tex]\large{\pmb{\underline{\underline{\sf{Examples~ Of~ Refraction:-}}}}}[/tex]
Bending of the sun's rays as they enter raindrops, forming a rainbow.[tex]{\huge{\underline{\small{\mathbb{\pink{HOPE \ THIS \ HELPED \ UH:)}}}}}}[/tex]
Cheers !! :3
Describe the mental math steps you would use to find 7(42) (this is the distributive property by the way. :] )
Answer:
multiply 7 by 42
= 294
42 x 7 can be done as mental math, but that is challenging for some people.
Answer: 294
Break up 42 like so: 42 = 40 + 2
Then we can say,
7*(42) = 7*(40+2) = 7*40 + 7*2 = 280 + 14 = 294
The mental math part is knowing that 7*4 = 28, then you add on a zero to get 7*40 = 280. This is added to 7*2 = 14 to get the final answer above.
What is the inverse of y =
1-7
?
4
Answer:
2
Step-by-step explanation:
Ms. Ironperson and Mr. Thoro are making Avenger posters to give children when they visit Avenger Academy. Ms. Ironperson has completed 12 posters and will complete 6 more per day. Mr. Thoro has not started yet but can make 12 per day. At some point Mr. Thoro will catch up and both will have finished the same number of posters. When this does happen, how many posters will each Avenger have completed? If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?
Answer:
1) When this does happen, how many posters will each Avenger have completed?
24 posters each.
2) If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?
y = 12 + 6x.......... Equation 1
y = 12x .......... Equation 2
Step-by-step explanation:
1) When this does happen, how many posters will each Avenger have completed?
We are told in the question:
Number of days = x
Number of posters = y
Ms. Ironperson has completed 12 posters and will complete 6 more per day.
y = 12 + 6x.......... Equation 1
Mr. Thoro has not started yet but can make 12 per day.
y = 12x................Equation 2
Hence, the equations needed to solve this problem:
y = 12 + 6x.......... Equation 1
y = 12x .......... Equation 2
We substitute 12x for y in equation 1
y = 12 + 6x.......... Equation 1
12x = 12 + 6x
Collect like terms
12x - 6x = 12
6x = 12
x = 12/6
x = 2
Hence, since x = the number of days,
The number of days = 2 days
Substitute 2 for x in Equation 2
y = 12x .......... Equation 2
y = 12 × 2
y = 24 posters.
Since y = number of posters,
number of posters = 24 posters.
We were told in the question that, when Mr Thoro catches up with Ms Ironperson, that would both have completed the same number of posters.
Hence, both Avengers would have completed 12 posters each.
Suppose Tommy walks from his home at (0, 0) to the mall at (0, 7), and then walks to a movie theater at (9, 7). After leaving the theater Tommy walks to the store at (9, 0) before returning home. If each grid square represents one block, how many blocks does he walk?
Answer:
32 blocks
Step-by-step explanation:
distance between home (0,0) and mall (0,7) = 7
distance between mall (0,7) and movies (9,7) = 9
distance between movies (9,7) and store (9,0) = 7
distance between store (9,0) and home (0,0) = 9
7 + 9 + 7 + 9 = 32 blocks
A long distance runner can run 2 miles every 17 minutes. At this rate how ling would it take the runner to run 16 miles.
Answer:
136 minutes
Step-by-step explanation:
Given :
2 miles ----> takes 17 min
1 mile -----> takes 17/2 min
hence the unit rate is (17/2) min per mile
Thus, 16 miles will take
= (17/2) miles per min x 16 miles
= (17/2) x 16
= 136 minutes
Answer:
136 min
Step-by-step explanation:
lets make it simple.
2 miles / 17 min = 16 miles / x
just cross multiply
2 x = 17 (16)
2 x = 272
x = 272 / 2
x = 136 min
Wich expression is equivalent to 0.33b+b+0.31b?
A.b+0.64
B.1.64b
C.1.02b
D.1+0.64b
Answer:
B. 1.64b
Step-by-step explanation:
0.33b+1b+0.31b
=1.64b
what number should be placed in the box to help complete the division calculation
Answer:
15
Step-by-step explanation:
12 X 15 is 180, which is closest to 187, we have to add a 5 in the space next to 71 and 180 under 187
What slope is perpendicular to m=3/4
Answer:
The slope of the perpendicular line is -4/3
Step-by-step explanation:
Perpendicular lines have slopes that multiply to -1
m * 3/4 = -1
Multiply by 4/3
m * 3/4 * 4/3 = -1 * 4/3
m = -4/3
The slope of the perpendicular line is -4/3
calculate the length of the altitude of an iso scales triangle whose equal sides are 13cm long with a base 24cm
Answer:
5 cm
Step-by-step explanation:
13² - 12² = x²
169 - 144 = x²
25 = x²
5 = x
the sum of twice a number and 15 less than the number is the same as the difference between -19 and the number. What is the number?
Answer:
-1
Step-by-step explanation:
Twice a number: 2n.
15 less than the number: n-15.
The sum of those: (2n) +(n-15) = 3n-15.
__
The difference between -19 and the number: -19-n
__
These values are the same, so we have ...
3n -15 = -19 -n
4n = -4 . . . . . . . . add n+15 to both sides
n = -1 . . . . . . . . . divide by -4
The number is -1.
Find the measure of x.
A. 90
B. 47
C. 43
D. 53
Answer:
C. 43
Step-by-step explanation:
Use of theorem:An angle inscribed across a circle's diameter is always a right angleAs per above:
x + 47 = 90x = 90 -47 x = 43Correct answer choice is C. 43
Answer:
C.) 43
Step-by-step explanation:
I got it right on founders edtell
How many rectangles are there?
Answer:
8 (read below)
Step-by-step explanation:
There is 8 if you re counting the bottom, light turqoise one. If not, then 7.
Answer:
17 or 18
Step-by-step explanation:
Yolanda is filling her bathtub. The table shows the number of gallons of water in the bathtub at different times since she started filling it. Time (minutes) Water (gallons) 1 16.50 1.5 24.75 2 33 Answer the following questions based on the information in the table. Part A Find the constant of proportionality (in gallons per minute) using the values in the first row of the table.
Answer:
Constant of proportionality
K= 16.5 gallons per minute
Step-by-step explanation:
Time t (minutes) Water g (gallons)
For t= 1, g= 16.50,
for t= 1.5 ,g= 24.75
For t= 2,g= 33
Let the function be
Gallons g= k(time t)
Where k is the constant of proportionality
16.5= k(1)....for when t= 1
24.75= k(1.5) ..for when t= 1.5
Solving gives
8.25=k(0.5)
8.25/0.5= k.
16.5 = k
K= 16.5 gallons per minute
helpppppp asappppp plsssss
Answer:
x = -2
Step-by-step explanation:
The segments described in the question are equidistant (meaning they are the same length). Therefore, using algebraic techniques, we can set these two equal to each other and solve for x.
4x - 8 = 6x - 4 Combine like terms by subtracting 6x from both sides.
-2x - 8 = -4 Combine like terms by adding 8 to both sides.
-2x = 4 Divide by -2 on both sides of the equation.
x = -2
5) Suppose a slice of a 12-inch pizza has an area of 20 square inches. What is the angle of
this slice?
Answer:
The angle of slice is approximately 16°.
Step-by-step explanation:
The slice of pizza represent the sector of a circle.
The area of a sector is:
[tex]A=\frac{1}{2}r^{2}\phi[/tex]
Here,
r = radius of the circle
Φ = angle in radians
Given:
A = 20 inches²
r = 12 inch
Compute the angle of the slice as follows:
[tex]A=\frac{1}{2}r^{2}\phi[/tex]
[tex]\phi=\frac{2\times A}{r^{2}}[/tex]
[tex]=\frac{2\times 20}{12\times 12}\\\\=0.2778[/tex]
The angle us 0.2778 radians.
Convert the angle into degrees as follows:
[tex]\text{Angle}=0.2778\times\frac{180}{\pi}=15.9168\approx 16^{o}[/tex]
Thus, the angle of slice is approximately 16°.
The spinner below shows 5 equally sized slices. Tammy spun the dial 25 times and got the following results. Fill in the table below. Round your answers to the nearest thousandths.
Answer:
a) 4/25, or 0.16, or 16%
b) 1/5, or 0.2, or 20%
c) The first option - the theoretical and experimental values should become closer the more trials that are performed.
Step-by-step explanation:
a) 4 of Tammy's 25 spins landed on black, so the experimental probability is 4/25, or 0.16, or 16%.
b) The spinner is split into 5 equal sections. Assuming it is fair, the chance of landing in any given section for a single spin is 1/5, or 0.2, or 20%.
c) The theoretical and experimental values should get closers the more trials you do.
For example, consider 1 coin flip vs 100. The theoretical probability of landing on a given side of a coin is 1/2, or 0.5, or 50%. With a single flip, your experimental probability will either be 0% or 100%, both off of the theoretical probability by 50%. After 100 flips however, the experimental and theoretical probabilities will be much closer to each other.
In an examination of purchasing patterns of shoppers, a sample of 36 shoppers revealed that they spent, on average, $50 per hour of shopping. Based on previous years, the population standard deviation is $4.80 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, calculate a 90% confidence interval.
Answer:
the 90% confidence interval is ( 48.684 , 51.316 )
Step-by-step explanation:
Given that :
the sample size = 36
Sample Mean = 50
standard deviation = 4.80
The objective is to calculate a 90% confidence interval.
At 90% confidence interval ;
the level of significance = 1 - 0.9 = 0.1
The critical value for [tex]z_{\alpha/2} = z_{0.1/2}[/tex]
[tex]= z_{0.05}[/tex] = 1.645
The standard error S.E = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
=[tex]\dfrac{4.8}{\sqrt{36}}[/tex]
[tex]=\dfrac{4.8}{6}[/tex]
= 0.8
The Confidence interval level can be computed as:
[tex]\bar x \ \pm z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
For the lower limit :
[tex]\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
[tex]=50 \ - 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}[/tex]
[tex]=50 \ - 1.645 \times \ 0.8 }}[/tex]
=50 - 1.316
= 48.684
For the upper limit :
[tex]\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
[tex]=50 \ + 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}[/tex]
[tex]=50 \ + 1.645 \times \ 0.8 }}[/tex]
=50 + 1.316
= 51.316
Thus, the 90% confidence interval is ( 48.684 , 51.316 )
The length of the shadow of a pole on level ground increase 90m, when the angle of elevation of the sum changes from 58-38.calculate the height of the pole, correct to 3sf
Answer: h = 137.4 metres
Step-by-step explanation:
Given that the length of the shadow of a pole on level ground increase 90m, that is, (x + 90)m will be the total length of the shadow. Also we are given that the angle of elevation of the sum changes from 58-38.
To calculate the height, we will employ trigonometry ratio. SohCahToa which are: tan 58 and tan 38.
Please find the attached files for the solution
(9,5) and (4,-7) find the distance between two points
Answer:
13 units
Step-by-step explanation:
Use the distance formula, d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex], where (x2, y2) and (x1, y1) are two different points on the line.
Plug in the values:
d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
d = [tex]\sqrt{(9 - 4)^2 + (5 + 7)^2}[/tex]
d = [tex]\sqrt{5^2 + 12^2}[/tex]
d = [tex]\sqrt{25 + 144}[/tex]
d = [tex]\sqrt{169}[/tex]
d = 13
Finding the Constant of Proportionality from a Graph
Hi there! :)
Answer:
[tex]\huge\boxed{8}[/tex]
Find the constant of proportionality using
rise ( y value) / run ( x value):
Therefore:
8 / 1 = 8 = constant of proportionality
We can go ahead and check our work as well:
16 / 2 = 8
24 / 3 = 8
32 / 4 = 8
Therefore, 8 is the correct constant of proportionality.