The value of curlF.dS is 72π if the F(x, y, z) = yzi 9xzj exyk, c is the circle x2 y2 = 9, z = 1
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have:
[tex]\rm F(x, y, z) = yzi+ 9xzj+ e^{xy}k[/tex]
And curl is x²+y²= 9 and z =1
In the parametric form:
[tex]\rm \vec{r}(t) = 3cost \vec{i}+3sint \vec{j}+\vec{k}[/tex] 0 ≤ t ≤ 2π
First two component represent the circle and last one represent the z =1
Using Stoke's theorem:
[tex]\rm \int\limits\int\limits_S {curl \ \ve{F}.d\vec{S}} = \int\limits_C {\vec{F}} \, .d\vec{r } = \int\limits^{2\pi}_0 {\fec{F}(\vec{r}(t)).\vec(r)t} \, dt[/tex]
Here:
[tex]\rm \vec{F}(\vec{r}(t)) = 3sint \vec{i}+27cost \vec{j}+e^{cost.sint}\vec{k}[/tex]
Now calculate the dot product of curl F and dS we get:
[tex]\rm \int\limits\int\limits_S {curl \ \ve{F}.d\vec{S}} = \int\limits^{2\pi}_0 (-9sin^2t+81cos^2t)dt[/tex]
After solving the above integral, we will get:
[tex]\rm \int\limits\int\limits_S {curl \ \ve{F}.d\vec{S}} = 72\pi[/tex]
Thus, the value of curlF.dS is 72π if the F(x, y, z) = yzi 9xzj exyk, c is the circle x2 y2 = 9, z = 1
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find the width of a rectangular prism if the volume is 165,000 mm3 the length is 100mm and the height is 55 mm
Answer:
Width is 30mm
Step-by-step explanation:
Volume = L×W×H
Volume= 165,000 mm³
Length= 100mm
Height= 55mm
Width= ?
L×H
100mm×55mm= 5500mm
volume ÷ L×W
165,000÷5500=30
width= 30mm
L×W×H=V
100×55×30=165000
Find the surface area of the pyramid.
Answer:
319
Step-by-step explanation:
So, to find the surface area, first we find the base area, which is: 11 x 11 = 121
Then, we have to find the area of the other faces. Since each face is a triangle, we can use the formula A = 1/2 x b x h.
So,
b = 11
h = 9
1/2 x 11 x 9 = 49.5
The, we multiply by 4, the number of sides: 49.5 x 4 = 198
Then, we add the 2, values: 121 + 198,
Which gives us: 319.
Hope this helped!
А support wire 12 yards long is attached to the top of a utility pole 10
yards tall and is then stretched taut. To the nearest tenth of a yard, find
how far from the base of the pole wire will be attached from the ground.
Hint: Solve using this equation:
2
2
x² + 10² = 12²
Answer:
6.6 yd
Step-by-step explanation:
[tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]
[tex]10^{2}[/tex]+[tex]b^{2}[/tex]=[tex]12^{2}[/tex] Substitute a= 10 and c=12
100+[tex]b^{2}[/tex]=144 Evaluate the Powers
[tex]b^{2}[/tex]=44 Subtract 100 on both sides.
b=[tex]\sqrt{44}[/tex] Square root both sides b>0 so you dont need ⊥
b=6.6 Use a calculator to evaluate.
Please help me on this!
The correct answer ofr this question is option D
Y varies directly with X. Y=10 when X=5, find y when X=14
Answer:
28
Step-by-step explanation:
y=kx
10=5k
k=2
y=2×14
y=28
If three coins are thrown what is the probcbility Obtaining at least two head?
Answer:
2 head and 1 tail form my side
Find the derivative of the function.
Answer:
b. 4x
Step-by-step explanation:
We can use the power rule for derivatives, which says [tex]\frac{d}{dx} x^n = nx^{n-1[/tex]
So, if [tex]f(x) = 2x^2 + 1[/tex]
then [tex]f'(x) = 4x[/tex].
The 1 goes away because the derivative of any constant is 0.
hope this helped!
Answer:
b. 4x
Step-by-step explanation:
We can use the power rule for derivatives, which says
So, if
then .
The 1 goes away because the derivative of any constant is 0.
Your broker charges a commission of 5.1% of the cost of the stock you sell. if you sell a batch of stocks worth $2,617.75, how much commission will you owe your broker? a. $133.51 b. $513.28 c. $110.56 d. $392.66
Commision is the percentage on a cost of good. The amount of commision you owe your broker is $133.51
How to calculate commision on a cost of goodCommision is the percentage on a cost of good. GIven the following parameters
Cost of good = $2,617.75
If your broker charges a commission of 5.1% of the cost, the amount charged is given as:
Amount charged = 5.1% of $2,617.75
Amount charged = 0.051 * $2,617.75
Amount charged = $133.51
Hence the amount of commision you owe your broker is $133.51
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Answer:
Is A.133.51
I took the quiz on
Step-by-step explanation:
Find the value of [tex]y[/tex] when [tex]x=7[/tex]
Hey there!
GUIDE:
2 negatives = positive
2 positives = positive
1 negative & 1 positive = negative
1 positive & 1 negative = negative
ANSWERING THE GIVEN QUESTION
y = -4x
y = -4(7)
y = -28
Because, remember we said a NEGATIVE (-4) & a POSITIVE (7) gives you a negative [-28]
Therefore, the answer should be: -28
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
which of the following is the solution for the inequality below? -3x+2<8
Answer:
x>-2
Step-by-step explanation:
First you have to subtract 2 from both sides, which leaves you with -3x=6, then you have to divide -3 on both sides to get the variable by itself. Which is x<-2, but you have to switch the sign because you multiplied/divided by a negative number, then you get left with x>-2........Hope that helped!!!!!!!!!!:)
find the area of this parallelogram 13cm 15cm 20cm
Answer:
260cm²
Step-by-step explanation:
area of this parallelogram 20×13=260cm²
3l of ice cream is 10$ 4l of ice cream is 12% which is the better choice
Answer:
4l of icecream
Step-by-step explanation:
10÷3=3.33
12÷4=3
An example of a(n) ___is 5, 12 and 13.
Answer:
Pythagorean triple
Step-by-step explanation:
This is usually expressed as a² + b² = c² Integer triples which satisfy this equation are Pythagorean triples. The most well known examples are (3,4,5) and (5,12,13).
which of the following numbers is a multiple of 5
A 53
B 79
C 21
D 65
Answer:
65
Step-by-step explanation:
It ends in 5 or 0. 65 divided by 5= 13
Find the distance between the given parallel planes. 4x − 5y z = 16, 8x − 10y 2z = 2
The distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.
What is a plane?
A plane is a flat surface on which a straight line joining any two points on it would wholly lie.
Given equations are
[tex]4x-5y+z=16[/tex]
[tex]8x-10y+2z=2[/tex]
The distance between two planes is given by the formula:
[tex]D=\dfrac{|d_2-d_1|}{\sqrt{a^2+b^2+c^2}}[/tex]
Here from equations
[tex]4x-5y+z=16[/tex]
[tex]8x-10y+2z=2[/tex]
We can also write the equation [tex]8x-10y+2z=2[/tex] as:
[tex]4x-5y+z=1[/tex]
So now the two equations are:
[tex]4x-5y+z=16[/tex]
[tex]4x-5y+z=1[/tex]
here a=4 b=-5 c =1 and d1=16 d2=1
Putting the values in the equation.
[tex]D=\dfrac{|-16+1|}{\sqrt{4^2+(-5)^2+(10^2)}}[/tex]
[tex]D=2.34[/tex]
Hence the distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.
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can someone pls help need this done by tomorrow
No, no lil one, you're going wrong.
1.a. Calculate the total surface area of the cube. 6(l^2) =144x6 = 864 sq. inch1.b. Calculate the volume of the cube. l^3 =12x12x12 = 1728 cu. inchSlove the rest by yourself
Remember:
Surface area of cuboid is 2(lb+bh+hl), where l is length, b is breadth and h is height. Volume of cuboid is lbh, where l, b, h mean the same as in 1.SOMEONE HELP ME PLEASE IM STUCK ON THIS
Step-by-step explanation:
2×2×2×2
3 3 3 3
2×2×2×2
3×3×3×3
16
3×3×3×3 (divide)
= 16/81
hope it helpsss!!
can you mark me as the brainliest
One of the legs of a right triangle measures 12 cm and its hypotenuse measures 20 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
other leg = 16 cm
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x be the other leg , then
x² + 12² = 20²
x² + 144 = 400 ( subtract 144 from both sides )
x² = 256 ( take square root of both sides )
x = [tex]\sqrt{256}[/tex] = 16
A triangle has one side that is 7 cm long and the other side is 3cm long.
Help please
In any triangle, a side is longer than the difference between the other two. A side is also less the the sum of the other two. If these two rules are not obeyed then a triangle cannot be formed by those sides.
a = 7 cm. b = 3 cm.
Then c > 7-3 = 4 cm and also, c < 7+3 = 10 cm.
4 cm < the third side < 10 cm
what is 5.136 rounded to the nearest tenth
Answer:
5.136 is 5.1 to the nearest tenth
Lines a and b are parallel. What is the measuee of angle S?
Answer:
The measure of angle s is 22°
Step-by-step explanation:
Given:
Horizontal lines A and B are parallel and are intersecting because a line is going through the both of them.Top right angle of line A is labeled to be 158°, while the top left angle in line B is labeled S° indicating this variable is the missing degrees.To find:
The angle of S, in degrees.∠1 and 158° are both on a straight line and supplementary.
(Supplementary angles are those angles that sum up to 180 degrees. )
So solving,
⇒ ∠1=180°-158°=22° ....> Angles ∠1 and S are interior angles
Due to lines A and B being parallel, all interior lines are equal.
As a result, the answer is therefore 22°.
What is the amplitude of this equation? y = -10cos(5x)
Answer:
The amplitude is 10.
Answer:
the amplitude of this equation is 10
Step-by-step explanation:
I took extra mathematics in high school :)
I hope this helps you! Good luck !
Lucia wants to spend less than $8 on her order. Which of the following represent amounts that are in Lucia's budget?
Answer:
x < 8
Step-by-step explanation:
If Lucia wants to spend less than $8 dollars on an order, the answer would be x is less than 8.
Jen and her friends are designing a robot for a STEM competition. The goal of the competition is to have a robot complete an obstacle course in the least amount of time.
Jen and her friends need to consider the robot’s height and its width at its base. The robot must be short enough and narrow enough to navigate through several arches along the obstacle course. The director of the competition laid out components of the obstacle course on a coordinate plane. Instead of giving the width and maximum height of the arch, the director created an expression based on the location of the arch on the coordinate plane and gave each team this expression to represent the height of the arch, in inches, at any value of x along the arch:
-x^2 + 5x + 24.
Factor the expression, and use the factors to find the x-intercepts of the quadratic relationship it represents.
Type the correct answer in each box, starting with the intercept with the lower value.
The x-intercepts occur where x =___ and x =___
The x-intercepts for the expression which is used by Jen and her friends to represent the height of the arch, in inches, at any value of x along the arch are 8,0) and (-3,0).
What is a factor of quadratic equation?The factor of a quadratic is the terms in linear form, which are when multiplied together, give the original quadratic equation as a result.
Jen and her friends need to consider the robot’s height and its width at its base. The robot must be short enough and narrow enough to navigate through several arches along the obstacle course.
The expression to represent the height of the arch, in inches, at any value of x along the arch:
[tex]-x^2 + 5x + 24.[/tex]
Factorize this expression by equating it to zero and changing its sign,
[tex]\begin{aligned}-x^2 + 5x + 24=0\\x^2 - 5x - 24=0\\x^2 - 8x +3x- 24=0\\x(x - 8)+3(x - 8)=0\\(x-8)(x+3)=0\\x=8,-3\end[/tex]
Thus, the x intercept of the equation is (8,0) and (-3,0)
Hence, the x-intercepts for the expression which is used by Jen and her friends to represent the height of the arch, in inches, at any value of x along the arch are 8,0) and (-3,0).
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Answer: x = 8,0 and x = -3,0
Step-by-step explanation:
What is the axis of symmetry of h(x) = 6x2 − 60x 147? x = −5 x = −3 x = 3 x = 5
The function h(x) = 6x² - 60x + 147 is a quadratic function, and the axis of symmetry of the function is x = 5
How to determine the axis of symmetry?The equation of the function is given as:
h(x) = 6x² - 60x + 147
Differentiate the function
h'(x) = 12x - 60
Set the function to 0
12x - 60 = 0
Add 60 to both sides
12x = 60
Divide both sides by 12
x = 5
Hence, the axis of symmetry of the function is x = 5
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Answer:
X = 5 is correct
Step-by-step explanation:
just took the test on edge and got 100%
aria buys a box of doughnuts, which come with differente fillings insinde. The flavors are: 3 jelly, 5 cream and 1 lemon. What is the probability that the first doughnut Maria eats has jelly inside?
Answer:
1/3
Step-by-step explanation:
3 + 5 +1 = 9
3/9 = 1/3
A student has some $1 and $5 bills in his wallet. He has a total of 17 bills that are worth $49. How many of each type of bill does he have?
The student has $1 bills and
(Type whole numbers.)
$5 bills.
Answer:
He has 8 five $5 bills and 9 $1 bills
Step-by-step explanation:
($5×8)+($1×9)=$49
6. In a survey, 25 out of 200 students indicated they would vote for Xaria for class president. If 1,000
students are voting in the election, how many would be expected to vote for Xaria?
What is the solution of the equation 4.5+m=10
Answer:
The first thing that we need to do is subtract 4.5 from both sides because that would removed the 4.5 from the left side and leave us with m by itself. So we get the following [tex]m=5.5[/tex] and that is our solution.
Hope this helps! Let me know if you have any questions
Answer:
5.5
Step-by-step explanation:
to find additional value, subtract the known
[because 4.5 plus (+) a number (m) is equal to (=) 10, the number (m) must be equal to (=) 4.5 minus (-) 10.]
10 - 4.5 = 5.5
to find if this is correct, add it back
4.5 + 5.5 = 10
m = 5.5
hope this helps:)
Find the length of the curve r=sqrt(1 cos 2 theta)
The length of the curve r=√(1+cos 2θ) is 2π after integrating over the limit 0 to π√2
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have:
[tex]\rm r=\sqrt{(1 +cos 2 \theta)}[/tex]
[tex]\rm r=\sqrt{2cos^2 \dfrac{2 \theta}{2}[/tex]
[tex]\rm r = \sqrt{2}cos\theta[/tex]
[tex]\rm \dfrac{dr}{d\theta}= -\sqrt{2}sin\theta[/tex]
Length:
[tex]\rm L = \int\limits^{\pi\sqrt2}_0 {\sqrt{r^2+(\dfrac{dr}{d\theta}})^2} \, d\theta[/tex]
After the value of r and dr/dθ and solve the definite integral, we will get:
L = 2π
Thus, the length of the curve r=√(1+cos 2θ) is 2π after integrating over the limit 0 to π√2
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