The plane has intercepts
y = z = 0 ⇒ 3x = 6 ⇒ x = 2
x = z = 0 ⇒ 2y = 6 ⇒ y = 3
x = y = 0 ⇒ z = 6
and thus passes through the points (2, 0, 0), (0, 3, 0), and (0, 0, 6).
Parameterize the portion of the plane (call it P) by the vector function,
[tex]\vec r(s,t) = \left\langle 2(1-s)(1-t), 3s(1-t), 6t \right\rangle[/tex]
where 0 ≤ s ≤ 1 and 0 ≤ t ≤ 1.
Compute the normal vector to P :
[tex]\vec n = \dfrac{\partial \vec r}{\partial t} \times \dfrac{\partial \vec r}{\partial s} = -\left\langle 18-18t, 12-12t, 6-6t \right\rangle[/tex]
Then the flux of F through P is given by the surface integral,
[tex]\displaystyle \iint_P \vec F \cdot d\vec S = \int_0^1 \int_0^1 \left\langle 6s(1-s)(1-t)^2, 90st(1-t), 72t(1-s)(1-t) \right\rangle \cdot \vec n \, ds \, dt \\\\ = - \int_0^1 \int_0^1 \left(108(t-1)^3 s^2 + 108(t-1)^2(5t+1) s + 432t(t-1)^2\right) \, ds \, dt \\\\ = - \int_0^1 18(t-1)^2(41t+1) \, dt \\\\ = \boxed{-\frac{135}2}[/tex]
What is the value of the expression 22 + 42 ÷ 22?
Answer:
8
Step-by-step explanation:
Here is a balanced hangar. A circle has a mass of 3 grams and a square has a mass of 2 grams. Which is the mass of a triangle? 3 grams. 7/5grams 9/6 11 grams
Answer:
Step-by-step explanation:
Givens
Circle: 3 grams Number: 1 right hand side Number LHS: 2
Square: 2 grams Number: 2 Number LHS: 5
Triangle: x Number: 5 Number LHS: 2
Formula
Mass RHS = Mass LHS
Solution
3*1 + 2*2 + 5x = 3*2 + 5*2 + 2*x Combine
3 + 2 + 5x = 6 + 10 + 2x
5 + 5x = 16 + 2x Subtract 5 from both sides
5-5+5x = 16-5 + 2x Combine
5x = 11 + 2x Subtract 2x from both sides
3x = 11 Divide by 3
x = 11/3
As you can see, I'm not getting any of the answers that you have provided. Ask your teacher how it was done. (The method used is correct).
costheta =12/13, 3pi/2
QUESTION 1
[tex]cos\ \theta = \frac{12}{13}\\\theta = cos^{-1}\frac{12}{13} = 22.62\textdegree = 0.3948\ (\text{radians})[/tex]
QUESTION 2
[tex]\frac{3\pi}{2} < \theta < 2\pi\ \text{then find}\ sin(2\theta)[/tex]
First, the fact that we have [tex]sin(2\theta)[/tex] means we have to adjust our range
[tex]\frac{3\pi}{2} < \theta < 2\pi\ \ \text{becomes}\ \ 3\pi < 2\theta < 4\pi\[/tex]
[tex]sin\ 2\theta = \frac{3\pi}{2}\\2\theta = sin^{-1} \frac{3\pi}{2}\\2\theta = \text{error}[/tex]
There are no solutions to inverse sin of [tex]\frac{3\pi}{2}\\[/tex]
If I have read a book at a rate of 20 chapters per hour. How many chapters does she read in 4 hours
20 × 4 = 80chapters
hope it helps...!!!
I Need some serious help
Answer:
3
Step-by-step explanation:
If you divide 42 oranges evenly among 6 people how many oranges will each person have
Answer:
7
Step-by-step explanation:
We have 42 oranges. we want to split the oranges evenly to 6 people. 42 divided by 6 people equals 7 oranges a person.
42÷6
=7
so each person will have 7 oranges.
Enter the correct answer in the box.
Write the expression 12-2 in simplest form.
Answer:
12-2 is 10
Step-by-step explanation:
Pattern A follows the rule "add 3" and Pattern B follows the rule "add 4." Pattern A 1 4 7 10 13 Pattern B 5 9 13 17 21 Which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B? Select all correct answers. (4, 13) (1, 4) (1, 5) (13, 17) (10, 17) (7, 13)
Answer:
(1,5) (7,13) (10,17) (7,13)
Step-by-step explanation:
1 4 7 10 13
5 9 13 17 21
Solve for X: Enter your answer in the box.
Answer: 6
Step-by-step explanation:
Year
1990
1995
2000
2005
2010
Cell Phone
Subscribers (millions)
4.9
38.3
118.1
229.8
360.4
Use the exponential regression to find an
equation that fits the data, where x is the years
since 1990.
The exponential regression that shows the relationship between the number of subcribers in millions (y) since 1990 is y = 4.9(1.37)ˣ
How to solve an exponential function?Let y represent the amount of subscribers in millions, x years since 1990.
From the table; at point (0, 4.9):
y= abˣ
4.9 = ab⁰
a = 4.9
At point (10, 118.1)
118.1 = 4.9(b)¹⁰
b = 1.37
The exponential regression that shows the relationship between the number of subcribers in millions (y) since 1990 is y = 4.9(1.37)ˣ
Find out more on exponential function at: https://brainly.com/question/12940982
What is the value of X
Answer:
X = 10.4
Step-by-step explanation:
Since the angle is a 90 degress angle we can assume that
39 + (5x-1) = 90 degrees.
Therefore we can subtract 39 from both sides which will give us
5x-1=51
Add 1 to both sides
5x = 52
Divide both sides by 5
x=52/5
The answer is
X = 10.4
Hope this helps! :)
A farmer plants crops on 60 acres of land. The circle graph shows the percentages of land used for some of the different types of crops.
Land for Crops
Corn
30%
Squash
45%
Other
5%
Carrots
Based on the circle graph, how many acres of land are used for carrots? TEKS 7.6G
Answer:
12 acres
Step-by-step explanation:
30+45+5 = 80 so theres 20% left.
20% of 60 is 12
what is located at ( -1.5 , -2 )
Answer:
in third quadrant... i thinkso
please help this is very important
4. sector angle = 120°
area of sector = 120/360* π*r^2
= 1/3 π *36 = 12π = 37.69 cm^2
area of isosceles ∆ = .5*36*sin 120 = 15.58cm^2
area of shaded portion = 37.69 - 15.58= 22.11 cm^2
5. sector area = 90/360 * π * 64 = 16π ft^2
area of right ∆ = 1/2*64= 32ft^2
shaded portion area = 16π-32 = 18.26ft^2
6. sector area = 60/360 π 36 = 6π m^2
triangle area = √3/4 * 36 = 9√3 m^2
shaded area = 18.84 - 9√3 = 3.26 m^2
7. sector area = 45/360*π*18^2 = 40.5 π yd^2
8. sector area = 90/360*π*16 = 64π cm^2
9. sector area = 60/360 * π * 169 = 28.16π m^2
10. sector area = 135/360*π*64 = 24π cm^2
1. circle area = π*5.5^2 = 30.25π cm^2
2. circle area = π*0.85*.85 = .7225π ft^2
3. circle area = π * 1/9 in^2
Angles and Parallel Lines
Answer:
a = 6
b = 25
Step-by-step explanation:
As alternative angles in a parallel line are equal to each other,
5a = 3a + 12
So, now we can find the value of a by making "a" the subject.
5a - 3a = 12
2a = 12
Divide both sides by 2.
a = 6°
And now let us find the value of b.
We know that interior angles in a triangle are added up to 180°.
So,
2b + 4b + 3a + 12 = 180
We can replace a with 6 and then we can make "b" the subject to find the value of b.
Let us solve it now.
2b + 4b + 3 × 6 + 12 = 180
6b + 18 + 12 = 180
6b + 30 = 180
6b = 180 - 30
6b = 150
Divide both sides by 6.
b = 25°
help this is a test grade and review but we never learned this
Judy earns $11.80 per hour working part time at a restuarant. How much money will she earn for 5 hours? NO DOLLAR SIGN IN YOUR ANSWER!The area of a rectangular city park is 15/56 square miles the width of the park is 3/7 miles what is length in miles of the park.
Answer:
Question 1: 59
Step-by-step explanation:
Question 1: 11.80*5=59
48
The two equations shown below represent different functions.
3
Function P: y = = +2
Function Q: y = x+2
1
: y
Identify each function as linear or nonlinear. State a reason why each function is
linear or nonlinear.
Function P
The function Q is a linear function because the function Q has a constant rate
How to identify the function types?The functions are given as:
Function P: y = 3/x + 2Function Q: y = 1/3x + 2A linear function is represented as:
y = mx + b
Where m represents the slope, and b represents the y-intercept
By comparing y = mx + b to the functions, we can see that the function Q is a linear function.
This is so because the function Q has a constant rate, while the function P does not have a constant rate
Read more about linear functions at:
https://brainly.com/question/4025726
PLEASE PLS HELP!!!! Find the height of the prism.
Answer:
[tex] \cos( \alpha ) = \frac{7}{25} \\ \alpha = (73.73979529169) \\ \ \sin(73.73979529169) = \frac{h}{25} \\ h = \sin(73.73979529169) \times 25 \\ h = 24[/tex]
the car is traveling at 80 kilometers per hour. what is the slope of the line?
Answer: y=80x
Step-by-step explanation:
It should be 80x ....try that
Which of the following statements is/are true regarding the figure above? Check all that apply. O A. It is a plane. O B. It is a point. C. It is a zero-dimensional object. D. It is a one-dimensional object. SUB
Answer:
b and d i think hope this helps
Step-by-step explanation:
The diameters of two circles are 12 and 9 what the difference in square centimeters between the areas of the two circles
Step-by-step explanation:
Area of circle= π(d/2)²For 1st Circle, A1= 36π
For 2nd Circle, A2= 81π/4
A1-A2 = 63π/4
π = 22/7
=49.5unit²
The differences in the areas of circles in square centimeters is 49.455
Formula for area of circle
[tex]A = \pi r^{2}[/tex]
Where,
A is the area of circle
r is the radius of circle
and π = 3.14
What is radius of a circle ?Radius of circle is the distance from the center of the circle to any point on it's circumference. It is calculated as :
[tex]Radius = \frac{diameter}{2}[/tex]
According to the given question
Diameter of one circle is 12cm and diameter of another circle 9cm.
Area of circle with diameter 12 cm = [tex]\pi (\frac{12}{2} )^{2}[/tex] = [tex](3.14)(6)^{2}[/tex] = 113.04 square cm
Area of circle with diameter 9 cm = [tex]\pi( \frac{9}{2} )^{2} =(3.14)(4.5)^{2} = 63.585[/tex] square cm
Therefore,
The difference between the areas of two circles = (113.04 -63.585) square centimeter = 49.455 square centimeter.
Learn more about the area of circle here:
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find the inverse of y=ln2x
Answer:
The exponential function, exp : R → (0,∞), is the inverse of the natural logarithm, that is, exp(x) = y ⇔ x = ln(y). Remark: Since ln(1) = 0, then exp(0) = 1. Since ln(e) = 1, then exp(1) = e.
Step-by-step explanation:The exponential function, exp : R → (0,∞), is the inverse of the natural logarithm, that is, exp(x) = y ⇔ x = ln(y). Remark: Since ln(1) = 0, then exp(0) = 1. Since ln(e) = 1, then exp(1) = e.
The mean of the following data is 20.7. Find the value of p 15 25 25 D 3 10 25 7
Answer:
the answer to that question is 5.314
Help
Brainleist
15 points
[tex] m \angle B = 22 \degree[/tex]
Explanation:
Given:
[tex]\sf m \angle A = 120 \\ \sf m\angle B =x \\\sf m \angle C = x+16[/tex]
To find:
[tex]\sf m\angle B \: = ?[/tex]
Solution:
We know that,
sum of all the interior angle of triangle equals 180 degrees.
[tex]\sf m \angle A + m\angle B + m \angle C = 180 \degree \\ \sf 120 + x + x + 16 = 180 \degree \\ \: \sf 2x+136= 180\degree \\ \: \sf 2x=180-136 \\ \:\sf 2x=44 \degree \\ \sf \: x= \frac{44}{2} \\ \:\sf x= 22 \degree[/tex]
Measure of angle B is equal to x hence,
[tex] m \angle B = 22 \degree[/tex]
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simplify the expression.
3/[tex]\sqrt{7}-\sqrt{2}[/tex]
[tex]\dfrac{3}{\sqrt 7- \sqrt 2}\\\\\\=\dfrac{3 \left( \sqrt 7+ \sqrt 2\right)}{\left(\sqrt 7- \sqrt 2 \right)\left( \sqrt 7+\sqrt 2\right)}\\\\\\=\dfrac{3 \left( \sqrt 7+ \sqrt 2\right)}{\left(\sqrt 7 \right)^2 - \left(\sqrt 2 \right)^2 }\\\\\\= \dfrac{3 \left( \sqrt 7+ \sqrt 2\right)}{7-2}\\\\\\=\dfrac{3 \left( \sqrt 7+ \sqrt 2\right)}5[/tex]
Doctor orders 100mg of amiordarone the bottle concentration is 5 mg/ml how many ml do you give?
Answer:
20 ml
Step-by-step explanation:
100 mg / ( 5mg /ml) = 20 ml
When paying down your student loan, a good strategy to pay down the principal is:
A. making payments in monthly installments.
B. paying more than the minimum payment each month.
c. beginning payments less than six months after leaving college.
D. paying less now and more later.
Answer:
It's A!
Step-by-step explanation:
A good strategy to pay down the principal of the student loan is making payments in monthly instalments, the correct option is A.
What is a Student Loan?A student loan is the amount borrowed by a student from a bank or any other financial institution for studies.
The borrowed amount is large and it becomes a burden if decided to pay all at once after studies on getting a job, a monthly payment of instalments is the right strategy.
To know more about Student Loan
https://brainly.com/question/3267326
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Solve for x.
Please help.
Answer: 4?
Step-by-step explanation: im prob wrong
Answer:
3.5
Step-by-step explanation:
Please help. ily:) Its rlly hard and i need bothe answers to do this.
Your answer is (3,6)
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(3,6)
Your Answer:
Your answer is (3,6)