An ellipse has the general equation
(x/a)² + (y/b)² = 1
(actually, this is an ellipse whose semimajor and -minor axes are parallel to the x- and y-axes, but one can rotate any ellipse so that it has the same configuration, and the area remains constant)
Convert to a kind of rescaled polar coordinates, using
x = a r cos(t)
y = b r sin(t)
Then the interior of such an ellipse is the set
E = {(r, t) : 0 ≤ r ≤ 1 and 0 ≤ t ≤ 2π}
The area of E is then given by the integral
[tex]\displaystyle \iint_E dA[/tex]
Compute the Jacobian determinant for this change of coordinates. The Jacobian is
[tex]J = \begin{bmatrix}x_r & x_t \\ y_r & y_t\end{bmatrix} = \begin{bmatrix}a \cos(t) & -a r \sin(t) \\ b \sin(t) & b r \cos(t)\end{bmatrix}[/tex]
Then we have Jacobian determinant
|det(J)| = |a b r cos²(t) + a b r sin²(t)| = |a b r| = |a b| r
since r ≥ 0.
The area of E is then
[tex]\displaystyle \iint_E dA = \iint_E |ab| r \, dr \, dt[/tex]
[tex]\displaystyle \iint_E dA = \int_0^{2\pi} \int_0^1 |ab| r \, dr \, dt[/tex]
[tex]\displaystyle \iint_E dA = 2\pi |ab| \int_0^1 r \, dr[/tex]
[tex]\displaystyle \iint_E dA = \boxed{\pi |ab|}[/tex]
3/7 times 2/3 equals
Answer:
2/7
Step-by-step explanation:
(----- equals fraction bar)
3/7 × 2/3
= 3 × 2
-----------
7 × 3
= 6/21
= 6 ÷ 3
------------
21 ÷ 3
= 2/7
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What is 2 1/5×(−5 1/3)? Write the answer as a mixed number in simplest form.
Answer:
-8 4/5
Step-by-step explanation:
With a tailwind , a bird flew at a ground speed of 3mi/h. Flying the same path against the same wind, the bird travels at a ground speed of 1.5mi/h. What is the bird's air speed? what is the wind speed?
The speed of a bird with respect to the wind Bird's air speed is 2.25 mi/h. The speed of the wind with respect to the ground wind's speed is 0.75 mi/h.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Relative speed is usually given in terms of the speed of body A with respect to another body B (Vab)
Vab = Va - Vb
Vab = Speed of A relative to B
Va = Speed of A
Vb = Speed of B
So, for this question, when the bird is travelling in the same direction of the wind, the speed of the bird with respect to the ground is 3 mi/h
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
Speed of bird with respect to the wind = x
Speed of bird with respect to ground = 3 mi/h
Speed of the wind with respect to the ground = y
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
x = 3 - y
When the bird is travelling in the opposite direction, the speed of the bird with respect to the ground is 1.5 mi/h
Speed of bird with respect to the wind = x
Speed of bird with respect to ground = 1.5 mi/h
Speed of the wind with respect to the ground = -y (Negative since the wind is in the opposite direction)
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
x = 1.5 - (-y)
x = 1.5 + y
We can then solve this system of equations
x = 3 - y
x = 1.5 + y
1.5 + y = 3 - y
y + y = 3 - 1.5
2y = 1.5
Divide both sides by 2
(2y/2) = (1.5/2)
y = 0.75 mi/h
x = 1.5 + y
x = 1.5 + 0.75
x = 2.25 mi/h
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PLEASE HELP ME OUT
NEED ASAP!!!
WILL GIVE BRAINLIEST
Answer:
GUUUURRRRLLLL!!!!!! Hey how are you !!!!!
Step-by-step explanation:
what is 7x17 in distributive law
Answer:
119
Step-by-step explanation:
I hope this helps!!:)
Solve the system of equations by the substitution method.
3x + 2y=22
x=5y-4
Type an ordered pair
Answer:
(6,2)
Step-by-step explanation:
To solve this equation using the substitution method we can plug in the given value of x into the equation, 3x+2y=22 and solve for y. Once we get the value of "y" then we can plug the y into our second equation which is x=5y-4.
3x+2y=22
plug in 5y-4 for the x value, so
3(5y-4)+2y=22 now distribute the 3 to the (5y-4) (multiply the 3 by 5y and -4)
3*5y= 15y and 3*-4= -12,
15y-12+2y=22 ←this is our equation after distributing
we can combine the 15y and 2y because they share the same variable
(15y+2y)
17y-12=22 add 12 to both sides to eliminate the -12 and divide by 17 to get rid of the 17 next to y or isolate the y variable
17y-12+12=22+12 → 17y=34 divide both sides by 17
[tex]\frac{17y}{17} =\frac{34}{17}[/tex] the 17's cancel and the 17 divides into 34, leaving us with
y=2
now substitute the y=2 into the equation x=5y-4
so x=5(2)-4 → x=10-4 → x=6
So we have the values for both our x and y values, all we need to do is put them in an ordered pair in the form (x,y)
so the ordered pair is (6,2)
Sorry people, I am so late. I totally forgot. I am giving out free pooints right now! Click answer fast!
Answer:
laaate
Step-by-step explanation:
Answer:
Thanks for the points!! :)
Step-by-step explanation:
PLzzz hruuy you will get 100 ponts limted time
Answer: I think it’s D
Step-by-step explanation:
Answer:
The domain is a set/group of x-values. The range is a set/group of y-values. The first option is not true because there are x-values which are greater than 0 (right side of graph). The second option is not true because the set of y-value stops before it hits the y=0. The third option is not true because there are no y-values which are less than 0 (bottom of graph). The fourth option is correct because the x-values stretch from -infinity on the left side of the graph to positive infinity of the right side of the graph.
:)
can i have help with this please
Answer:
a) 2 x 2 x 2
Step-by-step explanation:
If x2-6x+8=0, then x-6 or -2 =0
O True
False
Answer:
Step-by-step explanation:
The correct factors for this trinomial are
(x - 4)(x - 2)
I don't know where the two factors suggested in the problem come from, so I can't explain how I know they are wrong other than by giving you the correct factors of the given trinomial.
So the answer is false.
what is the 35th term of : 0.13 , 0.38 , 0.63 , 0.88 , 1.13
Answer:
206
Step-by-step explanation:
I think
Answer: 8.63
Step-by-step explanation:
-5 terms have been given so you need 30 more to reach 35.
-terms are going up by .25
30 * .25 = 7.5
7.5+1.13= 8.63
Write an equation in slope-intercept form for the line with slope and y-intercept 1. 4
Answer:
y=3x+1.4 (???)
Step-by-step explanation:
You didn't provide a slope or any points on the graph so I'm assuming you can just make whatever number you fancy the slope. Not very sure what you mean by this question... Try to give more info of the question!
If SV=38, SU=26, and the perimeter of SUV is 102, what is the value of RU?
Answer:
51
Step-by-step explanation:
What is the midpoint of the segment shown below?
Answer: D -9 -11
Step-by-step explanation:
A regular heptagon has sides measuring 3.2 inches and an apothem that measures 2.9 inches. What is the area of this heptagon?
Answer:
32.48 square inches
Step-by-step explanation:
The area of a polygon is [tex]A=\frac{nsa}{2}[/tex] where [tex]n[/tex] is the number of sides of the polygon, [tex]s[/tex] is the side length of the polygon, and [tex]a[/tex] is the length of the apothem.
We are given the polygon is a heptagon, so it has 7 sides, making [tex]n=7[/tex]
We are given the heptagon's side length is 3.2 inches, making [tex]s=3.2[/tex]
We are also given an apothem of 2.9 inches, making [tex]a=2.9[/tex]
Therefore, by using the formula for the area of a polygon, we get[tex]A=\frac{nsa}{2}=\frac{7*3.2*2.9}{2}=\frac{64.96}{2}=32.48[/tex]
In conclusion, the area of the heptagon is 32.48 square inches
Sara says, "If you subtract 15 from my number and multiply the difference by -6 , the result is -90." What is sara's number?
the answer should be 21
I hope that's the right answer I really wouldn't rely on me but hope that helps
Answer:
30
Step-by-step explanation:
Can you help me please I need help :,)
Answer:
24v+8
Step-by-step explanation:
Calculations
Answer:
24v+8
Step-by-step explanation:
-8(-1 - 3v)
-8(-3v -1)
distribute
24v+8
A hand-held digital music player was marked down by 1/4 of the original price. If the sales price is $200. What is the original price?
Group of answer choices
$266.67
$270.00
$225.00
$250.00
Answer:A boo
Step-by-step explanation: trust me :) ✨
help-
Use the cubes to find the surface area of the shape, in square inches.
Remember, some sides may not be visible in the picture.
18in.215in.213in.210in.28in.218in.2
Answer:
18 inches squared
Step-by-step explanation:
What is the value of x? −7.5(x−3)=3.75
[tex]{\boxed{ \Huge{ \blue{ \mathcal{{ Answer}}}}}}[/tex]
⇛-7.5(x−3) = 3.75
⇛-7.5x + 22.5 = 3.75
⇛-7.5x = 3.75 - 22.5
⇛-7.5x = -18.75
⇛x = -18.75 ÷ -7.5
⇛x = -18.75/-7.5
⇛x = 2.5
Answer:
2.5
Step-by-step explanation:
-7.5(x-3)=3.75
or, -7.5x+22.5=3.75
or, -7.5x= 3.75-22.5
or, -7.5x= -18.75
or, x= 18.75÷7.5
or, x= 2.5
Can anyone help me ASAP!
Answer:
Step-by-step explanation:
65
Answer:
91.9 feet to the nearest tenth.
Step-by-step explanation:
Let the required distance be x feet.
Using the Pythagoras theorem:
x^2 = 65^2 + 65^2
x^2 = 8450
x = 91.9.
Write the square of the first three multiples of 3.
Hello there!
The first 3 multiples of 3:
3, 6, 9.
3 squared (3 times itself) equals 9
6 squared (6*6)=36
9 squared (9*9)=81
Therefore, our answers are: 3, 6, 9 (9, 36, 81)Hope this helps!
~Just a felicitous girlie
[tex]SilentNature[/tex] is here to help
In the equation 3x+4=13, the 3 is called what?
Answer:
:Coefficient
Step-by-step explanation:
write 1 1/8 as an Improper fraction SOMEONE PLEASE HELP I ONLY HAVE 20 MINUTES LEFT
Answer: 9/8
Step-by-step explanation: 8x1+1=9
Hello there! :)
1+1/8
When converting numbers from mixed numbers to improper fractions, we follow some steps.
First, we multiply the whole number by the denominator.Then, we add the numerator.Multiply 1 times 8:
8
8 plus 1 (the numerator)
Therefore, our answer is: [tex]\frac{9}{8}[/tex]Hope this helps!
~Just a felicitous girlie
#HaveAnAwesomeDay
[tex]SilentNature (GraceRosalia)[/tex] here to help
PART IILASSESSMENT 1 Write ratio for each illustrations and ( word form) o 2 and (fraction form) 3. 15 sacks of rice and a boxes of canned goods (colon form) Express the following ratios in lowest term 4. 5. 15 = II 5. 80 100 6. 24:48= or 7. 468 students to 9 classrooms 8. 54 km to 3 hours III. Write equivalent ratios to each given ratio below. 9. 3 = 4 10. 20 8 = 11.6.18= Write the letter of the correct answer 12. Which of the following is the same as 50 is to 100? a 2 2 b. 4. c. 1 d. 5 5 6 2 5 13. A pupil answered 42 correct answers out of 50 questions What ratio can be written for the given quantities? 50 b. 50:42 c. 42.50 c. 50 is to 42 42 14. Grade 6 Newton has 12 girls and 18 boys. Which of the following DOES NOT describe the ratio of the girls to the boys? a 12 is to 18 b. 12:18 c. 12 d. 18:12 а. 18 15. What is the lowest term for the ratio 45 is to 60? a. 3 b. I c.2 4. 2 3 4 dl 16. What fraction of 45 meters is 15 meters! a 3/4 b. c. 1/3 d.
The ratio gives the number of times one value can be found in the other value.
The correct responses are;
1. The ratio is three to eight
2. The ratio in fraction form is [tex]\dfrac{12}{7}[/tex]
3. The ratio in column form is 15:9 = 5:3
II. 4. 5: 15 = 1 : 3
[tex]5. \ \displaystyle \frac{80}{100} = \frac{4}{5}[/tex]
6. 24 : 48 = 1 : 2
7. 468 students to 9 classroom = 52 student to 1 classroom
8. 54 km to 3 hours = 18 km to 1 hour
III. 9. [tex]\displaystyle \frac{3}{4}= \frac{6}{8}[/tex]
10. 20 : 8 = 5 : 2
11. 6 : 18 = 1 : 3
IV. 12 [tex]\displaystyle \frac{50}{100} = \frac{1}{2}[/tex] The correct option is c.
13. 42 out of 50 = 42 : 50
The correct option is c.
14.The ratio of girls to boys is 12:18 not 18:12
The option that DOES NOT describe the ratio is d. 18:12
15. [tex]\displaystyle \frac{45}{60} = \frac{3}{4}[/tex]
The correct option is a.
16. The fraction of 45 meters that is 15 meters is [tex]\displaystyle \frac{45}{60} =\frac{3}{4}[/tex]
The correct option is c.
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2. Find the axis of symmetry for the quadratic function, 2x2
- 40x = 0?
Answer:
x=1/10
Step-by-step explanation:
A frame of a house is being built. The face of the roof is shown as follows, where BA=AC and BD=20 feet.
Answer:
BC = 20
Step-by-step explanation:
if bd is 30 and ba and ac is the same it means that dc is 20 as well
sorry if i got this wrong
Which pair shoes equivalent expressions
Answer:
sketcher's
Step-by-step explanation:
how do I do this I forgot
Speed = distance / time
45 minutes = 0.75 hours
1 hour and 45 minutes = 1.75 hours.
70 km / 1.75 hours = 40 km per hour
Answer: 40 km per hour
will give brainliest no files will report Select the correct answer.
Answer:
A
Step-by-step explanation:
