Let R be region in the xy-plane and β>0 be the constant. What is the region R that will minimize the value of integral (x² + y² - β²).
i.e.
[tex]\int \int _R (x^2 +y^2 - \beta^2) \ dA[/tex]
Answer:
0
Step-by-step explanation:
Given that:
[tex]\int \int _R (x^2 +y^2 - \beta^2) \ dA[/tex]
where;
R is the region in the xy-plane.
To minimize our double integral, we have to determine the region over which the function we are integrating has a negative value.
x² + y² - β² ≤ 0 ; where β > 0 is a constant
x² + y² ≤ β² is the circle with center (0,0)
Radius "β" because R: x² + y² ≤ β²
The polar coordinates: x = rcosθ and y = rsinθ
x² + y² = r²
⇒ r limits : r = 0 → β
⇒ θ limits : r = 0 → 2π
[tex]\iint_R(x^2+y^2-\beta^2) \ dA =\int\limits ^{2 \pi}_{\theta=0} \int \limits ^{\beta}_{r=0}( \beta^2 -\beta^2) \ rd \ rd\ \theta[/tex]
[tex]\int \int _R (x^2 +y^2 - \beta^2) \ dA[/tex] = 0
Enter the value of the underlined digit. 7.806 (7 is under lined)
Answer:
Ones place
Step-by-step explanation:
Hope this helped, Have a Wonderful Day/Night!!
please solve this question
Answer:
I think its C
Step-by-step explanation:
Answer:
a 84
Step-by-step explanation:
add them all together then subtract by 360
Scientific notation 0.0094592
Scientific notation 0.94592
Answer:
The answer will be listed below.
Step-by-step explanation:
The scientific notation of 0.0094592 would be 9.4592x10^-3 power. The scientific notation of 0.94592 would be 9.4592x10^-1. To put a standard notation into scientific notation, simply move the decimal left to right until you have a number in the ones place that isn't zero.
Where does the pendulum have the most potential energy
Answer:
1 because its the most high up.
Step-by-step explanation:
The higher a ball is, it has mor e potential energy plz mark brainliest if correct
1. Olivia has read 40 pages of a 70-page book. What percent of pages has Olivia read? (Round your answer to the nearest tenth). A. 40% B. 42.9% C. 57.196 D. 28%
If Olivia has read 40 pages of a 70-page book. Then 57.196% of pages has Olivia read
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Olivia has read 40 pages of a 70-page book.
We need to find percent of pages has Olivia read
Let x be the percent of books olivia read.
This can be done by 70 x=40
Divide both sides by 70
x=40/70
x=0.5719
Now multiply this with 100
0.5719×100
57.196
Hence 57.196% percent of pages has Olivia read
To learn more on Percentage click:
https://brainly.com/question/28269290
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Which integer represents the situation. Jacob owes his dad $5.
Answer:
-5
Step-by-step explanation:
Its negative 5 because it being given to the dad
1953+1038please answer ............
Answer:
2991
Step-by-step explanation:
The points (15,36) and (30,72) form a proportional relationship. Find the slope of the line through
the points. Then use the slope to graph the line.
The slope is
(Simplify your answer.)
Answer:
[tex]\frac{18}{5}[/tex]
Step-by-step explanation:
Given coordinates;
(15,36) and (30,72)
Unknown:
Slope of the line = ?
Solution:
(15,36) and (30,72);
Slope is the rise divided by the run. To find the slope, we use the expression below;
Slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
y₁ = 36
y₂ = 72
x₁ = 15
x₂ = 30
Insert the parameters and solve;
Slope = [tex]\frac{72 - 36 }{30 -15}[/tex] = [tex]\frac{36 }{15}[/tex]
Slope = [tex]\frac{18}{5}[/tex]
3. Which interval represents the range of the function h(x) = 2x2 - 12x + 13 ?
Which of the following could be the equation of a line parallel to the line y =4
Answer:
Since slope of line y = 0 and y = 4
Step-by-step explanation:
Given:
y = 4
Computation:
Equation of slope;
y = ax + c
So,
y = (a)(0) + 4
Since slope of line y = 0 and y = 4
Answer:
y=0
Step-by-step explanation:
Jimmy borrowed $450 to start a lawn-mowing business. He charges $35 per lawn and it costs him $8 in operating costs per lawn.
What is the y-intercept of the line representing Jimmy's costs?
Answer: $450
Step-by-step explanation:
Given that:
Amount borrowed = $450
Amount charged per lawn = $35
Operating cost per lawn = $8
Jimmy's cost (C(x)) :
Amount borrowed + operating cost
If x lawns are mowed :
$450 + $8 per lawn
$450 + $8x
C(x) = 450 + 8x
Intercept (value of y when x = 0
Value of C(x) ; when x = 0
C(x) = 450 + 8(0)
C(x) = 450 + 0
C(x) = 450
here u go the question
Answer:
$31.08
Step-by-step explanation:
A pencil factory has increased the amount of
pencils produced from 1200 to 1500 pencils. What
is the percentage increase?
HURRY
Answer: 300 pencils
25 percent also
Step-by-step explanation:
25
Percentage Calculator: What is the percentage increase/decrease from 1200 to 1500? = 25.
use the defintion of the derivative to find the derivative of the given function. f(x)= 5 square root of x
Answer:
The derivative of function [tex]f(x)=5\sqrt{x}[/tex] is [tex]\frac{5}{2\sqrt{x} }[/tex]
Step-by-step explanation:
We need to find derivative of the given function [tex]f(x)=5\sqrt{x}[/tex]
Finding the derivative:
[tex]\frac{d}{dx}(5\sqrt{x} )[/tex]
Using the rule (a.f)' = a(f)', taking out constant value 5
[tex]=5\frac{d}{dx}(\sqrt{x} )[/tex]
We know [tex]\sqrt{x} =x^{\frac{1}{2}[/tex] Replacing [tex]\sqrt{x}[/tex]
[tex]=5\frac{d}{dx}(x^{\frac{1}{2}} )[/tex]
Applying derivative rule: [tex]\frac{d}{dx}(x^a)= a.x^{a-1}[/tex]
[tex]=5\times\frac{1}{2}(x^{\frac{1}{2}-1} )\\=\frac{5}{2}(x^{-\frac{1}{2}} )\\=\frac{5}{2x^{\frac{1}{2}}}\\=\frac{5}{2\sqrt{x} }[/tex]
So, the derivative of function [tex]f(x)=5\sqrt{x}[/tex] is [tex]\frac{5}{2\sqrt{x} }[/tex]
Compare using >, = or <.
-3_-5
Answer:
-3>-5
Step-by-step explanation:
A markdown, or discount, is an example of a percent increase. Answer TRUE or FALSE.
True
O False
Answer:
true
Step-by-step explanation:
ABCD is an isosceles trapezoid with diagonals that intersect at point P. If AB || CD, AC = 7y -30, BD = 4y + 60, and
CD = 5y + 14, find the length of CD
A. 124
B. 164
C. 180
D. 244
What is -6y + 3 = 3?
Answer:
y=0
Step-by-step explanation:
What is the value of the expression when a = 5 and b = 2?
2a+b−3
6
9
11
24
Answer:
the answer is c because 2 *5 is 10+2 is 12-3 is 9
Step-by-step explanation:
improper fraction as mixed number in simplist form 14/6
Answer: 2 1/3
Step-by-step explanation: 2 and 1/3.
14/6 = 2.3333... which is 2 1/3 as a mixed number.
Answer:
2 1/3
Step-by-step explanation:
simpliying this you would make it into 7/3 then divide each by thre then get 2 1/3
30 POINTS PLEASE HELP Solve 2 (e)^3t =10 for t. Round to three decimal places
Answer:
jjk
Step-by-step explanation:
,,45
Complete the even numbers
Answer: change in y over Change in x(slope)
2. 3/3 or 1
4. 5/4
6.4/5
8.1/4
10.-2/-3
12.1/-3
14.-9/9 or -1
Can someone please help me
Answer: (2,-4) is point a
Step-by-step explanation: when looking for a plotted point, the x axis can drop down to negatives since they y axis is negative
The fastest elevators in the Burj Khalifa can travel 330 feet in just 10 seconds How fast does the elevator go in 1 foot?
Answer:
0.03030
Step-by-step explanation:
10/330=0.03030303
Answer:
33
Step-by-step explanation:
the elevator can travel 330 feet in 10 second 330/ 10
Write an equation of the line with a slope of -7 and y-intercept of 1
Answer:
y=-7x+1
Step-by-step explanation: Hope this helps!!
Can i have brainliest?
Write an equation for the line parallel to y=2x+6 that contains P(-7,-4)
Answer:
This is the best i got
Step-by-step explanation:
HELP ME QUICKLY!!!!!!!!!!!!!!!It takes Luis 15
minutes to read 3
pages. How long
Will it take him to
read 90 pages?
Answer:
450 min hope this helps!
Step-by-step explanation:
Answer
It will take him 450 minutes to read 90 pages.
Explanation
Luis can read 3 pages every 15 minutes.
You are trying to find how long it will take him to read 90 pages.
Set up this ratio.
[tex]\frac{15}{3} =\frac{x}{90}[/tex]
To get from 3 to 90, you multiply by 30. Do the same thing to 15.
15 times 30 is 450.
It will take Luis 450 minutes to read 90 pages.
8.03 as a improper fraction
Answer:no
Step-by-step explanation:
sally used all of the paint shown below to make a certain tint of orange paint.
Answer:
We can't see the paint, and what's the question?
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
Zahara constructs 5 mirror frames in 30 minutes. At that rate, how many mirror frames can Zahara make in 9 hours
Answer:
90 mirrors
Step-by-step explanation:
If 5 mirrors=30 mins
then x=9 hrs
therefore 30÷60 to covert it to hours is equal to 0.5hr
5×9hrs÷0.5hr=90
therefore x=90