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
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
8.03 as a improper fraction
Answer:no
Step-by-step explanation:
Compare using >, = or <.
-3_-5
Answer:
-3>-5
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:
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:
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
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
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
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
A markdown, or discount, is an example of a percent increase. Answer TRUE or FALSE.
True
O False
Answer:
true
Step-by-step explanation:
here u go the question
Answer:
$31.08
Step-by-step explanation:
What is -6y + 3 = 3?
Answer:
y=0
Step-by-step explanation:
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
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]
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.
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]
30 POINTS PLEASE HELP Solve 2 (e)^3t =10 for t. Round to three decimal places
Answer:
jjk
Step-by-step explanation:
,,45
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.
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!!
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
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
3. Which interval represents the range of the function h(x) = 2x2 - 12x + 13 ?
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.
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
1953+1038please answer ............
Answer:
2991
Step-by-step explanation:
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
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:
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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