The formula for the area of an ellipse is Arnab. Using a + b = 20 write the area of
the ellipse as a function of a by solving for a and then plugging in your results
into the formula for the area of an ellipse to replace b.
Answers
[tex]A=\pi ab\qquad \qquad \begin{array}{llll} a+b=20\\ b=20-a \end{array}\qquad \qquad \stackrel{\textit{substituting}}{A=\pi a(20-a)}\implies A=\pi (20a-a^2)[/tex]
The area of the ellipse is given by the function A(a) = 20πa - πa², where a is a parameter representing one of the semi-major axes of the ellipse.
To write the area of the ellipse as a function of a using the given constraint a + b = 20, we first need to solve for b in terms of a and then substitute the expression for b into the formula for the area of the ellipse.
Given the equation for the ellipse:
x²/a² + y²/b² = 1
We have the constraint: a + b = 20
Now, let's solve for b in terms of a:
b = 20 - a
Now, we'll substitute this expression for b into the formula for the area of the ellipse:
Area (A) = πab
Area (A) = πa(20 - a)
Area (A) = 20πa - πa²
So, the area of the ellipse is given by the function A(a) = 20πa - πa², where a is a parameter representing one of the semi-major axes of the ellipse.
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Related Questions
How do I divide using "partial remainders"?
Answers
Step-by-step explanation:
When the modulus is ∞, the result is equal to the value in ST(0). Otherwise, C2 is set, and the result in ST(0) is called the partial remainder. The exponent of the partial remainder will be less than the exponent of the original dividend by at least 32. Using partial remainders, dividing multiples of 4 from 46 until you can't divide anymore. You can't divide anymore because 2 is less than 4. So, 2 is the remainder.
What is the sum of (X^2-1+7-3x-x2)(x)
Answers
x^3-5x^2+6x
Step by step solution:
(x^2-1+7-3x-2x)(x)
x^3-x+7x-3x^2-2x^2
x^3+6x-5x^2
The right way to write it is the power of x decreasing so it would be x^3-5x^2+6x
Simplify the expression.
−10−3
Answers
Answer:
-13
Step-by-step explanation:
Suppose a quadratic equation has the form x^2 + x + c = 0. Show that the constant c must be less than 1/4 in order for the equation to have two real solutions.
Answers
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then for the equation to have 2 real roots , the discriminant must be greater than zero , that is
b² - 4ac > 0
x² + x + c = 0 ← is in standard form
with a = 1, b = 1, c = c , then
b² - 4ac > 0
1² - (4 × 1 × c) > 0
1 - 4c > 0 ( subtract 1 from both sides )
- 4c > - 1
Divide both sides by - 4, reversing the inequality as a result of dividing by a negative quantity.
c < [tex]\frac{1}{4}[/tex]
Who ever is right i will mark brainilest
Answers
Answer:
no
yes
no
yes
Step-by-step explanation:
thats the answer
A phone company is offering several different prepaid data plans.
Prepaid Single Phone Plan Prepaid Family Plan
$30 for 1 GB $30 for 1 GB
$35 for 6 GB $40 for 6 GB
$45 for 16 GB $50 for 16 GB
$65 for Unlimited Data $70 for Unlimited Data
Answers
A right triangle has side lengths of 5 inches, 12 inches, and 13 inches. The triangle will be rotated 180° about a point.
What is the length of the longest side of the triangle after the rotation? Enter the answer in the box?
Answers
13in will be the longest like before .
Refer to the attachment for more observation.
The length of the longest side of the triangle after the rotation is 13 inches.
What is Right Angle?It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.
Ancient geometry defined a right angle as the intersection of two straight, or right, lines in relation to dimensional axes.
Given:
A right triangle has side lengths of 5 inches, 12 inches, and 13 inches.
As, we know that the longest side is the Hypotenuse which is 13 inches and the base is 12 inches and perpendicular is 5 inches.
After 180° rotation only the base and perpendicular change the longest side still remain the same.
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[tex]Simplify..... \\ \\ \frac{6x ^{4} {y}^{2} \times 4 {x}^{6} {y}^{3} }{12 {x}^{5} {y}^{4} } [/tex]
..............................
Answers
Hope it helps.
Don't forget to click the Brainliest button if you like my answer and if you have any query, please feel free to ask in the comment section.
help what’s the answer
Answers
Answer: A. Vertical angles
Step-by-step explanation:
They are vertically opposite angles.
Correct me if I am incorrect.
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Which inequality includes q = 24 in the solution set?
1/2q>12
3/4q<18
6≥1/4q
9≤1/3q
Answers
Answer:
Im 99% sure its B
Step-by-step explanation:
Piper is located at (3, -12) on a map. Bobbi is located at
(3, 2). How far apart are they?
Answers
Check the picture below.
Create your own example for each cases of multiplying
polynomials With complete solution
Case 1: Distributive Property
Case 2: FOIL Method
Case 3: Binomial to Polynomial
Pls needed badly
If you have nothing to answer dont answer
Answers
I NEED HELP PLEASEEEEEEEE÷E
Answers
Answer:
C = -1 1/9° or -1.11°
Step-by-step explanation:
Use the formula given, and input 30 for F
[tex]C = 5/9(F - 32)\\\\C = 5/9(30 - 32)\\\\C = 5/9(-2)\\\\C = -10/9 = -1 \frac{1}9 = -1.11[/tex]
30°F ≈ -1.11°C
-Chetan K
This value is approximate.
==================================================
Explanation:
You're given a temperature of 30 degrees F and your teacher wants to know the Celsius version of this temperature. Plug in F = 30 and simplify.
[tex]C = \frac{5}{9}(F-32)\\\\C = \frac{5}{9}(30-32)\\\\C = \frac{5}{9}(-2)\\\\C \approx 0.5555*(-2)\\\\C \approx -1.111\\\\[/tex]
The temperature 30 degrees F converts to approximately -1.111 degrees C. Fahrenheit temperatures below 32 degrees are below 0 when converted over to Celsius.
You have a Rectangle with sides of 5ft and 8ft; solve for its perimeter and area.
Answers
Answer:
Perimeter = 2(l+w) = 2*(5+8) = 26ft
Area = wl = 8*5 = 40
Step-by-step explanation:
pretty sure :)
−4x − 10x what is the answer??????
Answers
Answer:
-14x
Step-by-step explanation:
help me plzzz i really need help its also in Spanish plzzzzzzzzzzzz help meeeee(ToT)(ToT)(ToT)
Answers
Answer:
1. veinte (10 * 2 = 20)
2. tres ( 12 ÷ 4 = 3)
3. veinte (18 + 2= 20)
4. diez ( 15 - 5 = 10)
5. once (14 - 3 = 11)
Liam cuts a 48-inch piece of string into two pieces. One piece is 12 inches longer than the other. If s represents the length of the shorter string, which diagram best represents this scenario?
Answers
The length of the shorter string is 18 inch while that of the longer string is 30 inch.
An equation is an expression used to show the relationship between two or more variables and numbers.
Let s represent the length of the shorter string.
One piece is 12 inches longer than the other
Length of longer string = s + 12
Since a 48-inch piece of string is cut into two pieces. Hence:
s + (s + 12) = 48
2s + 12 = 48
2s = 36
s = 18
Length of longer string = 18 + 12 = 30
The length of the shorter string is 18 inch while that of the longer string is 30 inch.
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Jack’s school bag contains 8 books each of weight 3/8 pounds, and 6 folders of weight 1/2 pound. b) What fraction of the total weight is folders?
Answers
Answer:
6 pounds
Step-by-step explanation:
3/8×8/1=24/8=3
6/1×1/2=6/2=3
3+3=6
Yoni has a ribbon that measures 5/3 yards. She wants to cut it into 3 equal pieces. What is the length of each piece of ribbon? 5\8 yards 5/6 yards 5/9 yards 5/3 yards
Answers
Answer:
Step-by-step explanation:
[tex]\frac{1}{3} * \frac{5}{3} = \frac{1 * 5}{3*3} = \frac{5}{9}[/tex]
The answer is 5/9 as you can see. 5/9 = 20 inches each.
1 yard = 36 inches
(5/9 * 36) = 5 * 4 = 20 inches.
Answer:
5/9
Step-by-step explanation:
I have a trick id like to teach here. Whenever you have a fraction being divided by a whole number, you can multiply the denominator by the diviser
So what I did was multiply the 3 by the diviser(3) and got 9
This left me with 5/9
evaluate the expression when b=3/10 and x= -2/15
3x-b
Answers
Answer:
3x - b
3 (-2/15) - 3/10
-6/15 -3/10
-60/150 - 45/150
- 105/150
Paula's Pies is famous
for their apple pie. At
Thanksgiving, they receive
orders for 296 pies. If
Paula can prepare 8 pies
in 3 hours, then how many
hours will it take her
prepare the order?
(PLEASE MAKE THE WORK A RATIO TABLE!)
Answers
Sets of 8pies
296/8=37No if time for 8pies=3h
No of time for 37 sets of 8pies:-
3(37)=111hHelp help help math math help
Answers
Answer:
63°
Step-by-step explanation:
Angle 2 is congruent in angle that has 63°
Refer to the attached pic
Question
The width of the rectangle is 40% of its length. What is the area of the rectangle?
The length is 20 feet. What is the anwser in feet squared
Answers
Answer:
160 ft²
Step-by-step explanation:
The width is 40% of the length, so is ...
0.40 × 20 ft = 8 ft
The area is the product of length and width:
A = LW
A = (20 ft)(8 ft) = 160 ft²
What is the value of
negative 3/4 with negative 4 as a exponent
Answers
Answer:
=[tex]\frac{256}{81}[/tex]
(Decimal: 3.160494)
Step-by-step explanation:
[tex](\frac{3}{4} )^-4[/tex]
[tex](\frac{4}{3} )^4[/tex]
[tex]\frac{4^4}{3^4}[/tex]
=[tex]\frac{256}{81}[/tex]
(Decimal: 3.160494)
:)
I hope this helps
Suppose the regression line for the number of runs scored in a season, y , is given by ˆy=−790+5400x , where x is the team's batting average. For a team with a batting average of 0.235, find the expected number of runs scored in a season. Round your answer to the nearest whole number. If we can expect the number of runs scored in a season is 400, then what is the assumed team's batting average? Round your answer to three decimal places.
Answers
Answer:
479 = expected runs
0.220 = assumed batting average
Step-by-step explanation:
ˆy=−790+5400x
For an x value of 0.235, we have to calculate ˆy, or the predicted value. Plugging 0.235 in for x, we get
-790 + 5400 * 0.235 = 479
If ˆy = 400, we have to calculate x. Plug 400 in for y in our equation to get
400 = -790 + 5400x
add 790 to both sides to isolate the x and its coefficient
1190 = 5400x
divide both sides by 5400 to solve for x
x= 0.220
Jill bought 7 pounds of melon and 0.9 pounds of cherries. How much fruit did she buy in all
Answers
Answer:
7.9 pounds of fruit
Step-by-step explanation:
In all means to add, so 7 + .9 = 7.9 pounds
hello, please help me thanks:)
Answers
Step-by-step explanation:
2x + 5y
first add 2 and 5
and join x and y and it
answer is 2+ 5
=7 and x+y = xy
it axle answer is
= 7xy
Can someone help me please I will mark u brilliant
Answers
Answer:
i believe it would be likely
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
A train travels from point A to B at a speed of 100km/h. how long it will take to travel 25 km
Answers
Answer:
Step-by-step explanation:
25 km / 100 km/hr = 0.25 hr or 15 minutes
It will take 0.25 hours to travel 25 km.
Given
A train travels from point A to B at a speed of 100km/h.
Distance;
Distance is defined as the product of speed and time.
The following formula is used to calculate the time;
[tex]\rm Time =\dfrac{Distance}{Speed}\\\\[/tex]
Substitute all the values in the formula;
[tex]\rm Time =\dfrac{Distance}{Speed}\\\\\rm Time =\dfrac{25}{100}\\\\Time = 0.25 \ hours[/tex]
Hence, it will take 0.25 hours to travel 25 km.
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Help I’m so confused
Answers
Answer:
5x: linear; monomial
-7: constant; monomial
x^2 + 4: quadratic, binomial
x^2 - 3x + 11: quadratic, trinomial
2x - 9: linear, binomial
Step-by-step explanation:
Name using degree: just count the highest number of variables in a single term. if it's 0, its a constant polynomial, if it's 1 it's linear, 2 quadratic, 3 cubic
Name using number of terms: just count the number of "things" added or subtracted. If there's one, it's a monomial, two: binomial, three: trinomial.