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.

The Formula For The Area Of An Ellipse Is Arnab. Using A + B = 20 Write The Area Ofthe Ellipse As A Function

Answers

Answer 1

[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]

Answer 2

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

Help me please I'm stuck on this question​

Answers

Answer:

n= 2.9

1:2.9

Step-by-step explanation:

Divide by 15 on both sides

15 divided by 15 is 1

43 divided by 15 is 2.8666666666=>

It states "Give any decimals in your answer to 1 d.p.

Mean we round it to one decimal place

so it is 2.9

Thus the answer for n is 2.9

Hope this helps!

Can someone pls help me!! And if u can explain how u do it I will very thankful for that..

Answers

Answer:

For the first question is 8y, and the second question would be 80

Step-by-step explanation:

The perimeter of a shape is calculated by adding it's sides together, and 2y+2y+2y+2y=8y. If y=10, we can substitute y for 10 in which 8*10 is 80.

convert 24580 m into km with process ​

Answers

Answer:

24.58 km

Step-by-step explanation:

1 km = 1000 m

1 m = 1 / 1000 km

24580 m

= 24580 / 1000

= 24.58 km

Solve. 9(8 - x) = 3x brainly EEE PLSS

Answers

Answer:

x=6

Step-by-step explanation:

9(8-x)=3x

9 x 8=72

72-9x=3x

72=12x

72/12=6

x=6

PLEASE HELP IM REALLY NEED HELP

Answers

Answer:

x=7

Step-by-step explanation:

3.5/3= 1.1666666666

6*1.16666666= 7

x=7

If a < b then ka < kb

Answers

What? That dose not make any sense

Pls help!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

See below:

Step-by-step explanation:

First fill in:

180* . Every triangle has interior measurments of 180* total

Second fill in: Reason is definition of sum of triangle's interior angles

Third fill in: 2x. Everything in this equation is asking for the angles. First angle is 28, second angle is 2x, and third angle is x-4.

Fourth fill in: x=52

I found this by doing the following:

First, 180-28, so we can see how many degree we are left with.

152.

Now, make an equation:

152=2x+x-4

Simplify

152=3x-4

Add 4 to both sides to cancel out the -4.

156=3x

divide 156/3=52.

Now we know that x=52.

Although the question doesn't ask for this, you would now substitue 52 back into each of the equations to find that degree. For example, 2x=2(52), or 104*.

Answer:

See image

Step-by-step explanation:

All the angles of a triangle add up to 180°

The given diagram shows all the measures: 28°, x - 4° , and 2x

So add them up, set equal to 180 and solve for x. Combine like terms and subtract 24 from both sides of the equation. Divide both sides by 3. x = 52

Mark used 14 bananas, 15 oranges, and 24 strawberries in his fruit salad.
Dani used 7 bananas, 9 oranges, and 12 strawberries. Did Mark and Dan
use the same ratio of bananas to strawberries? *

Answers

Answer:

yes-

Step-by-step explanation:

im not to sure if its right but

7+7=14

12+12=24

which expression represents 100 less than 3 times the sum of 18 and 2

Answers

Answer: 3 times (18+ 2) - 100

3 (18+2) - 100 = -40

Step-by-step explanation:

1 5/8 ÷ (−1 3/5) Please help

Answers

The answer is (-75/104)

A car is 15 feet long. A truck is 80% longer than the car. How long is the truck?
Enter numerical answer only. (just the number)

also thank you to everyone that has been helping me out when i have quetions.
also be as fast as you can cause this quiz is do in 30 min cause i am staying after school.

Answers

Answer:

27

Step-by-step explanation:

Answer:

27 feet

Step-by-step explanation:

One way to do this is: 15 * 0.8 = 12 and you can add the original 15 feet to get 27 feet in total. I converted the 80 percent to a decimal and added it back to the original number.

Another way to do this is: 15 * 1.8 and the result is also 27 feet.

why you always angry why you always quiet why do you sleep alone when I know you don't like it maybe you might be different will it kill you to tell me the truth what in the hell does a man have to do to be loved by you

Answers

Answer:

Beause you did love to be loved by you

Step-by-step explanation:

Maybe a spoon full of sugar will help but I'm not going to love you because love this pure is hard to find in world so scard from humanity and the hideous presence of me

Tomatoes that regularly sell for $0.55 per pound are on sale for 20% off the regular price. What is the sale price?

Answers

Answer:

$0.44

Step-by-step explanation:

lmk if you want an explanation

Two wheelchair ramps, each 10 feet long, lead to the two ends of the entrance porch of Mr. Bell's restaurant. The two ends of the porch are at the same height from the ground, and the start of each ramp is the same distance from the base of the porch. The angle of the first ramp to the ground is 24°.

Answers

Answer:

It must have an angle of exactly 24°.

Step-by-step explanation:

Answer:

It must have an angle of exactly 24°.

Step-by-step explanation:

I got a 100% on my mastery test

6(3x+12-4x)=2x+2+3x solve for x

Answers

Answer:

its 70/11 or 6.36

Step-by-step explanation:

Help pelsss thank you math sucks

Answers

Answer:

103

Step-by-step explanation:

180-77=103

What is the x-value of the vertex of f(x) = -x2 + 9x - 11 ?

Answers

Answer:

I believe it would be 9/2 !

Step-by-step explanation:

Use technology to find points and graph the line -4y=-x+20

plotting on a graph

Answers

Step-by-step explanation:

First we need to isolate the y, by dividing -4 on both sides. This will give you y = 1/4x - 5.

Now you can properly graph the equation:

Since -5 is the y-intercept (the point in which the line intercepts the y-axis), we will place our first point at (0,-5) on the graph.

In order to find the next point, we will use the slope of the line and do rise/run. So we will go upwards 1 unit and to the right 4 units.

(Image of graph will be attached above⤴⤴⤴)

Hope this helps you :)

help as soon as possible
The greatest common factor of y^4. y^6 and y^5 is

Answers

Answer:

Answer:GCF: y^4

Step-by-step explanation:

Factors of:

y^4= (y) (y) (y) (y) = y^4 (1)

y^5 = (y) (y) (y) (y) (y) = y^4 (y)

y^6 = (y) (y) (y) (y) (y) (y) = y^4(y^2)

A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch. How much does it cost to fund 4.5 inches of the construction?

Answers

Answer:

=$114.750

Step-by-step explanation:

Length of new board cast tower=4.5 Inches

Cost of construction(per inch)=$25.50

To find cost=?

                 =25.50x4.5

                 =$114.750

                      ...................................................................................

The required cost of the construction of a 4.5-inch tower is $114.75.

Given that,
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch, how much it cost to fund 4.5 inches of the construction is to be determined.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
The cost of construction is $25.50 per inch.
The cost of 4.5 inches of construction = 25.50 × 4.5 = $114.75.

Thus, the required cost of the construction of a 4.5-inch tower is $114.75.

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3. A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually. (a) Write an equation to represent the amount of money in the account as a function of time in years. (b) Find the amount of time it takes for the account balance to reach $800. Show your work. Answer:

Answers

Answer:

31.334... years

Step-by-step explanation:

Initial value = $500

r = 1.5%

t = ?

A = (500)[tex]e^{.015*t}[/tex]

I was unsure if the question was asking to express the equations in terms of t =, but i did those steps anyway just in case.

A/500 = [tex]e^{.015*t}[/tex]

ln A/500 = ln[tex]e^{.015*t}[/tex]

ln A/500 = .015*t

ln(A/500)/.015 = t

t = ln(A/500)/.015

To find the amount of time it takes for the account balance to reach $800, we plug in $800 for A in the equation that solves for t.

t= ln(800/500)/.015 = 31.334...(rounded) years

We also could have solved by plugging in $800 into the original equation and then solving for t, but i found it to be easier to find the equation for t prior to solving. Hope this helps!

he returns on share A follow the market model with coefficients αA = 0.01, βA =
1.25. If at time t, R~ MT = 0.02 and the actual return on share A is 0.025, calculate
∈�At (the error term)

Answers

Answer:

2 or more so it's be like 3 I guess he doesn't have the right for the tiger and in the heights block he it is a great game and to

What is x + 1 and x + 2

Answers

Answer:

I don't get what you're asking.

Do you want me to solve for x? :D

(✿◡‿◡) HAPPY HOLIDAYS!!!

Ok so you add them up and you should get X=1 and X=2 that should be it!!

can I have some help?

Answers

Answer:

[tex]x = \sqrt{58} [/tex]

Step-by-step explanation:

first, you should draw a line to separate the triangle from the rectangle

You can get the height if the triangle by saying 16-9

This will give you 7

The base of the triangle is 3 because the opposite side is given and the opposite sides of a rectangle are equal

Now that we have the measurements of the triangle we can use the Pythagorean theorem

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

[tex] {x}^{2} = {7}^{2} + {3}^{2} [/tex]

[tex] {x}^{2} = 49+ 9[/tex]

[tex] {x}^{2} = 58[/tex]

[tex]x = \sqrt{58} [/tex]

The position of a scuba diver relative to the water surface was −22 1/3 feet. He saw something interesting beneath him and increased his depth by 12 1/2 feet.

What is the position of the scuba diver now relative to the water surface?

Enter your answer as a mixed number, in simplified form, in the box.

Answers

Answer=-34 5/6

Explanation= just do this: -22 1/3 - 12 1/2
You subtract since the diver is diving deeper DOWN

Answer:

-34 5/6

Step-by-step explanation:

Hope this helps

Have a blessed day

What is the result of 3/ 1/6
2
9
18
27

Answers

Step-by-step explanation:

remember 3 things

1. 3 = 3/1 (any integer is also a fraction of itself divided by 1).

2. 3 / 1/6 = 3/1 / 1/6 = 3/1 × 6/1 (dividing by a fraction is the same as multiplying with the upside-down fraction).

3 a/b × c/d = ac / bd. in our case 3/1 × 6/1 = 18/1 = 18

The answer would be 18? multiple num. by den. 3•6=18

The owner of a retail store is tracking his inventory for an annual report. The graph shows the remaining inventory for a particular item and the number of days that have passed since the stock was replenished. Which type of function best models the relationship between the number of days and the inventory remaining? A. a linear function with negative slopes

Answers

y = -2.8x +69.4

Let y represent units of inventory, and x represent days since the last replenishment. We are given points (x, y) = (3, 61) and (13, 33). The line through these points can be described using the 2-point form of the equation of a line:
... y -y1 = (y2-y1)/(x2 -x1)(x -x1)
Filling in the given point values, we have ...
... y -61 = (33 -61)/(13 -3)(x -3)
Simplifying and adding 61, we get ...
... y = -2.8x +69.4

Use what you know about operations and their properties to write three expressions equivalent to the expression shown.

10(2+3)−8⋅3

Answers

1) Simplify 2 + 3 to 5.

10 * 5 - 8 * 3

2) Simplify 10 * 5 to 50.

50 - 8 * 3

3) Simplify 8 * 3 to 24.

50 - 24

4) Simplify.

24

f(x)=2x 2 +8x Find f(−1)

Answers

Answer:

-6

Step-by-step explanation:

f(x)=2x^2+8x

f(-1)=2(-1)^2+8(-1)

f(-1)=2(-1)(-1)-8

f(-1)=2(1)-8

f(-1)=2-8

f(-1)=-6

Please Help - Suppose f(t)=6t−8−−−−√.


(a) Find the derivative of f.

f′(t) =

-3/(sqrt(t-8)(t-8))



(b) Find an equation for the tangent line to the graph of y=f(t) at the point (t,y)=(33,6/5).

Tangent line: y =

Answers

[tex](a)\\\\\\\text{Given that,}~~\\\\ f(t) =\dfrac 6{\sqrt{t-8}}\\\\\\\\\implies f'(t) = 6\left[\dfrac{\left(\sqrt{t-8}\right) \cdot 0 - \dfrac 1{2\sqrt{t-8 }}}{\left(\sqrt{t-8}\right)^2}\right]\\\\\\\\\implies f'(t) = -6\left(\dfrac {\dfrac 1{2\sqrt{t-8}}}{t-8}\right)\\\\\\\implies f'(t) = -6\left(\dfrac{1}{2\sqrt{t-8} (t-8)}\right)\\\\\\\implies f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}[/tex]

(b)

[tex]\text{Given that,}\\\\y=f(t)\\\\\text{Slope of y,} ~~ f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}\\\\\text{At point (33, 6/5)}\\\\\\f'(t) = -\dfrac 3{(33-8)^{\tfrac 32}} = - \dfrac 3{ (25)^{ \tfrac 32}} = - \dfrac 3{5^3} = -\dfrac 3{125}\\\\\\\text{Equation with given points,}\\\\y - \dfrac 65 = -\dfrac 3{125} ( t - 33)\\\\\\\implies y =-\dfrac 3{125} t +\dfrac{99}{125} + \dfrac 65\\\\\\\implies y = -\dfrac 3{125} t +\dfrac{249}{125}[/tex]

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