what do i put in the blank?

Answer:

Step-by-step explanation:

The question doesn't seem complete, but the question is likely to ask for 2 things: the equation of the ellipse and it's foci. So I'll respond to that. Also, the ellipse will be at the center since the artist wants the largest.

Firstly, the equation of an ellipse at the center is given by:

(x²/a²) + (y²/b²) = 1 where a > b.

Since the artist wants to make the largest ellipse, then the length of the rectangle will be the length of the ellipse, same applies to the width.

Since the length is 60, then a = 60/2 = 30

Since the width is 40, then b = 40/2 = 20

Therefore, the equation of the ellipse is:

(x²/30²) + (y²/20²) = 1

To find the foci we need to know the center and this can be gotten by

c² = a² – b²

c² = 30² – 20² = (30 + 20)(30 – 20) = (50)(10) = 500

c = √(500) = 10√(5).

The foci, since it's at th center would be:

(–10√(5), 0) and (+10√(5), 0)

The largest ellipse that the artist can make on the considered rectangular wooden piece will have area as: [tex]\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\[/tex](assuming its major and minor axes lie on x and y axis respectively)

Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, then if major axis is on x-axis and minor axis is on y-axis, then the equation of that ellipse would be:
[tex]\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} =1[/tex]

For this case, as we have rectangular piece of board the maximum ellipse will have it's major axis of length 60 inches, and of minor axis as 40 inches.

Thus, we have:

[tex]a = 60/2 = 30\: \rm inches\\b = 40/2 = 20 \: inches[/tex]

Thus, if the rectangle is placed such that the major axis is on x-axis, and minor axis is on y-axis, then the equation of that ellipse would be:

[tex]\dfrac{x^2}{30^2} + \dfrac{y^2}{20^2} = 1\\\\\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\[/tex]

Thus, the largest ellipse that the artist can make on the considered rectangular wooden piece will have area as: [tex]\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\[/tex](assuming its major and minor axes lie on x and y axis respectively)

Learn more about ellipse here:
https://brainly.com/question/16868628

Answer:

hi, hope you are good!, hope you have the greatst holidays ever!

Step-by-step explanation:

Answer:

aww thank you, u are too kind :) I appreciate that u are generous enough to give free points to people, I thank you for your generosity. Happy holidays and stay safe <333

Step-by-step explanation:

Answer:

The answer is =3x2−x−24 which is the choices B.

Step-by-step explanation:

(3x + 8)(x – 3)

=3x2−x−24

Answer:

If Chrissy eats 6 cookies so 54 cokies are left. .

Step-by-step explanation:

Answer:

n = 18

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

if he has 500 and wants to have 200 left subtract 500-200=300

then if he spends 24 each week divide 300/24=12.5

the maximum number is 12 because cant have a remainder

at the end of the summer he would have 212 left.. 12x24=288..500-288=212

Answer:

12 weeks .

Step-by-step explanation:

24 x 12 = 288 . 24 x 13 = 312 .

500 - 288 = 212 . 500 - 312 =188 .

its 12 because if you do 13 its to below the price so you'll have some change left .

Answer:

D. 7

Step-by-step explanation:

Answer:

kakaakasksjnxznxccchjvgv

Step-by-step explanation:

Answer:

[tex]400[/tex]

Step-by-step explanation:

[tex]We\ know\ that,\\'The\ sum\ of\ n\ no.\ positive\ odd\ integers\ is\ given\ by\ the\ formula:\\S_O=n^2\\Hence,\\Here,\\As\ n=20,\\The\ sum\ of\ the\ first\ 20\ positive\ odd\ integers=20^2=400\\[/tex]

Answer:

I think the answer is 20

Answer:

C: 20

Step-by-step explanation:

Answer:

15 dollers

Step-by-step explanation:

Answer:

$15

The difference is 3 dollars

Answer:

27 :)

Step-by-step explanation:

Answer:

27!

Step-by-step explanation:

Answer: Mark up percent = 20%

Step-by-step explanation:

Given: Cost price of each T-shirt = $5.00

Amount required = $450

Total students = 75

Market price for each T-shirt to raise the required amount = (Amount required ) ÷ 75

= $450 ÷ 75

= $ 6

Mark up percent = [tex]\dfrac{\text{Market price - Cost price}}{\text{Cost price}}\times100[/tex]

[tex]=\dfrac{6-5}{5}\times100\\\\=20\%[/tex]

Hence, Mark up percent = 20%

Answer:

= 29.09

thats the answer

Answer:

b

Step-by-step explanation:

Answer:

The answer is D= Dana filtered the sample and larger granules of the sample were left behind

Step-by-step explanation:

I got it correct ✌

Answer: 2 to last

Step-by-step explanation:

Answer:

6x2−3x−20

Step-by-step explanation:

Let's simplify step-by-step.

x2+5x2−3x−20

=x2+5x2+−3x+−20

Combine Like Terms:

=x2+5x2+−3x+−20

=(x2+5x2)+(−3x)+(−20)

=6x2+−3x+−20

9514 1404 393

Answer:

Step-by-step explanation:

The commonly used symbols for ratios are a colon or a fraction bar. Words can also be used.

  6 : 7 = 6/7 = 6 to 7

__

When the ratio is part of a proportion, then it might be written ...

  6 is to 7

as in ...

  6 : 7 :: 12 : 14 . . . . . . . 6 is to 7 as 12 is to 14

Answer:

81

Step-by-step explanation:

Answer:

im not sure if this is the answer you wanted hope it helped though

Step-by-step explanation:

Applying the BODMAS rule where B=Brackets ,O=of,D=Division,M=multiplication,

A=Addition,S =subtraction

For any equation in which multiple operation is to be done its depends on the preference of the operation to be performed.

The preference followed is BODMAS

In the above question first multiplication will be performed first and then the addition is performed.

10+10*0+10

10+0+10

Answer is 20

Answer:

D. a car goes 7 feet and then reversed 7 feet.

Step-by-step explanation:

The statement above can be set up in a simple equation.

7 - 7 = 0

This can best represent the equation 10 + (-10) = 0, because they both end up with the same result.

10 + (-10) = 10 - 10 = 0

Answer:

Step-by-step explanation:

You can think of BF in 3 equal parts. 2 parts belong to BH and 1 part goes to HF

3x = 24

x = 24/3

x = 8

BH is twice as long as FH

BH = 2*8 = 16

Answer:

A. Juan wins the race

B. At about 7 minutes J(t )= A(t)

C. 2 minutes

Step-by-step explanation:

A. Juan wins the race. This is because she covers the distance in a shorter time interval than Antonio

B. At about 7 minutes J(t )= A(t). to get this, just look at the point that the two curves intersect on the graph, and trace it down to the time axis to read off the time.

C. J(t) is greater than A(t) with about 2 minutes. To get this, we just subtract the time Juan arrived at the finish line from the time Antonio arrived, this is = 15 -13 = 2 minutes

Answer:

k = 0.25t^2

Step-by-step explanation:

Given the equation :

b = 0.25t

b = number of inches that has burned away

t = time

From our knowledge of variation;

Since candle length will decrease with time ;

b α 1/ t

b = k/t

Where k is the proportionality constant

Comparing the equation :

b = 0.25t

k/t = 0.25t

k = 0.25t^2

Answer:

14.16

Step-by-step explanation:

Do 1/6 of 94 and you get this answer

6x

Step-by-step explanation:

1.2(4x-1)=8x-2=6x

Answer:

<C =10°

Step-by-step explanation:

The sum of angles in a triangle is 180°. Hence,

<C+<D+<E =180

Given

<C =x-4

<D = 11x-11

<E = x+13

Substitute

x-4+11x-11+x+13 = 180

13x-2 = 180

13x =180+2

13x = 182

x = 182/13

x = 14

Get <C

Since <C = x-4

<C = 14-4

<C =10°

Answer: <C =10°

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's a function because no x value has two y values.

Answer:

72 feet

Step-by-step explanation:

Given that:

The speed of Erica while descending down the mountain = 36 feet per hour

Time at which the descent was started = 10 AM

Time at which the descent was finished = 6 PM

To find:

The change in elevation after two hours ?

Solution:

First of all, let us learn about the relation between speed, distance and time.

The formula between speed, distance and time is given as:

[tex]Speed = \dfrac{Distance }{Time}[/tex]

Here, we are given that:

Speed = 36 feet per hour

Time = 2 hours

We have to find the Distance now.

Putting the given values:

[tex]36 = \dfrac{Distance}{2}\\\Rightarrow Distance = 36 \times 2\\\Rightarrow Distance = \bold{72\ feet}[/tex]

Change in elevation = 72 feet