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uysha [10]
3 years ago
8

The minimum and maximum distances from a focus to a point on an ellipse occur when that point on the ellipse is an endpoint of t

he major axis (a vertex).
Please select the best answer from the choices provided

T
F
Mathematics
2 answers:
DedPeter [7]3 years ago
8 0
The answer to your question is True
Sauron [17]3 years ago
7 0
The answer is True.

Explanation:
Let a =  major axis
Let b = minor axis
Let c =  focal length.

Consider the right focus, located a distance c from the center of the ellipse (at the origin).
From the right focus to the right point on the major axis is equal to a-c. This is the minimum distance.
From the right focus to the left point on the major axis is equal to a+c. This is the maximum distance. 
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Help!! 10 PTS!!
Sliva [168]

Answer:

x = sqrt(433/64) - 7/8 and x = -sqrt(433/64) - 7/8 So there are two.  Let me know if there's something you don't understand.

Step-by-step explanation:

First you want to get them into the form where just y is on one side.

5-y=x^2+x

-y=x^2+x-5

y = -x^2 - x + 5

y+1 = 3/4x

y = 3/4x - 1

Let me know if you don't get how I did that.

To find where they intersect you just set them equal to each other and solve for x.

-x^2 - x + 5 = 3/4x - 1

Before you go solving you are going to want to avoid multiplying and dividing.  Especially dividing here.  if you divide something by (x-a) you make it so a cannot be used.  take 1 for instance.  graphing 1 is just a horizontal line at y=1.  If you divide it by (x-a) in particular lets say (x-1) if you try and solve for x=1 you get 1/0 and you can't divide by 0.  If you graph it on a calculator or computer you'll see the graph doesn't exist at x=1 either.

So yeah, no multiplying or dividing.  So we turn this into a quadratic.

-x^2 - x + 5 = 3/4x - 1

-x + 5 = x^2 + 3/4x - 1

5 = x^2 + 7/4x - 1

0 = x^2 + 7/4x - 6

There are a few ways to solve but I am going to complete the square.  If you don't understand how to solve it let me know and I will more specifically walk through it.

(x + 7/8)^2 - 433/64 = 0

(x + 7/8)^2 = 433/64

x + 7/8 = +/- sqrt(433/64)

x = +/- sqrt(433/64) - 7/8

So there are two answers here.  Positive sqrt(433/64) - 7/8 and negative sqrt(433/64) - 7/8 Or approximately 1.726 and -3.476 respectively.  To check try plugging these into the original two functions y = -x^2 - x + 5 and y = 3/4x-1 and make sure they give the same answer.

Let me know again if there's something you don't get.  When oing intersections though you set the two equations equal to each other and solve for x however you can.

6 0
3 years ago
The tail of a kite is 1.5 feet plus twice the length of the kite. Together, the kite and tail are 15.5 ft long. Find the length
Dimas [21]

Answer:

The answer would be D because 1.5 plus twice the length of the kite would be 2k. 1.5+2k

Hope this helps

4 0
3 years ago
Read 2 more answers
What is the approximate solution of this system of equations?
Effectus [21]
Hmm, I'd say it's the first option.
3 0
3 years ago
PLEASE HELP ASAP
White raven [17]

Answer:

(A) It should choose High school Z for the most consistent attendance among its students.

(B) It should choose High school W with the highest average attendance.

Step-by-step explanation:

We are given the data for attendance in the table below, where Low represents the fewest days attended and High represents the most days attended for a single student.

<u>School</u>         Hight School W      High School X       High School Z

Low                       108                          112                          130

High                      180                          180                         180

Range                    72                           68                           50

Mean                    169                          160                          162

Median                 150                          124                          151

IQR                       47.5                         49.5                        39.5

S.D. (σ)                 29.5                         32.4                        27.5

(A) It is stated that the school district wants to award the school that has the most consistent attendance among its students.

Now, to check which high school should it choose; we will look for the standard deviation (σ) of each of the three schools because consistency is measured through standard deviation and the school with the lowest standard deviation means that it has the most consistent attendance among its students.

So, after looking at the standard deviation of all the three schools; the High School Z has the lowest standard deviation of 27.5.

This means that it should choose High school Z.

(B) It is stated that the school district wants to award the school with the highest average attendance.

Now, to check which high school should it choose; we will look for the Mean of each of the three schools because average is measured through mean of the data, and the school with the highest mean means that it has the highest average attendance.

So, after looking at the Mean of all the three schools; the High School W has the highest average of 169.

This means that it should choose High school W with the highest average attendance.

4 0
3 years ago
Read 2 more answers
Where do two perpendicular lines intersect
andrew-mc [135]
They intersect at a right angle
5 0
3 years ago
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