All categories

3 years ago

Which of the following statements best describes the relationship between any point on an ellipse and each of its two foci

Mathematics

2 answers:

vazorg [7]3 years ago

8 0

Answer:

<h2>D. the sum of the distances to each focus equals a certain constant.</h2>

Step-by-step explanation:

In mathematics, an elipse is defined as a curve which surrounds two focal points. The relation between the two focal points and a points on the curve is what defines an elipes, which is "the sum of the two distances to the focal points is a constant".

Therefore, the right answer to this question is D, because that's the defintion of an elipse.

Bezzdna [24]3 years ago

6 0

Answer:

Option D is correct.

Step-by-step explanation:

The relationship between any point on an ellipse and each of its foci is:

The sum of the distances to each focus equals a certain constant. The constant will be 2a

If d₁ and d₂ are the distances then their sum is d₁ + d₂ = 2a.

Option D is correct.

You might be interested in

X intercept of (x-3)(x-5)

jok3333 [9.3K]

Answer: a linear Function (y=x-5)

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must

Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

(x) should be the width of the rectangle base;
(h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

the radius $\mathbf{r = \dfrac{x}{2}}$

and, the perimeter of the window can now be expressed as:

$\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}$

$\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}$

Given that the perimeter = 600 cm

∴

$\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}$

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}$

Since h > 0, then:

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}$

By rearrangement and using the inverse rule:

$\mathbf{ x< \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }$

$\mathbf{ x= \dfrac{ 1200}{\Big( 2 +\pi \Big) } }$

$\mathbf{ x= 233.39 \ cm }$

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

$\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}$

$\mathbf{A = x \Big [ 300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ] +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}$

$\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}$

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

$\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}$

$\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \ =0}$

Making x the subject of the formula, we have:

$\mathbf{x = \dfrac{1200}{4 +\pi}}$

x = 168.03 cm

Taking the second derivative:

$\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}$

$\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )$

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

brainly.com/question/9964510?referrer=searchResults

6 0

3 years ago

What is the difference between the areas of a circular target region with radius 5 m and a target region with radius 7 m? Round

Oliga [24]

That would be 7²π-5²π=49π-25π=24π≈75

6 0

3 years ago

Read 2 more answers

Hong will run at least 24 miles this week. So far, he has run 16 miles. What are the possible numbers of additional miles he wil

Anna71 [15]

Answer:
8 miles

Steps:
Since he is AT LEAST running 24 miles and he already ran 16. He only had 8 more miles to go. 24 miles is the minimum he is running, he could run more.

4 0

3 years ago

9. A retaining wall on the playground is

soldi70 [24.7K]

Dghfjgjghcjjfjfjgjgjcjxjxjf

6 0

3 years ago