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1 year ago

which of the following expresses the coordinates of the foci of the conic section shown below? (x-2)^2/4+(y+5)^2/9

Mathematics

1 answer:

elena55 [62]1 year ago

6 0

Step-by-step explanation:

$\frac{(x - 2) {}^{2} }{4} + \frac{(y + 5) {}^{2} }{9} = 1$

This is the equation of the ellipse. Since the denominator is greater for the y values, we have a vertical ellipse. Remember a>b, so a

The formula for the foci of the vertical ellipse is

(h,k+c) and (h,k-c).

where c is

Our center (h,k) is (2, -5)

${c}^{2} = {a}^{2} - {b}^{2}$

Here a^2 is 9, b^2 is 4.

${c}^{2} = 9 - 4$

${c}^{2} = 5$

$c = \sqrt{5}$

So our foci is

$(2, - 5 + \sqrt{5} )$

and

$(2, - 5 - \sqrt{5} )$

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I don't know how to solve it.

Nataly [62]

Step-by-step explanation:

Take the first derivative

$\frac{d}{dx} ( {x}^{3} - 3x)$

$3 {x}^{2} - 3$

Set the derivative equal to 0.

$3 {x}^{2} - 3 = 0$

$3 {x}^{2} = 3$

${x}^{2} = 1$

$x = 1$

$x = - 1$

For any number less than -1, the derivative function will have a Positve number thus a Positve slope for f(x).

For any number, between -1 and 1, the derivative slope will have a negative , thus a negative slope.

Since we are going to Positve to negative slope, we have a local max at x=-1

Plug in -1 for x into the original function

$( - 1) {}^{3} - 3( - 1) = 2$

So the local max is 2 and occurs at x=-1,

For any number greater than 1, we have a Positve number for the derivative function we have a Positve slope.

Since we are going to decreasing to increasing, we have minimum at x=1,

Plug in 1 for x into original function

${1}^{3} - 3(1)$

$1 - 3 = - 2$

So the local min occurs at -2, at x=1

8 0

1 year ago

Two solid metal spheres have masses of 5 kg and 135 kg respectively. If the radius of the smaller one is 4 cm, find the radius o

Cerrena [4.2K]

Answer: 12 cm

Step-by-step explanation:

The masses of the spheres are proportional to their volums, and the cube of the ratio is k^3=135/5=27 ==> k=3

The greater radius is 3*4=12 (cm)

8 0

2 years ago

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