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Lynna [10]
1 year ago
14

Center: (10,-10)

Mathematics
1 answer:
vova2212 [387]1 year ago
7 0

This is the standard form equation \frac{(x - 10)^2}{100} + \frac{(y + 10)^2}{-100} = 1

What is the ellipse?

The equation for an ellipse is typically written as x² a²  + y² b² = 1. x²  a² + y² b²  = 1. An ellipse with its origin at the center is defined by this equation. The ellipse is stretched further in both the horizontal and vertical directions if a > b, a > b, and if b > a, b > a, respectively.

The standard form of the equation of an ellipse with center (h, k)and major axis parallel to the x-axis is:

\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1

where,

a > b

the length of the major axis is 2a

the coordinates of the vertices are (h±a,k)

the length of the minor axis is 2b

the coordinates of the co-vertices are (h,k±b)

the coordinates of the foci are (h±c,k),

where c² = a² − b².

so,

\frac{(x - 10)^2}{100} + \frac{(y + 10)^2}{-100} = 1

Hence, this is the standard form equation \frac{(x - 10)^2}{100} + \frac{(y + 10)^2}{-100} = 1.

To learn more about ellipse, visit

brainly.com/question/16904744

#SPJ1

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Find the equation of the straight line passing through the point (3,3) which Is perpendicular to the line y=-1/2 x+4
Nataly [62]

Answer:

y = 2x - 3.

Step-by-step explanation:

The perpendicular line will have slope - 1 / -1/2 = 2.

Using the point-slope form of the straight line:

y - y1 = m(x - x1)

Here m = 2 and (x1, y1) = (3, 3) so we have:

y -3 = 2(x - 3)

y = 2x - 6 + 3

y = 2x - 3.

3 0
3 years ago
-2x + y=9<br> -4x - y=9 <br> What is the answer
Dmitry_Shevchenko [17]

-2x + y = 9

-4x - y = 9

----------------- +

-6x = 18

x = -3

-2x + y = 9

-2(-3) + y = 9

6 + y = 9

y = 3

3 0
3 years ago
Read 2 more answers
The values in a dataset are 3.5, 2.5, 2.5, 3.5, and 3.0. If Xbar (sample mean) = sigma X / n, what is the mean for the sample?
RideAnS [48]

Answer:

\bar x = 3.0

Step-by-step explanation:

Given

x: 3.5, 2.5, 2.5, 3.5, 3.0

Required

The sample mean

This is calculated using:

\bar x = \frac{\sum x}{n}

So, we have:

\bar x = \frac{3.5+ 2.5+ 2.5+ 3.5+ 3.0}{5}

\bar x = \frac{15.0}{5}

\bar x = 3.0

4 0
3 years ago
Does the series converge or diverge? If it converges, what is the sum? Show your work. ∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

Check attachment for better understanding

3 0
3 years ago
Write an equation to find the number of hours it will take Lily to reach her goal.
andrey2020 [161]

Answer: 1 hour and 20 mins

Step-by-step explanation:

Lily has to walk 4 more miles to complete her goal and with the pace of 3m/h she will have to for 1 hour 20 mins, to complete her goal.

Distance to be covered= 4 miles          Speed= 3 miles per hour

Time= Distance/Speed

Time= 4/3

Time= 1.33 hours

Time= 1 hour and 20 mins

4 0
2 years ago
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