All categories

3 years ago

Write the standard equation for the ellipse with the given conic form.

Mathematics

1 answer:

Andrei [34K]3 years ago

6 0

We complete the square

$4 x^2 + y^2 - 16x + 2y + 13 = 0$

$4 x^2 - 16x + y^2 + 2y = -13$

$4 (x^2 - 4x) + (y^2 + 2y) = -13$

$4 (x^2 - 4x + 4) + (y^2 + 2y +1 ) = -13 +16 + 1$

$4 (x - 2)^2 + (y+1)^2 = 4$

$\dfrac{ (x - 2)^2 }{1^2} + \dfrac{ (y+1)^2}{2^2} = 1$

That's standard form with axes 1 and 2

You might be interested in

What function is shown by the graph below?

Airida [17]

Answer:

The function $f(x)=\sqrt{x+2}$ is shown by the graph below ⇒ 2nd answer

Step-by-step explanation:

To find the right function chose two points from the graph and substitute the x-coordinate of each point in the function to find the y-coordinate, if they are the same with the corresponding y-coordinates of the points, then the function is shown by the graph

From the figure:

The curve passes through points (-2 , 0) and (2 , 2)

∵ $f(x)=\sqrt{x-2}$

∵ x = -2

- Substitute x by -2

∴ $f(-2)=\sqrt{-2-2}$

∴ $f(-2)=\sqrt{-4}$ ⇒ it is impossible no square root for (-) number

∴ $f(x)=\sqrt{x-2}$ is not the function shown by the graph

∵ $f(x)=\sqrt{x+2}$

∵ x = -2

- Substitute x by -2

∴ $f(-2)=\sqrt{-2+2}$

∴ $f(-2)=\sqrt{0}$

∴ f(-2) = 0 ⇒ same as the y-coordinate of x = -2

∵ x = 2

- Substitute x by 2

∴ $f(2)=\sqrt{2+2}$

∴ $f(2)=\sqrt{4}$

∴ f(2) = 2 ⇒ same as the y-coordinate of x = 2

∴ The function $f(x)=\sqrt{x+2}$ is shown by the graph below

7 0

3 years ago

H(t)=-16(t-1)^2+16 What is the maximum height the ball reaches and how long does it take?

Aleksandr-060686 [28]

Given t = time and h = height

$h(t) = - 16(t - 1)^{2} + 16$

From the equation.

$y = a(x - h)^{2} + k$

h is the axis od symmetry

(h, k) is the vertex.

In the equation, h is 1 and k is 16.

So the maximum value is 16 at t = 1.

The ball reaches maximum at 16 and it takes t = 1 to reach the maximum point.

4 0

2 years ago

Complete parts (a) and (b) using the probability distribution below.

katen-ka-za [31]

Μ = (0×0.026) + (1×0.072) +(2×0.152) + (3×0.303) + (4×0.215) + (5×0.164) + (6×0.066)
μ = 0 + 0.072 + 0.304 + 0.909 + 0.86 + 0.82 + 0.396
μ = 3.361 ≈ 3.4

We need the value of ∑X² to work out the variance
∑X² = (0²×0.026) + (1²×0.072) + (2²×0.152) + (3²×0.303) + (4²×0.215) + (5²×0.164) + (6²×0.066)
∑X² = 0+0.072+0.608+2.727+3.44+4.1+2.376
∑X² = 13.323

Variance = ∑X² - μ²
Variance = 13.323 - (3.4)² = 1.763 ≈ 2

Standard Deviation = √Variance = √1.8 = 1.3416... ≈ 1.4

The correct answer related to the value of mean and standard deviation is the option D

An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.

7 0

3 years ago

Reggie, Alvin, and Jose are member of a relay running team. Reggie finished his leg of the race 2.45 seconds faster than Alvin a

lorasvet [3.4K]

From the given, we expressed the time that each of the team members ran in mathematical expression.

Reggie = 57.12 seconds
Alvin = 57.12 + 2.45 seconds = 59.57 seconds
Jose = 57.12 - 3.81 seconds = 53.31 seconds
We then sum up all the time we calculate to determine the total time for the team. The answer is therefore 170 seconds.

8 0

2 years ago

Simplify the following radicals. 1. √16 2. √17 3. √18 4. √19 5. √20

Pavel [41]

Answer:

Step-by-step explanation:

$1) \sqrt{16}= \sqrt{4*4}=4\\\\\\2) \sqrt{17}$