Answer:
The standard form of the equation of the ellipse is
Step-by-step explanation:
The standard form of the equation of an ellipse with center (h , k) is
, where
- The coordinates of the vertices are (h , k ± a)
- The coordinates of the co-vertices are (h ± b , k)
- The coordinates of the foci are (h , k ± c), where c² = a² - b²
∵ The vertices of the ellipse are (-3 , 7), (-3 , 1)
∴ h = -3
∴ k + a = 7 ⇒ (1)
∴ k - a = 1 ⇒ (2)
- Add (1) and (2) to find k
∴ 2k = 8
- Divide both sides by 2
∴ k = 4
- Substitute the value of k in (1) or (2) to find a
∵ 4 + a = 7
- Subtract 4 from both sides
∴ a = 3
∵ The co-vertices of the ellipse are (-5 , 4), (-1 , 4)
∴ k = 4
∴ h - b = -5 ⇒ (1)
∴ h + b = -1 ⇒ (2)
∵ h = -3
- Substitute the value of h in (1) or (2) to find b
∴ -3 + b = -1
- Add 3 to both sides
∴ b = 2
∵ The standard form of the equation of the ellipse is
- Substitute the values of h, k, a, and b in the equation
∴
∴
The standard form of the equation of the ellipse is
<u>Options</u>
Answer:
Step-by-step explanation:
Given the solution to an inequality
{x|x>2/3}
The solution set does not include , therefore, it must be open at the left. Recall that we use a curvy bracket ( to denote openness at the left.
Since x is greater than , the solution set contains all values of larger than up till infinity. Since infinity is an arbitrarily large value, we also use an open bracket at the right.
Therefore, another way to represent the solution {x|x>2/3} is:
The correct option is C.
Answer:
Hold up lemme do the math
Step-by-step explanation:
Answer:
Distance traveled in 6 revolution = 56.52 ft
Step-by-step explanation:
Formula:
Circumference of circle = 2πr
r - Radius of circle
It is given that,
A hula hoop has a three foot diameter.
Diameter = 3 ft
Therefore the radius r = diameter/2 = 3/2 = 1.5 ft
<u>To find the circumference of loop</u>
r = 1.5 ft
Circumference = 2πr = 2 * 3.14 * 1.5 = 9.42 ft
<u>To find the distance traveled in 6 revolution</u>
Distance traveled in one revolution = 9.42 ft
Distance traveled in 6 revolution = 6 * 9.42 = 56.52 ft