Answer:
Step-by-step explanation:
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
Answer:
150+25x = 600
Step-by-step explanation:
Hope this helped!
Answer:
91
Step-by-step explanation:
When x goes from 1 to 2, y increases by 4 from -5 to -1
When x goes from 2 to 3, y increases by 5 from -1 to 3
We are adding 4 each step
The formula for an arithmetic sequence is
an = a1 + d(n-1)
where a1 is the first term a1 =-5
d is the common difference or what we add each time = 4
and n is the term number n=25
a25 = -5 + 4(25-1)
a25 = -5+4(24)
-5 +96
91
The 25th term is 91
Answer:
11.47
Step-by-step explanation:
The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.
Find the last side of the triangle using the Pythagorean theorem.
<em>good luck, i hope this helps :)
</em>