Rewrite 1/2 3/4 as a unit rate
1 answer:
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The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y = one twelfth (x - 5)² ⇒ 1st answer
Step-by-step explanation:
The form of the equation of the parabola is (x - h)² = 4p(y - k), where
- The vertex of the parabola is (h , k)
- The focus is (h , k + p)
- The directrix is at y = k - p
∵ The focus of the parabola is at (5 , 3)
- Compare it with the 2nd rule above
∴ h = 5
∴ k + p = 3 ⇒ (1)
∵ The directrix is at y = -3
- By using the 3rd rule above
∴ k - p = -3 ⇒ (2)
Solve the system of equations to find k and p
Add equations (1) and (2) to eliminate p
∴ 2k = 0
- Divide both sides by 2
∴ k = 0
- Substitute the value of k in equation (1) to find p
∵ 0 + p = 3
∴ p = 3
Substitute the values of h , k , and p in the form of the equation above
∵ (x - 5)² = 4(3)(y - 0)
∴ (x - 5)² = 12 y
- Divide both sides by 12
∴ (x - 5)² = y
- Switch the two sides
∴ y = (x - 5)²
The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y = (x - 5)²
Learn more:
you can learn more about the quadratic equations in brainly.com/question/8054589
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Given :
A trailer will be used to transport several 40-pound crates to a store.
The greatest amount of weight that can be loaded into the trailer is 1,050 pounds.
An 82-pound crate has already been loaded onto the trailer.
To Find :
The greatest number of 40-pound crates that can be loaded onto the trailer.
Solution :
Weight left = 1050 - 80 = 970 pound.
Let, number of 40 pounds crates that can be loaded are x.
Since, crate cannot be in fraction, so maximum crate that can be loaded is 24.
Hence, this is the required solution.