The data is plotted as points so a relationship can be visualized. Is there a relationship? If yes, explain the relationship.
1 answer:
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<u>Given</u>:
Given that the figure of similar triangles.
The altitude of the triangle is x.
The length of the left part is 30.
The length of the right part is 15.
We need to determine the value of x.
<u>Value of x:</u>
The value of x can be determined using the geometric mean theorem.
Thus, we have;
Substituting the values, we have;
Cross multiplying, we get;
Taking square root on both sides, we have;
Thus, the value of x is 15√2
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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