A bridge is built in the shape of a parabolic arch. The bridge has a span of s 1

Question

A bridge is built in the shape of a parabolic arch. The bridge has a span of s 180 feet and a maximum height of h 40 feet Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center. Find the height of the arch at a distance of 10 feet from the center. feet (Round to two decimal places as needed.) Find the height of the arch at a distance of 30 feet from the center. feet (Round to two decimal places as needed.) Find the height of the arch at a distance of 50 feet from the center. feet (Round to two decimal places as needed.)

Explanation / Answer

standrad equation of parabola is

-x^2 = 4ay

-(90)^2 = 4 * 40 a

a = 8100 / 160

a = 50.625

so,equation becomes

x^2 = - 50.625 * 4 y

plugging x = 10

100 = - 50.625 * 4 y

y = - 0.49 feet

height when distance is 10 feet = 39.51 feet

plugging x = 30

900 = - 50.625 * 4 y

y = -4.44

so, height when distance = 30 feet is 35.56 feet

plugging x = 50

2500 = - 50.625 * 4 y

height when distance is 30 feet is 27.65 feet

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.