Question

The bridge connects two hills 100 feet apart. The arch on the bridge is in a parabolic form. The highest point on the bridge is 10 feet above the road at the middle of the bridge as seen in the figure.

Based on the information given above, answer the following questions:

1. The equation of the parabola designed on the bridge is

a. x² = 250y

b. x² = −250y

c. y² = 250x

d. y² = 250y

2. The value of the integral\(\int_{-50}^{50}\cfrac{x^2}{250}dx\) is

a. \(\cfrac{1000}3\)

b. \(\cfrac{250}3\)

c. 1200

d. 0

3. The integrand of the integral \(\int\limits_{-50}^{50}x^2dx\) is _________ function.

a. Even

b. Odd

c. Neither odd nor even

d. None

4. The area formed by the curve \(x^2=250y\), x - axis , y = 0 and y = 10 is

a. \(\cfrac{1000\sqrt2}3\)

b. \(\cfrac34\)

c. \(\cfrac{1000}3\)

d. 0

5. The area formed between \(x^2=250y\) , y - axis , y = 2 and y = 4 is

a. \(\cfrac{1000}3\)

b. 0

c. \(\cfrac{1000\sqrt2}3\)

d. none of these

Answer 1

1. b) x² = −250y

2. a) \(\cfrac{1000}3\)

3. a) Even

4. c) \(\cfrac{1000}3\)

5. d) none of these

Answer 2

1. (b) x² = -250y

2. (a) \(\frac{1000}3\)

\(\int\limits^{50}_{-50} \frac{x^2}{250} dx =\frac 1{250} \left[ \frac{x^3}3\right]_{-50}^{50} \)

\(=\frac{1000}3\)

3. (a) Even

4. (c) \(\frac{1000}3\)

\(2 \int \limits_{0}^{50} \frac{x^2}{250} dx = \frac{1000}3\)

5. (d) None of these