Question

1. Compute the direction (in degrees) of the vectors \( (2,-3) \). A. \( 103.2^{\circ} \) B. \( 203.5^{\circ} \) C. \( 403.7^{\circ} \) D. \( 303.7^{\circ} \) 2. What geometric figures are described by the following equations? (a) \( 4 y^{2}-12 y+16 x+41=0 \) (b) \( x^{2}-10 x y+y^{2}+x+y+1=0 \) (c) \( x^{2}+4 y^{2}+2 x-8 y+1=0 \) (d) \( x^{2}+y^{2}-6 x+8 y+20=0 \) A. (a) parabola; (b and c) ellipse; (d) circle B. (a) parabola; (b) hyperbola; (c) ellipse; (d) circle C. (a and c) hyperbola; (b) ellipse; (c) circle D. (a) parabola; (b) hyperbola; (c and d) ellipse 3. A motorboat, operating at full throttle, made a trip 4 miles upstream (against a constant current) in 15 minutes. The return trip (with the same current and at full throttle) took 12 minutes. Find the equivalent speed of the boat in still water. A. \( 14 \mathrm{mi} / \mathrm{hr} \) B. \( \quad 18 \mathrm{mi} / \mathrm{hr} \) C. \( 15 \mathrm{mi} / \mathrm{hr} \) D. \( 16 \mathrm{mi} / \mathrm{hr} \) 4. If a function \( f \) is continuous for all values of \( x \), which of the following statements is/are always true? 1. \( 2 \int_{a}^{b} f(x) d x=\int_{2 a}^{2 b} f(x) d x \) II. \( \int_{a}^{b} f(x) d x=\int_{b}^{a}-f(x) d x \) III. \( \left.\left|\int_{a}^{b} f(x) d x\right|=\int_{a}^{b} \mid h^{x}\right) \mid d x \) A. I only B. I and II only C. II only D. II and III only

          1. Compute the direction (in degrees) of the vectors \( (2,-3) \).
A. \( 103.2^{\circ} \)
B. \( 203.5^{\circ} \)
C. \( 403.7^{\circ} \)
D. \( 303.7^{\circ} \)
2. What geometric figures are described by the following equations?
(a) \( 4 y^{2}-12 y+16 x+41=0 \)
(b) \( x^{2}-10 x y+y^{2}+x+y+1=0 \)
(c) \( x^{2}+4 y^{2}+2 x-8 y+1=0 \)
(d) \( x^{2}+y^{2}-6 x+8 y+20=0 \)
A. (a) parabola; (b and c) ellipse; (d) circle
B. (a) parabola; (b) hyperbola; (c) ellipse; (d) circle
C. (a and c) hyperbola; (b) ellipse; (c) circle
D. (a) parabola; (b) hyperbola; (c and d) ellipse
3. A motorboat, operating at full throttle, made a trip 4 miles upstream (against a constant current) in 15 minutes. The return trip (with the same current and at full throttle) took 12 minutes. Find the equivalent speed of the boat in still water.
A. \( 14 \mathrm{mi} / \mathrm{hr} \)
B. \( \quad 18 \mathrm{mi} / \mathrm{hr} \)
C. \( 15 \mathrm{mi} / \mathrm{hr} \)
D. \( 16 \mathrm{mi} / \mathrm{hr} \)
4. If a function \( f \) is continuous for all values of \( x \), which of the following statements is/are always true?
1. \( 2 \int_{a}^{b} f(x) d x=\int_{2 a}^{2 b} f(x) d x \)
II. \( \int_{a}^{b} f(x) d x=\int_{b}^{a}-f(x) d x \)
III. \( \left.\left|\int_{a}^{b} f(x) d x\right|=\int_{a}^{b} \mid h^{x}\right) \mid d x \)
A. I only
B. I and II only
C. II only
D. II and III only

1. Compute the direction (in degrees) of the vectors (2,-3).
A. 103.2^∘
B. 203.5^∘
C. 403.7^∘
D. 303.7^∘
2. What geometric figures are described by the following equations?
(a) 4 y^2-12 y+16 x+41=0
(b) x^2-10 x y+y^2+x+y+1=0
(c) x^2+4 y^2+2 x-8 y+1=0
(d) x^2+y^2-6 x+8 y+20=0
A. (a) parabola; (b and c) ellipse; (d) circle
B. (a) parabola; (b) hyperbola; (c) ellipse; (d) circle
C. (a and c) hyperbola; (b) ellipse; (c) circle
D. (a) parabola; (b) hyperbola; (c and d) ellipse
3. A motorboat, operating at full throttle, made a trip 4 miles upstream (against a constant current) in 15 minutes. The return trip (with the same current and at full throttle) took 12 minutes. Find the equivalent speed of the boat in still water.
A. 14 mi / hr
B. 18 mi / hr
C. 15 mi / hr
D. 16 mi / hr
4. If a function f is continuous for all values of x, which of the following statements is/are always true?
1. 2 ∫a^b f(x) d x=∫2 a^2 b f(x) d x
II. ∫a^b f(x) d x=∫b^a-f(x) d x
III. .|∫a^b f(x) d x|=∫a^b| h^x) | d x
A. I only
B. I and II only
C. II only
D. II and III only

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