1. Mathematics
2. Calculus and Analysis
3. Complex Analysis
4. 74080

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Question 1 Multiple Choice

The two sides of a right triangle have lengths 2.92 and 3.98. Find the hypotenuse.

□ 6.90

□ 3.34

□ 4.94

□ 3.20

Question 2 Multiple Choice

An equation used in the study of protein molecule is
In A+ In h - In(1 - h)
Solve for h

□ h = A / (A + 1)

□ h = A / (A - 1)

□ h = (A + 1) / A

□ h = (A - 1) / A

Question 4 Multiple Choice

Write the following matrices as a system of three equations.

□ t+2u+3v=1
4t5u+6v=2
7t+8u+6v=3

□ t+4u+7v=1
2t+5u+8v=2
3t+6u+9v=3

□ t-2u+3v=0
-4t+5u-6v=0
7t-8u+9v=0

Question 5 Multiple Choice

Complex roots of a polynomial always come in conjugate pairs.

□ True

□ False

Question 8 Multiple Choice

Given the following equation, find XL of a circuit with resistance, R. of 5 ohms, impedance, Z, of 4 ohms, and a capacitor, XC, with a value of 8 ohms.

Z = R + j(XL - XC)

□ (1/j) + 8

□ (8+j))/j

□ j - 8

□ j + 8

Question 9 Multiple Choice

Given a triangle with the following given parts, find the value of side c.

a = 3.5, b = 1, C = 29 degrees

□ 7.13

□ 2.67

□ 3.80

□ 3.92

Question 10 Multiple Choice

If the horizontal and vertical components of a vector A are given by
Ay = 3 sin 66
Ax = 3 cos 66
And vector B are given by
By = 25 sin 12
Bx = 25 cos 12
Find the x and y components, position angle, and magnitude of the resultant vector.

□ Rx = 25.67; Ry = 7.94; angle = 72.82;

□ Rx = 7.94; Ry = 25.674; angle = 72.82;

□ Rx = 25.00; Ry = 3.00; angle = 39;

□ Rx = 25.67; Ry = 7.94; angle = 17.19;

Question 11 Multiple Choice

A car is traveling a t 88 km/hr. What is the angular velocity of a point on the outer edger of the tire if the tire diameter is 40 cm?

□ 2.2 rad/s

□ 7333 rad/min

□ 1222 rad/s

□ 4400 rad/hr

Question 12 Multiple Choice

Solve the following system of equations:

□ x = 1, y = 1

□ x = 2 ± 2
y = -4 2

□ x = 2; y = 1

□ x = -2 2
y = 4 2

Question 13 Multiple Choice

The design specifications for a cross section of a beam gives a ratio of width to height of 0.6. If a contractor wants to maximize the beam size fitting through a square opening with an area of 50 square cm, what are the ideal dimensions of the beam.

□ height = 7.07 cm, width = 4.24 cm

□ height = 5.00 cm, width = 3.00 cm

□ height = 4.24 cm, width = 7.07 cm

□ height = 6.00 cm, width = 3.60 cm

Question 14 Multiple Choice

Find the product.
(4ax-3) (5ax+7)

□ 9a2x2 + 2az - 4

□ 20a2x2 + 13ax - 21

□ 4a2x2 - 14ax - 21

□ 20a2x2 - 15ax - 4

Question 15 Multiple Choice

What are the slope, y-intercept, and equation of the line formed by the points
(-5, -10) and (12, 20)

□ slope = 1.76, y-intercept = 1.18, y = -1.76x + 1.18

□ slope = 1.76, y-intercept = -1.18, y = -1.76x - 1.18

□ slope = 0.57, y-intercept = 13.2, y = -0.57x + 13.2

□ slope = 0.57, y-intercept = -13.2, y = 0.57x - 13.2
Question 16 Multiple Choice

Convert 34º 48¢ to radian measure:

□ 0.5934

□ 0.6000

□ 0.6074

□ 0.6119