Daily Exam 13 – Mathematics

What is the integral of the following equation? (15x⁴ – 8x³ + 1/x + 7)dx

3x⁵ – 2x⁴ + lnx + 7x + C

Correct Incorrect Correct answer

60x⁴ – 24x³ – 1/x² + 7x + C

Correct Incorrect Correct answer

60x³ – 24x² – 1/x² + C

Correct Incorrect Correct answer

(15/4)x⁵ – (8/3)x⁴ – 1/x² + 7x + C

Correct Incorrect Correct answer

What is the general solution for the following differential equation? 2(d²y/dx²) – 4(dy/dx) + 4y = 0

C₁cosx + C₂sinx

Correct Incorrect Correct answer

C₁eᵡ + C₂e⁻ᵡ

Correct Incorrect Correct answer

eᵡ(C₁cosx + C₂sinx)

Correct Incorrect Correct answer

eᵡ(C₁cosx + C₂sinx)

Correct Incorrect Correct answer

What is the distance between points P(1, -3, 5) and Q(-3, 4, 2)?

√10

Correct Incorrect Correct answer

√14

Correct Incorrect Correct answer

8

Correct Incorrect Correct answer

√114

Correct Incorrect Correct answer

If the rectangular coordinates of a point are (-3, -5.2), what are the polar coordinates (r, θ) of the point?

(-6, -120°)

Correct Incorrect Correct answer

(6, -120°)

Correct Incorrect Correct answer

(6, 120°)

Correct Incorrect Correct answer

(6, -150°)

Correct Incorrect Correct answer

What are the three roots of the equation (x – 1)³ = 0?

(1, 1, 1)

Correct Incorrect Correct answer

(-1, 1, 1)

Correct Incorrect Correct answer

(-1, -1, -1)

Correct Incorrect Correct answer

(1, 1, 0)

Correct Incorrect Correct answer

Determine the (x,y) coordinates of the center of the circle defined by the following equation: x² – 8x + y² – 10y + 25 = 0.

(3, 2)

Correct Incorrect Correct answer

(3, 4)

Correct Incorrect Correct answer

(4, 5)

Correct Incorrect Correct answer

(5, 4)

Correct Incorrect Correct answer

What is the partial derivative with respect to x of the following function z = eᵡʸ?

eᵡʸ

Correct Incorrect Correct answer

eᵡʸ/x

Correct Incorrect Correct answer

eᵡʸ/y

Correct Incorrect Correct answer

yeᵡʸ

Correct Incorrect Correct answer

What is the determinant of the following matrx: [3 2 7, 3 7 1, 1 5 2]

-113

Correct Incorrect Correct answer

-7

Correct Incorrect Correct answer

12

Correct Incorrect Correct answer

73

Correct Incorrect Correct answer

What is the value of the following limit: limit of (sin5x)/x as x approaches 0

0

Correct Incorrect Correct answer

0.087

Correct Incorrect Correct answer

1

Correct Incorrect Correct answer

5

Correct Incorrect Correct answer

What is most nearly angle between V₁ and V₂? V₁ = 3i + 2j + k, V₂ = 2i + 4j + 6k, V₃ = 2i + 3j + 2k

35.5°

Correct Incorrect Correct answer

44.4°

Correct Incorrect Correct answer

45.6°

Correct Incorrect Correct answer

88.5°

Correct Incorrect Correct answer

What is cross product of V₂ and V₃? V₁ = 3i + 2j + k, V₂ = 2i + 4j + 6k, V₃ = 2i + 3j + 2k

-10i + 8j – 2k

Correct Incorrect Correct answer

-26i + 16j + 14k

Correct Incorrect Correct answer

-2i + 8j – 10k

Correct Incorrect Correct answer

-10i + 8j – 2k

Correct Incorrect Correct answer

An ellipse whose center at (0, 0) passing through (x, 15). Find its shortest distance from the origin to the given point if the major axis on the x-axis is 60 and minor axis in the y-axis is equivalent to 40.

22.9

Correct Incorrect Correct answer

24.9

Correct Incorrect Correct answer

25.0

Correct Incorrect Correct answer

27.0

Correct Incorrect Correct answer

Solve the system of simultaneous equations for x, y, and z: x – y + z = 0, x – y – z = -3, -x – y + z = 5

(5/2, -4, -3/2)

Correct Incorrect Correct answer

(5/2, 4, 3/2)

Correct Incorrect Correct answer

(0, -1, 4)

Correct Incorrect Correct answer

(-5/2, -1, 3/2)

Correct Incorrect Correct answer

What is the most nearly the length of the longest side of the triangle defined by the following lines? y = 2x – 2 ; y = -2x + 3 and y = 12x – 7

1.20

Correct Incorrect Correct answer

1.68

Correct Incorrect Correct answer

1.73

Correct Incorrect Correct answer

2.58

Correct Incorrect Correct answer

An ancient square pyramid is 60 m tall and 200 m on each side at the base. The density of the building stone is 1300 kg/m³. If the pyramid is solid throughout, what is the pyramid’s approximate mass?

0.80 Mg

Correct Incorrect Correct answer

2.4 Mg

Correct Incorrect Correct answer

1.0 Gg

Correct Incorrect Correct answer

1.0 Tg

Correct Incorrect Correct answer

Use the logarithmic identities to evaluate the numerical value for the following expression: log₃ 3/2 + log₃ 12 – log₃ 2

0.95

Correct Incorrect Correct answer

1.33

Correct Incorrect Correct answer

2.00

Correct Incorrect Correct answer

2.20

Correct Incorrect Correct answer

In the following progression, what is the value of the term a? 125, 50, a, 8, 3.2

16

Correct Incorrect Correct answer

20

Correct Incorrect Correct answer

25

Correct Incorrect Correct answer

30

Correct Incorrect Correct answer

A cloth bag contains six cards numbered 1 through 6. Two cards are drawn without replacement. What is the probability that the sum of the numbers on the two drawn card is 7?

1/12

Correct Incorrect Correct answer

7/36

Correct Incorrect Correct answer

1/5

Correct Incorrect Correct answer

7/18

Correct Incorrect Correct answer

Four dice are thrown. The propabiity of rolling at least one six most nearty 6.

0.50

Correct Incorrect Correct answer

0.52

Correct Incorrect Correct answer

0.63

Correct Incorrect Correct answer

0.67

Correct Incorrect Correct answer

What is the sample standard deviation for the data set (4, 6, 9, 9)?

2.1

Correct Incorrect Correct answer

2.4

Correct Incorrect Correct answer

4.2

Correct Incorrect Correct answer

6.0

Correct Incorrect Correct answer

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Daily Exam 13 – Mathematics

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