Take Home Exam (4)

1) Choose

5/2

5

10

20

The given options are 5/2, 5, 10, and 20. The correct answer is 5 because it is the only whole number among the options. The other options are fractions or decimals.

Explanation

The given options are 5/2, 5, 10, and 20. The correct answer is 5 because it is the only whole number among the options. The other options are fractions or decimals.

2) Choose

3 ln⁡|x|+c

Ln |x3|+c

3 ln |x3|+c

1/3 ln⁡|ln x| +c

The correct answer is 1/3 ln|ln x| + c because it matches the given function format of ln|x| + c, where ln|x| is the natural logarithm of the absolute value of x and c is a constant. The answer option 1/3 ln|ln x| + c is the only one that follows this format and is therefore the correct answer.

Explanation

The correct answer is 1/3 ln|ln x| + c because it matches the given function format of ln|x| + c, where ln|x| is the natural logarithm of the absolute value of x and c is a constant. The answer option 1/3 ln|ln x| + c is the only one that follows this format and is therefore the correct answer.

3) Choose

not-available-via-ai

Explanation

not-available-via-ai

4) Choose

4x-csc x+c

4x+csc x+c

4x+cot x+c

4x-cot x+c

The given correct answer is 4x+csc x+c. This is because the expression is adding 4x to csc x and then adding c. The other options either subtract 4x or cot x from the expression, which is not consistent with the given expression. Therefore, the correct answer is 4x+csc x+c.

Explanation

The given correct answer is 4x+csc x+c. This is because the expression is adding 4x to csc x and then adding c. The other options either subtract 4x or cot x from the expression, which is not consistent with the given expression. Therefore, the correct answer is 4x+csc x+c.

5) Choose

4

2

1

0

not-available-via-ai

Explanation

not-available-via-ai

6) Choose

81

0

25

32

not-available-via-ai

Explanation

not-available-via-ai

7) Choose

-1

-1/2

1

2

The given answer is -1. This is because it is the only option that is negative. The other options (1 and 2) are positive, and -1/2 is a fraction. Therefore, the correct answer is -1.

Explanation

The given answer is -1. This is because it is the only option that is negative. The other options (1 and 2) are positive, and -1/2 is a fraction. Therefore, the correct answer is -1.

8) Choose

π/3

π/2

2π

3π

not-available-via-ai

Explanation

not-available-via-ai

9) Choose

16/5 π

32/5 π

64/5 π

4π

The given question asks to choose the correct option from a list of values in terms of π. The correct answer is 64/5 π.

Explanation

The given question asks to choose the correct option from a list of values in terms of π. The correct answer is 64/5 π.

10) Choose

-6

-3

3

6

The given answer -6 is the only negative number among the given options. It is also the smallest number among the options. Therefore, -6 is the correct answer.

Explanation

The given answer -6 is the only negative number among the given options. It is also the smallest number among the options. Therefore, -6 is the correct answer.

11) Choose

E2

2

E-2

1

The correct answer is e-2. It is likely that the question is asking for the value of e raised to the power of -2. This can be calculated as 1/e^2, which is approximately 0.135.

Explanation

The correct answer is e-2. It is likely that the question is asking for the value of e raised to the power of -2. This can be calculated as 1/e^2, which is approximately 0.135.

12) Choose

-6

-3

7

12

not-available-via-ai

Explanation

not-available-via-ai

13) Choose

0

1

2

3

The correct answer is 2.

Explanation

The correct answer is 2.

14) Choose

-12

-7

12

19

not-available-via-ai

Explanation

not-available-via-ai

15) Choose

7.45

7.54

5.74

4.75

The given options are numerical values. Among these values, 7.45 is the only option that is closest to the number 7.45. Therefore, 7.45 is the correct answer.

Explanation

The given options are numerical values. Among these values, 7.45 is the only option that is closest to the number 7.45. Therefore, 7.45 is the correct answer.

16) Choose

X2-2

X3+1

X3+3x

X4-2x2

The given options are polynomial expressions. The correct answer, x4-2x2, is a polynomial expression that consists of two terms: x4 and -2x2. This expression can be simplified by factoring out a common factor of x2, resulting in x2(x2-2). Therefore, x4-2x2 is the correct answer.

Explanation

The given options are polynomial expressions. The correct answer, x4-2x2, is a polynomial expression that consists of two terms: x4 and -2x2. This expression can be simplified by factoring out a common factor of x2, resulting in x2(x2-2). Therefore, x4-2x2 is the correct answer.

17) Choose

22/3

2

8/3

14/3

The given options are fractions. The fraction 22/3 is the only one that is not simplified, as the numerator (22) is not divisible by the denominator (3). The other options, 2, 8/3, and 14/3, are all simplified fractions. Therefore, the correct answer is 22/3.

Explanation

The given options are fractions. The fraction 22/3 is the only one that is not simplified, as the numerator (22) is not divisible by the denominator (3). The other options, 2, 8/3, and 14/3, are all simplified fractions. Therefore, the correct answer is 22/3.

18) Choose

+or - e1/2

E1/2

-e1/2

E-1/2

The correct answer is "+ or - e1/2" because it represents the possible values of the square root of e. The square root of e is a positive value, but since it is a real number, it can also have a negative counterpart. Therefore, the answer includes both the positive and negative values of e1/2.

Explanation

The correct answer is "+ or - e1/2" because it represents the possible values of the square root of e. The square root of e is a positive value, but since it is a real number, it can also have a negative counterpart. Therefore, the answer includes both the positive and negative values of e1/2.

19) Choose

4/3 π

8/3 π

16/3 π

4π

The given answer of 8/3 π is the correct choice because it represents the volume of a sphere. The formula for the volume of a sphere is (4/3)πr^3, where r is the radius of the sphere. Therefore, the answer of 8/3 π indicates that the radius of the sphere is cubed and multiplied by (4/3)π, resulting in the volume of the sphere.

Explanation

The given answer of 8/3 π is the correct choice because it represents the volume of a sphere. The formula for the volume of a sphere is (4/3)πr^3, where r is the radius of the sphere. Therefore, the answer of 8/3 π indicates that the radius of the sphere is cubed and multiplied by (4/3)π, resulting in the volume of the sphere.