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Ann [662]
2 years ago
12

If f(x) = x3 – 2x2, which expression is equivalent to f(i)?

Mathematics
1 answer:
Ahat [919]2 years ago
8 0

Answer:

2 - i

Step-by-step explanation:

Substitute i for x. Remeber i means imaginart number.

{i}^{3}  - 2 {i}^{2}

Use the Imaginary number exponents rules

{i}^{2}  =  - 1

{i}^{3}  =  - i

i {}^{4}  = 1

Simplify the equation.

- i - ( - 2)

- i + 2

Write as a complex number in form a+bi

2 - i

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Find two numbers with a sum of 20 and a difference of 14.
Alekssandra [29.7K]
The anwser is 17 and 3. 17+3=20, and the difference is 14!
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2 years ago
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A museum requires a minimum number of chaperones proportional to the number of students on a field trip. The museum requires a m
Stells [14]

Answer: See explanation

Step-by-step explanation:

Here is the complete question:

A museum requires a minimum number of chaperones proportional to the number of students on a field trip. The museum requires a minimum of 3 chaperones for a field trip with 24 students. Which of the following could be combinations of values for the students and the minimum number of chaperones the museum requires? Choose 2 answers.

A. Students: 72

Minimum of chaperones: 9

B. Students: 16

Minimum of chaperones: 2

C. Students: 60

Minimum of chaperones: 6

D. Students: 45

Minimum of chaperones: 5

E. Students: 40

Minimum of chaperones: 8

Since the museum requires a minimum of 3 chaperones for a field trip with 24 students. This means that there will be 24/3 = 8 students per chaperone.

We then divide the number of students given in the question by the number of chaperone to know our answers. This. Will be:

Students: 72

Minimum of chaperones: 9

This will be: 72/9 = 8

Therefore, this is correct.

B. Students: 16

Minimum of chaperones: 2

This will be: 16/2 = 8

This is correct

C. Students: 60

Minimum of chaperones: 6

This will be: = 60/6 = 10.

Therefore, this is wrong

D. Students: 45

Minimum of chaperones: 5

This will be 45/5 = 9

Therefore, this is wrong.

E. Students: 40

Minimum of chaperones: 8

This will be: 40/5 = 8.

Therefore, this is wrong.

Therefore, options A and B are correct.

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The cube with side 2 is cut from the corner of rectangular prism with dimensions 4×3×5. Find the volume and total surface area o
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Answer:

Volume: 52 Units Squared

Surface Area: 94 units.

Step-by-step explanation:

The volume is relatively simple to find. Just subtract the original volume by the 2x2x2 cube's volume. The original volume is 60. The cube's volume is 2x2x2 which is 8. 60-8=52.

The surface area is harder to find. Try to envision the corner of the rectangle being cut out. We see that each side of the cube has a surface area of 2x2 which is 4. In the picture, we see that three sides of the rectangle has been partially removed. But since each side of the cube has an equal surface area, it is safe to minus 3 of the sides that has been partially removed by 3. However, since that it is the corner, the "dent" that the cube made in the rectangle also needed to be counted. As we said, each of the sides of a cube has a surface area of 4, so since that the dent has 3 sides, we see that the surface area of the dent is 4x3 which is 12. Now we need to count the unaffected sides of the rectangle. There are three of them. Just multiply the edges to find the surface area of each side. Add all of the values up: 11+16+12+8+15+12+20=94 units.

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2. Which group of numbers is in size order?
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Answer:

B. 3.09-3.10-3.2-3.5 is the answer

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