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Oxana [17]
4 years ago
13

Divide. a.1 − 2i/2i b. 5 − 2i/5 + 2i c.√3 − 2i/−2 − √3i

Mathematics
1 answer:
Umnica [9.8K]4 years ago
5 0

Answer:

(a) \frac{-1i}{2}-1[/tex]

(b) \frac{20i+21}{29}

(c) i

Step-by-step explanation:

We have to perform division

(a) \frac{1-2i}{2i}

So after division

\frac{1-2i}{2i}=\frac{1}{2i}-\frac{2i}{2i}=\frac{-1i}{2}-1

(b) We have given expression \frac{5-2i}{5+2i}

After rationalizing \frac{5-2i}{5+2i}\times \frac{5-2i}{5-2i}=\frac{(5-2i)^2}{25+4}=\frac{25+4i^2+20i}{29}=\frac{20i+21}{29}

(c) We have given expression \frac{\sqrt{3}-2i}{-2-\sqrt{3i}}

After rationalizing

\frac{\sqrt{3}-2i}{-2-\sqrt{3i}}\times \frac{-2+\sqrt{3i}}{-2+\sqrt{3i}}=\frac{-2\sqrt{3}+7i+2\sqrt{3}}{7}=\frac{7i}{7}=i

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Since there are 8 students, each student gets 1/8 of the available cake. Since there is 3/4 of a cake available, they will get 1/8 of 3/4.


Source: https://www.wyzant.com/resources/answers/142015/there_are_8_students_in_a_group_and_3_4_cake_how_much_cake_will_each_student_get_if_divided_evenly

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Expand the following.<br> (3x + 2)2<br> A.9x2+6x+4<br> B.9x2+4<br> C.3x2+4<br> E.9x2+12x+4
PolarNik [594]

Step-by-step explanation:

E

working ;

(3x+2)^2

*Apply Perfect Square Formula : (a+b) =a^2+2ab+b^2

a = 3x,b = 2

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finally Answer is:

= 9x^2 + 12x +4

5 0
3 years ago
two positive numbers x and y, with the maximum value 4, add up to 5. what is the difference between the maximum and minimum valu
Svetach [21]

Answer:

  92

Step-by-step explanation:

Since the sum of the two numbers is 5, we can represent one of them by x and the other by 5-x. Then the desired product is ...

  x²(5-x)³

A graphing calculator can show the extreme values of this on the interval 1 ≤ x ≤ 4. The maximum is 108 at x=2; the minimum is 16 at x=4.

The difference between the maximum and minimum is 108-16 = 92.

_____

If you like, you can take the derivative and set it to zero.

  f(x) = x²(5 -x)³

  f'(x) = 2x(5 -x)³ +x²(-3)(5-x)² = x(5 -x)²(2(5-x) -3x)

  f'(x) = 5x(5-x)²(2-x)

This will be zero for x=0, x=5, and x=2. The points at x=0 and x=5 represent minima in the product. The values x=0 and x=5 are not in the domain of interest. The point at x=2 represents a maximum.

To find the function extremes on an interval, we need to evaluate the function where the derivative is zero, and also at the ends of the interval. So, the function values of interest are ...

  f(1) = 1²·4³ = 64

  f(2) = 2²·3³ = 108 . . . . product maximum

  f(4) = 4²·1³ = 16 . . . . . . product minimum

The difference between the maximum and minimum is 92.

5 0
3 years ago
Lucy is walking on a hill while playing with a yo-yo. She completes a trick that takes 8 seconds, and over this period of time,
GenaCL600 [577]

Answer:

1/32(x-4)^2+1/16(x-7)^2-12.5

Step-by-step explanation:

I just took my integer test LOL.

i aced it

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