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harina [27]
2 years ago
12

PLATO:Find the missing term. If y = 1 + i, then y3 − 3y2 + ( ) − 1 = -i .

Mathematics
1 answer:
laila [671]2 years ago
3 0

Answer:

X= 6i

Step-by-step explanation:

We have the following equation:

y^3 - 3y^2 + X - 1 = -i    (1),

where X is the missing term.

So, we know that y = 1 + i. Where i = sqrt(-1).

Substituting y = 1 + i in the equation (1):

(1 + i)^3 - 3(1 + i)^2 + X - 1 = -i

(1)^3 + 3(i)(1)^2 + 3(1)(i)^2 + (i)^3 - 3(1 + 2(1)(i) + (i)^2) + X - 1 = -i

Simplifying:

1 + 3i -3i - i - 3(1 + 2i -1) + X - 1 = -i

1 - i -6i + X - 1 = -i

-i - 6i + X = -i

- 6i + X = 0

X= 6i

So the missing term is X= 6i

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Mike bought five items for lunch that Cost a total of 4.55 .Hit dogs cost .1.10 each and cookies cost 0.75 each. What equation c
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Answer:

c + h = 5 and

0.75c + 1.10h = 4.55

Step-by-step explanation:

Assume that Mike bought only cookies and hot dogs.

The total can be represented as:

Cookies + Hot\ Dogs = 5 --- (1)

And the amount spent can be represented as:

Cost\ of\ cookies + Cost\ of\ hot\ dogs = 4.55 --- (2)

Required

Determine the system of equation

Let c represents the number of cookies and h, number of hot dogs.

Cookies + Hot\ Dogs = 5 implies c + h = 5

And

Cost\ of\ cookies + Cost\ of\ hot\ dogs = 4.55

Cost of cookies = 0.75 * c

Cost of hot dogs = 1.10 * h

So, we have:

0.75c + 1.10h = 4.55

Hence, the equations are:

c + h = 5 and

0.75c + 1.10h = 4.55

Solving for c and h

Make c the subject in c + h = 5

c = 5 - h

Substitute 5 - h for c in 0.75c + 1.10h = 4.55

0.75(5- h) + 1.10h = 4.55

3.75- 0.75h + 1.10h = 4.55

3.75 +0.35h = 4.55

Collect Like Terms

0.35h = 4.55 - 3.75

0.35h = 0.8

Solve for h

h = 0.8/0.35

h = 2.28571428571

h =2 -- approximated

Recall that:

c = 5 - h

c = 5 - 2

c =3

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