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mestny [16]
2 years ago
3

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

Mathematics
2 answers:
erastova [34]2 years ago
6 0
The problem is: What is the value of the expression


\displaystyle{ i^0\cdot i^1\cdot i^2\cdot i^3\cdot i^4.

We know that i^0=1 and i^2=-1. Thus:

i^0=1\\\\i^1=i\\\\i^2=-1\\\\i^3=i^2\cdot i=-1 \cdot i=-i\\\\i^4=(i^2)^2=(-1)^2=1.

So, 

i^0\cdot i^1\cdot i^2\cdot i^3\cdot i^4=1 \cdot i \cdot (-1)  \cdot (-i) \cdot 1=  i \cdot (-1)  \cdot (-i)= i \cdot i=-1.


Answer: B) -1.
Tom [10]2 years ago
5 0

The answer is B. -1 on Edg ;))

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LMN is a straight angle. Find m LMP and m NMP​
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Answer:

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2 years ago
The area of the rectangle is 64.8 square centimeters. What is the perimeter of the rectangle? One group of ten tenths and one gr
9966 [12]

Answer:

(a) Perimeter = 32.2\ cm

(b) 100

Step-by-step explanation:

Solving (a):

Given

Shape: Rectangle

Area = 64.8

Required

Calculate the perimeter.

Area is calculated as:

Area = L * W

Where

L = Length and W = Width

Substitute 64.8 for Area

64.8 = L * W

Make L the subject:

L = \frac{64.8}{W}

Perimeter is calculated as:

P = 2 * (L + W)

Substitute 64.8/W for L

P = 2 * (\frac{64.8}{W} + W)

P = \frac{129.6}{W} + 2W

To solve further, we take the derivative of P and set it to 0, afterwards.

dP = -\frac{129.6}{W^2} + 2

Set to 0

0 = -\frac{129.6}{W^2} + 2

Collect Like Terms

\frac{129.6}{W^2} = 2

Cross Multiply:

2W^2= 129.6

Divide through by 2

W^2 = 64.8

Take square roots

W = \sqrt{64.8

W = 8.05

Recall that:

L = \frac{64.8}{W}

So:

L= \frac{64.8}{8.05}\\

L= 8.05

The perimeter is:

Perimeter = 2 * (8.05 + 8.05)

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Solving (b):

Given

((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)

Required

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So, the expression becomes:

((1 Group of 10 * \frac{1}{10}) and (1 group of 8 * \frac{1}{10}))/(6 groups of 3 * \frac{1}{10})

This gives:

((1 Group of \frac{10}{10}) and (1 group of \frac{8}{10}))/(6 groups of \frac{3}{10})

Group means product, so the expression becomes:

\frac{(1 * \frac{10}{10} \ and\ 1 * \frac{8}{10})}{6 * \frac{3}{10}}

And, as used here means addition

\frac{(1 * \frac{10}{10} +  1 * \frac{8}{10})}{6 * \frac{3}{10}}

Simplify:

\frac{(1 * 1 +  1 * 0.80)}{6 *0.30}

\frac{(1 +  0.80)}{1.80}

\frac{1.80}{1.80}

= 1.00

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