Start with second, third and fourth degree of imaginary unit i:

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

Since 233=232+1=4·58+1, then $i^{233}=i^{4\cdot 58+1}=(i^4)^{58}\cdot i^1=1^{58}\cdot i=i$ .

Answer: $i^{233}=i$

5 0

1 year ago

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Uma empresa transporta armários para escritórios para uma localidade distante 425km. Seu custo é de R$2,10 por km rodado. Quando

MariettaO [177]

Answer:

1. $14.88

2. $12.40

Step-by-step explanation:

An english translation:

A company transports office cabinets to a location 425km away. Its cost is R $ 2.10 per km traveled. When the cabinets are assembled, the vehicle's capacity is 60 units. When they are disassembled the capacity increases 6 times. We ask: 1- What is the cost per assembled cabinet? 2- What is the savings per cabinet, when these are taken apart.

Solution:

425 km with 2.10 per km means:

425 * 2.10 = $892.50 total cost

Now, when assembled, there goes 60 cabinets, so cost per assembled cabinet is:

Cost per assembled cabinet = 892.5/60 = $14.875 = $14.88

The capacity of 60 after disembling, it becomes:

60 * 6 = 360

So, cost per cabinet becomes:

892.5/360 = $2.48

The savings is how much you save up if they were assembled:

14.88 - 2.48 = $12.40

Savings = $12.40

8 0

2 years ago