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3 years ago

Simplify the expression i⁸²

Mathematics

1 answer:

Elza [17]3 years ago

6 0

Answer:

We can use a trick here. Let's look at the first few exponents of i to realize this:

i^0 = 1

i^1 = i

i^2= -1

i^3 = -i

i^4 = 1

i^5 = i

i^6 = -1

i^7 = -i

we can see that the pattern (1, i, -1, -i) repeats. Since 82/2 = 41, and 41 is only divisible by 1, i^41 = i, and i^2 = -1. -1*i = -i, so i^82 = -i.

Step-by-step explanation:

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2^5/4 = 2^5/2^a = c a= b= c= What are the answers pls

monitta

Answer:

mass of 1 mole 2^5/4=2^5/2a=c=0g

Step-by-step explanation:

8 0

2 years ago

A town has a population of 17000 and grows at 3% every year. To the nearest year, how long will it be until the population will

Mumz [18]

Answer:

The population will reach 20,400 after 6 years.

Step-by-step explanation:

Exponential function:

$y(t)=y_0(1+r)^t$

y(t)= Population after t years

$y_0$ = initial population

r= rate of grow

t= time.

A town has a population of 17,000 and grows at a rate 3% every year.

y(t)= 20,400, $y_0$ = 17,000, r=3%=0.03, t=?

$20,400=17,000(1+0.03)^t$

$\Rightarrow \frac{20,400}{17,000}=(1.03)^t$

$\Rightarrow \frac{102}{85}=(1.03)^t$

Taking ln function both sides

$\Rightarrow ln|\frac{102}{85}|=ln|(1.03)^t|$

$\Rightarrow ln|\frac{102}{85}|=t\ ln|(1.03)|$

$\Rightarrow t=\frac{ln|\frac{102}{85}|}{\ ln|(1.03)|}$

⇒ t = 6 year.

The population will reach 20,400 after 6 years.

6 0

4 years ago

Mrs. jack bought 150 T-shirt for $1920 from a factory calculate the cost of one T-shirt

o-na [289]

Answer: $12.80

Step-by-step explanation:

$1980/ 150 t shirts =$12.80 per shirt

6 0

3 years ago

Read 2 more answers

A stock has a P/E ratio of 3.25 and a earnings per share of $9.25. What is the price per share of the stock?

astra-53 [7]

Answer:

$6.00

Step-by-step explanation:

7 0

3 years ago

What is the output, or dependent variable or quantity? Х f(x) у DONE

Ipatiy [6.2K]

Answer:

x is the input, or independent variable and f(x) is the output, or dependent variable or quantity. f(2) represents the output (y-value) when x = 2. The value of f(2) is 2.

Step-by-step explanation:

If the values of a variable depends on the other variable, then it called dependent variable.

If the value of a variable does not depend on the other, then it is called independent variable.

If a function is f(x)=x, then x is an independent variable and f(x) is a dependent variable.

The given function is

Here, x is the input, or independent variable and f(x) is the output, or dependent variable or quantity.

The notation f(a) represents the output (y-value) when x = a. So, f(2) represents the output (y-value) when x = 2.

Substitute x=2 in the given function.

The value of f(2) is 2.

3 0

3 years ago