What is the graph of g?

What does i^739 equal? explain how you found your answer.

Sophie [7]

<h3>Answer: -i</h3>

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Explanation:

i = sqrt(-1)

Lets list out the first few powers of i

i^0 = 1
i^1 = i
i^2 = -1
i^3 = i*i^2 = i*(-1) = -i
i^4 = (i^2)^2 = (-1)^2 = 1

By the time we reach the fourth power, we repeat the cycle over again (since i^0 is also equal to 1). The cycle is of length 4, which means we'll divide the exponent over 4 to find the remainder. Ignore the quotient. That remainder will determine if we go for i^0, i^1, i^2 or i^3.

For example, i^5 = i^1 because 5/4 leads to a remainder 1.

Another example: i^6 = i^2 since 6/4 = 1 remainder 2

Again, we only care about the remainder to find out which bin we land on.

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Turning to the question your teacher gave you, we have,

739/4 = 184 remainder 3

So i^739 = i^3 = -i

<h3>-i is the final answer</h3>

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Side notes:

if i^a = i^b, then a-b is a multiple of 4
Recall that the divisibility by 4 trick involves looking at the last two digits of the number. So i^739 is identical to i^39.

4 0

3 years ago

A motorboat can maintain a constant speed of 15 miles per hour relative to the water. The boat makes trip upstream to a certain

Ira Lisetskai [31]

Answer:

The speed of the current is 2 miles per hours

Step-by-step explanation:

Given as :

The speed of motorboat = x = 15 miles per hour

The time taken by motorboat trip upstream = 51 minutes

The time taken by motorboat trip downstream = 39 minutes

Let The speed of the current = y miles per hour

Let The total distance cover = A miles

So ,

Speed = $\dfrac{\textrm Distance}{\textrm Time}$

So, x - y = $\dfrac{A}{51}$

I.e 15 - y = $\dfrac{A}{51}$

And x + y = $\dfrac{A}{39}$

I.e 15 + y = $\dfrac{A}{39}$

$\dfrac{x-y}{x+y}$ = $\dfrac{39}{51}$

I.e $\dfrac{x-y}{x+y}$ = $\dfrac{13}{17}$

Or, 17 × (x - y) = 13 × (x + y)

Or, 17 x - 17 y = 13 x + 13 y

Or, 17 x - 13 x = 13 y + 17 y

Or, 4 x = 30 y

Now, ∵ x = 15 miles per hour

So, 4 × 15 = 30 y

Or, y = $\dfrac{60}{30}$

∴ y = 2 miles per hour

Hence The speed of the current is 2 miles per hours Answer

8 0

3 years ago

The weight of a car is modeled with the polynomial x2 + 10x + 200. The weight of a x3 + x + 100. Which polynomial represents the

Zolol [24]

<h3>The combined weight of a car and truck is given as the polynomial P(W) = x³ + x² + 11 x + 300</h3>

Step-by-step explanation:

The weight of the car is given as:

P(C) = x² + 10 x + 200

The weight of the truck is given as:

P(T) = x³ + x + 100

Now, the combined weight of both vehicles is given as

= Weight of Car P(C) + Weight of Truck P(T)

P(W) = x² + 10 x + 200 + x³ + x + 100

= x³ + x² + (10 x + x)+ (200 + 100)

= x³ + x² + 11 x + 300

⇒ The combined weight of a car and truck is given as the polynomial P(W) = x³ + x² + 11 x + 300

3 0

3 years ago

What is the slope and how f the linear 4x + 2y=24

lorasvet [3.4K]

Answer: y=-2x+12

Step by Step explanation:

4x+2y=24
-4x -4x
-------------------
2y=-4x+24
---- ----- -----
2 2 2

y=-2x+12

7 0

4 years ago

Read 2 more answers

The graphs below have the same shape. what is the equation o the red graph?

maw [93]

So the equation of the red graph is already given to us: $f(x) = x^2$ . I assume you meant the blue graph?

We can use the vertex form: $y = a(x - h)^2+ k$ , where $(h,k)$ is the vertex. (We can ignore $a$ because $a$ is 1 for this graph.) Remember that the vertex is the maximum or minimum of a parabola and the point that the line of symmetry passes through. For f(x) the vertex is (0,0).