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3 years ago

Simplify each of the following powers of i. i^15

Mathematics

2 answers:

frutty [35]3 years ago

7 0

Answer: $-i$

Step-by-step explanation:

You need to remember:

1. The Product of powers property: $(a^m)(a^n)=a^{(m+n)}$

2. The Power of a power property: $(a^m)^n=a^{mn}$

In this case, given:

$i^{15}$

You need to follow these steps in order to simplify it:

1. Apply the Product of powers property:

$i^{15}=i^{12}i^2i$

2. Apply the Power of a power property:

$(i^{4})^3i^2i$

3. Finally, since $i^4=1$ and $i^2=-1$ , you get:

$=(1)(-1)(i)=-i$

11111nata11111 [884]3 years ago

3 0

Answer:

-i

Step-by-step explanation:

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A wheel with radius 1 foot makes 1 revolution in 4 seconds. What is the linear velocity, in feet per second, of a point on the e

3241004551 [841]

Radius = r = 1 foot

Angular velocity = w = 1 revolutions in 4 seconds

So,

w = 0.25 revolutions per second

Since,

1 revolution = 2π radians

We can write the above equation as:

w = 0.25 x 2π radians per second = 0.5π radians per second

Linear Velocity = v = r w

Using the values, we can write:

v = 1 x 0.5π

= 0.5 π

= π/2 feet per second

Therefore, the correct answer is option B

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3 years ago

A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s

yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}$

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

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2 years ago

If g(x) = 10 - 2x then which of the following is the value of g(7)?

slega [8]

Answer:

g(7)= -4

Step-by-step explanation:

10-2(7)

10-14

=-4

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2 years ago