What is multiplicity

18 is what percent of 24?

Mkey [24]

If you do 18/24 you’ll get the answer of 0.75. Which is equal to 75%

6 0

3 years ago

Read 2 more answers

Show that a = −1 + √3i and b = 2 satisfy 1/a+b=1/a + 1/b

Zarrin [17]

Answer:

LHS = $\frac{1 - \sqrt3i}{4}$ = RHS = $\frac{1 - \sqrt3i}{4}$

Step-by-step explanation:

Data provided in the question:

a = −1 + √3i and b = 2

to prove:

$\frac{1}{a+b}=\frac{1}{a} + \frac{1}{b}$

Considering the LHS

⇒ $\frac{1}{a+b}$

substituting the value of a and b, we get

⇒ $\frac{1}{−1 + \sqrt3i+2}$

or

⇒ $\frac{1}{1 + \sqrt3i}$

on multiplying and dividing by conjugate ( 1 - √3i )

we get

$\frac{1}{1 + \sqrt3i}\times\frac{1 - \sqrt3i}{1 - \sqrt3i}$

or

$\frac{1 - \sqrt3i}{(1^2 - (\sqrt3i)^2}$

or

$\frac{1 - \sqrt3i}{1 + 3}$ (as (√i)² = -1 )

or

$\frac{1 - \sqrt3i}{4}$

Now,

considering the RHS

$\frac{1}{a} + \frac{1}{b}$

substituting the value of a and b, we get

⇒ $\frac{1}{-1 + \sqrt3i} + \frac{1}{2}$

or

⇒ $\frac{2\times1 + ( -1 + \sqrt3i)\times1}{(-1 + \sqrt3i)\times2}$

or

⇒ $\frac{2 + ( -1 + \sqrt3i)}{(-1 + \sqrt3i)\times2}$

or

⇒ $\frac{1 + \sqrt3i}{(-1 + \sqrt3i)\times2}$

now,

on multiplying and dividing by conjugate ( -1 - √3i )

we get

$\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1 - \sqrt3i}{-1 - \sqrt3i}$

or

$\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1( 1 + \sqrt3i)}{-1 - \sqrt3i}$

or

$\frac{(1 + \sqrt3i}^2\times(-1){((-1)^2 - (\sqrt3i)^2)\times2}$

or

$\frac{(1^2 + (\sqrt3i)^2+2(1)(\sqrt3i)\times(-1)}{(1 + 3)\times2}$

or

$\frac{(1 - 3 + 2\sqrt3i)\times(-1)}{(4)\times2}$

or

$\frac{(-2 + 2\sqrt3i)\times(-1)}{(4)\times2}$

or

$\frac{-2( 1 - 2\sqrt3i)\times(-1)}{(4)\times2}$

or

$\frac{( 1 - 2\sqrt3i)}{(4)}$

Since, LHS = RHS

hence satisfied

3 0

3 years ago

Solve <br> X - 2/3 = 6 1/3

tankabanditka [31]

Hi,

We have the question as x-2/3 = 6 1/3

First of all, we will convert 6 whole number 1/3 in a fraction form, to get: 19/3

x- 2/3 = 19/3

so, x= 19/3 + 2/3

After taking LCM

x= 63/9

x= 7

The value of x is 7.

Hope it helps! :)

4 0

4 years ago

Please help I don't understand i'm in the lowest class?

Anna71 [15]

Answer:

Step-by-step explanation:

6 0

2 years ago

29. BASKETBALL When Jerald shoots a free throw, the ball is 6 feet from the floor and has

tatuchka [14]

Answer:

a) j(t) = -16t^2 +20t +6

b) 1 second

c) less time

Step-by-step explanation:

The general equation for vertical motion is ...

$h(t)=-\dfrac{1}{2}gt^2+v_0t+h_0\\\text{where $v_0$ is the initial upward velocity, and $h_0$ is the initial height}$

__

a) j(t) = -16t^2 +20t +6 . . . . . filling in the given initial values, with g=32 ft/s^2

__

b) We want to find the larger of the solutions to ...

j(t) = 10 = -16t^2 +20t +6

Subtracting 6 and dividing by -4, we have ...

-1 = 4t^2 -5t

4t^2 -5t +1 = 0 . . . . add 1, put in standard form

(4t -1)(t -1) = 0 . . . . . factor

t = 1/4 or 1

The ball is in the air 1 second before reaching the hoop.

__

c) In generic terms, the equation of motion for a given shooting height at the same upward velocity will be ...

10 = -16t^2 +20t + h0

-16t^2 +20t +(h0 -10) = 0

Using the quadratic formula, we find the larger solution to be ...

t = (-(20) -√(20² -4(-16)(h0 -10)))/(2(-16))

t = (5/8) + √(64h0 -240)/32 = (5 +√(4h0 -15))/8

This value increases as h0 increases, so the ball will be in the air less time when Raymond shoots.

7 0

4 years ago