ANSWER

EXPLANATION
The given fraction is,

To get an equivalent fraction, we multiply both the numerator and the denominator by the same quantity that will give us
w²+w-20
in the denominator.
This implies that,

We multiply out the numerators and denominators using the distributive property to obtain,

This simplifies to
Answer:
The rectangular coordinates of the point are (3/2 , √3/2)
Step-by-step explanation:
* Lets study how to change from polar form to rectangular coordinates
- To convert from polar form (r , Ф) to rectangular coordinates (x , y)
use these rules
# x = r cos Ф
# y = r sin Ф
* Now lets solve the problem
∵ The point in the rectangular coordinates is (√3 , π/6)
∴ r = √3 and Ф = π/6
- Lets find the x-coordinates
∵ x = r cos Ф
∵ r = √3
∵ Ф = π/6
∴ x = √3 cos π/6
∵ cos π/6 = √3/2
∴ x = √3 (√3/2) = 3/2
* The x-coordinate of the point is 3/2
- Lets find the y-coordinates
∵ y = r sin Ф
∵ r = √3
∵ Ф = π/6
∴ y = √3 sin π/6
∵ sin π/6 = 1/2
∴ y = √3 (1/2) = √3/2
* The y-coordinate of the point is √3/2
∴ The rectangular coordinates of the point are (3/2 , √3/2)
So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:
<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>
- -10 | 1 + 2 - 82 - 28
- ---------------------------
Now firstly, drop the 1:
- -10 | 1 + 2 - 82 - 28
- ↓
- -------------------------
- 1
Next, you are going to multiply -10 and 1, and then combine the product with 2.
- -10 | 1 + 2 - 82 - 28
- ↓ - 10
- -------------------------
- 1 - 8
Next, multiply -10 and -8, then combine the product with -82:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80
- -------------------------
- 1 - 8 - 2
Next, multiply -10 and -2, then combine the product with -28:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80 + 20
- -------------------------
- 1 - 8 - 2 - 8
Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).
<u>Putting it together, the quotient is
</u>
Answer:
-2
Step-by-step explanation:
6i-5=-17
6i=-17+5
6i=-12
i=-12/6
i=-2