Answer:
b = -8
Step-by-step explanation:
6b = -42
Divide by 6 on both sides
b = -8
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)
(4x-3)(x+5)
= 4x^2+20x-3x-15
= 4x^2+ 17x -15.
The final answer is 4x^2+ 17x -15~
Answer:
WQ = 2.67 to the nearest hundredth.
Step-by-step explanation:
The area of triangle PQX = 1/2 * PX * QX.
The area of the rectangle = 8 * YX .
But YX = 2 PX so its area = 8 *2PX = 16*PX.
We are given that area of PQX is 1/6 of the area of WXYZ, so we have the equation:-
16 PX = 6* 1/2*PX * QX
16 = 3QX
QX = 16/3 = 5.33
Finally WQ = WX - QX
= 8 - 5.33
= 2.67
