Answer:
Step-by-step explanation:
substitute x = r*cos(θ), y = r*sin(θ) ==> r²(cos²(θ) + sin²(θ)) = 2r²cos(θ)sin(θ). Cancel the r² on both sides. On the left, use pythagorean identity cos²(θ) + sin²(θ) = 1. On the right apply double angle identity sin(2θ) = 2cos(θ)sin(θ).
This yields 1=sin(2θ). (I assume you meant to type sin(2θ) on the right hand side of the equation).
Answer:
The image of the point (1, -2) under a dilation of 3 is (3, -6).
Step-by-step explanation:
Correct statement is:
<em>What are the coordinates of the image of the point (1, -2) under a dilation of 3 with the origin.</em>
From Linear Algebra we get that dilation of a point with respect to another point is represented by:
(Eq. 1)
Where:
- Reference point with respect to origin, dimensionless.
- Original point with respect to origin, dimensionless.
- Dilation factor, dimensionless.
If we know that 
, 
and 
, then the coordinates of the image of the original point is:
![\vec P' = (0,0) +3\cdot [(1,-2)-(0,0)]](https://tex.z-dn.net/?f=%5Cvec%20P%27%20%3D%20%280%2C0%29%20%2B3%5Ccdot%20%5B%281%2C-2%29-%280%2C0%29%5D)
The image of the point (1, -2) under a dilation of 3 is (3, -6).
Answer:
C). 0.83193
Step-by-step explanation:
There are total of 90 passengers of which 27 are for business.
The probability of passengers for business = 27/90
The probability of passengers for business p = 0.3
The probability of passengers not for business q = 1-The probability of passengers for business
= 1-0.3
= 0.7
Random sample of 5 passenger, probability of at least one business passenger = 1 - probability of no business passenger
probability of no business passenger
= 5C0(0.3)^0 * (0.7)^5
= 1 *1*0.16807
= 0.16807
probability of at least one business passenger = 1 - probability of no business passenger
= 1-0.16807
=0.83193
Answer:
Step-by-step explanation:
6x2 + 5x - 4
6x2 + 8x - 3x - 4
2x(3x + 4) - 1(3x + 4)
(2x - 1) (3x + 4)
These are the factors
All the points are describing a rational number! (C)
