First we look for the angle of the vector, which will be given by:
tan (x) = (- 2/3)
Clearing x we have:
x = ATAN (-2/3) = - 33.69 degrees.
Which means that the angle is 33.69 degrees measured clockwise from the x axis.
Equivalently the angle is
360-33.69 = 326.31 degrees
326.31 degrees measured counterclockwise from the x axis.
The vector is then:
v = 10 (cos (326.31) i + sin (326.31) j)
answer
v = 10 (cos (326.31) i + sin (326.31) j)
Answer:
Length of rectangle is: ![Length=12x^3y^6](https://tex.z-dn.net/?f=Length%3D12x%5E3y%5E6)
Step-by-step explanation:
The area of rectangle = ![24x^6y^{15}](https://tex.z-dn.net/?f=24x%5E6y%5E%7B15%7D)
Width of rectangle = ![2x^3y^9](https://tex.z-dn.net/?f=2x%5E3y%5E9)
We need to find length of rectangle
The formula used is: ![Area=Length\times Width](https://tex.z-dn.net/?f=Area%3DLength%5Ctimes%20Width)
Putting values and finding length
![Area=Length\times Width\\24x^6y^{15}=Length\times 2x^3y^9\\Length=\frac{24x^6y^{15}}{2x^3y^9} \\Length=12x^{6-3}y^{15-9}\\Length=12x^3y^6](https://tex.z-dn.net/?f=Area%3DLength%5Ctimes%20Width%5C%5C24x%5E6y%5E%7B15%7D%3DLength%5Ctimes%202x%5E3y%5E9%5C%5CLength%3D%5Cfrac%7B24x%5E6y%5E%7B15%7D%7D%7B2x%5E3y%5E9%7D%20%5C%5CLength%3D12x%5E%7B6-3%7Dy%5E%7B15-9%7D%5C%5CLength%3D12x%5E3y%5E6)
So, Length of rectangle is: ![Length=12x^3y^6](https://tex.z-dn.net/?f=Length%3D12x%5E3y%5E6)
Answer:
(a) 1, 2, 3, 6, 8
Step-by-step explanation:
Given
![Median = 3](https://tex.z-dn.net/?f=Median%20%3D%203)
![Mean = 4](https://tex.z-dn.net/?f=Mean%20%3D%204)
Required
The sequence of hours worked each day
<em>See attachment for options</em>
From the question, we understand that:
![Median = 3](https://tex.z-dn.net/?f=Median%20%3D%203)
This means that, the middle number is 3 (when sorted)
So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively
Next, is to determine the mean of (a) and (d)
The mean of a data is calculated as:
![\bar x = \frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
So, we have:
(a)
![\bar x = \frac{1+ 2+ 3+ 6+ 8}{5}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B1%2B%202%2B%203%2B%206%2B%208%7D%7B5%7D)
![\bar x = \frac{20}{5}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B20%7D%7B5%7D)
![\bar x = 4](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%204)
(d)
![\bar x = \frac{1+ 2+ 3+ 4+ 5}{5}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B1%2B%202%2B%203%2B%204%2B%205%7D%7B5%7D)
![\bar x = \frac{15}{5}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B15%7D%7B5%7D)
![\bar x = 3](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%203)
Option (a) is true, because it has:
![Median = 3](https://tex.z-dn.net/?f=Median%20%3D%203)
![Mean = 4](https://tex.z-dn.net/?f=Mean%20%3D%204)
520 x 0.2 = 104
520 + 104 = 625
Curtley's annual heating cost before he got his loft insulated was $624.00