North is the direction of positive y-axis. East is the direction of positive x-axis. So West will be the direction of negative x-axis.
Northwest will mean, in between north and west i.e. in between y-axis and the negative x-axis which is the mid of the 2nd quadrant. Thus the vector pointing northwest will form an angle of 135 degrees with positive x-axis.
The magnitude of unit vector is 1 and is forming an angle of 135 degrees. In terms of its components, we can write:
x-component = 1 cos (135) =
y-component = 1 sin (135) =
Thus the unit vector will be =
In vector form, component form the vector can be written as:
Answer:
A
Step-by-step explanation:
Pick any point on any side of the line. substitute X and Y in the inequality for (x,y)-the point you chose. If you simplify and the inequality is true, shade in that side. If it is false, shade in the other side.
Answer:
B
Step-by-step explanation:
The exponential function 
shows the exponential growth if 
Consider choice B.
If x=1, then 
if x=2, then 
if x=3, then 
if x=4, then 
This means that the function 
represents the table B.
Answer:
the daily fee =33 dollars
and the mileage charge.=0.35
Step-by-step explanation:
let d: be daily fee and m for mileage
cost of rental =(d*number of days)+ (m*number of mileage)
her first trip: 4d+440m=286
her second trip: 3d+190m=165.5
solve by addition and elimination
4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286
3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)
12d+1320m=858
12d+760m=662
subtract two equation to eliminate d
12d+1320m-12d-760m=858-662
560m=196
m=7/20=0.35 for on mileage
d: 4d+440m=286
4d=286-440(0.35)
d=(286-154)/4 33 dollars
First, we sketch a picture to get a sense of the problem. g(x)=x is a diagonal line through (0,0) with slope = = 1. Since we are interested in the area between x = -4 and x = 8, we find the points on the line at these values. These are (-4, -4) and (8,8).
f(x) is a parabola. It's lowest point occurs when x = 0. It is the point (0,7). At x = -4 and x=8 it has the values 11.8 and 26.2 respectively. That is, it contains the points (-4, 11.8) and (8,26.2).
From these we make a rough sketch (see attachment). This is a sketch and mine is very incorrect when it comes to scale but what matters here is which of the curves is on top, which is below and whether they intersect anywhere in the interval, so my rough sketch is good enough. From the sketch we see that f(x) is always above (greater than) g(x).
To find the area between the curves over the given interval we integrate their difference and since f(x) is strictly greater than g(x) we subtract as follows: f(x) - g(x). The limits of integration are the values -4 and 8 (the x-values between which we are looking for the area.
Now let's integrate:
The integral yields:
^{3} }{3} +7(8)- \frac{ (8)^{2} }{2}) -(\frac{.3 (-4)^{3} }{3} +7(-4)- \frac{ (-4)^{2} }{2}) = 117.6](https://tex.z-dn.net/?f=%20%5Btex%5D%28%5Cfrac%7B.3%20%288%29%5E%7B3%7D%20%7D%7B3%7D%20%2B7%288%29-%20%5Cfrac%7B%20%288%29%5E%7B2%7D%20%7D%7B2%7D%29%20-%28%5Cfrac%7B.3%20%28-4%29%5E%7B3%7D%20%7D%7B3%7D%20%2B7%28-4%29-%20%5Cfrac%7B%20%28-4%29%5E%7B2%7D%20%7D%7B2%7D%29%20%3D%20117.6)
[/tex]
We evaluate this for 8 and for -4 subtracting the second FROM the first to get:
