Answer:
![\[\sqrt{5}\]](https://tex.z-dn.net/?f=%5C%5B%5Csqrt%7B5%7D%5C%5D)
Step-by-step explanation:
The given vector is represented by (2,-1).
This can be represented in general form as (x,y) where x=2 and y=-1.
Magnitude of the vector represented as (x,y) is given by ![[\sqrt{x^{2}+y^{2}}\]](https://tex.z-dn.net/?f=%5B%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D%5C%5D)
Evaluating for the given values of x and y,
![\[\sqrt{2^{2}+(-1)^{2}}\]](https://tex.z-dn.net/?f=%5C%5B%5Csqrt%7B2%5E%7B2%7D%2B%28-1%29%5E%7B2%7D%7D%5C%5D)
![\[=\sqrt{4+1}\]](https://tex.z-dn.net/?f=%5C%5B%3D%5Csqrt%7B4%2B1%7D%5C%5D)
![\[=\sqrt{5}\]](https://tex.z-dn.net/?f=%5C%5B%3D%5Csqrt%7B5%7D%5C%5D)
Length of the vector is
The inequality that shows the maximum number of dresses she can buy is $7.15p+$9.95=$60 the maximum # of dresses she can buy is 7
For the answer to the question above,
The mean value theorem states the if f is a continuous function on an interval [a,b], then there is a c in [a,b] such that:
<span>f ' (c) = [f(b) - f(a)] / (b - a) </span>
<span>
So [f(a) - f(b)] ( b - a ) = [sin(3pi/4) - sin(pi/4)]/pi </span>
= [sqrt(2)/2 - sqrt(2)/2]/pi = 0
So for some c in [pi/2, 3pi/2] we must have f ' (c) = 0
In general f ' (x) = (1/2) cos (x/2)
We ask ourselves for what values x in [pi/2, 3pi/2] does the above equation equal 0.
0 = (1/2) cos (x/2)
0 = cos (x/2)
x/2 = ..., -5pi/2, -3pi/2, -pi/2, pi/2, 3pi/2, 5pi/2,...
x = ..., -5pi, -3pi, -pi, pi. 3pi, 5pi, ....
and x = pi is the only solution in our interval.
So c = pi is a solution that satisfies the conclusion of the MVT
Make them both over 54:
so 7/9= 42/54
and 5/6= 35/54
now you can easily see that 7/9 is larger than 5/6
