Given 2 numbers, a and b. The number exactly in the middle of a and b is
![\displaystyle{ \frac{a+b}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Cfrac%7Ba%2Bb%7D%7B2%7D%7D%20)
.
For example, the number exactly in the middle of numbers 5 and 17 is (5+17)/2=22/2=11.
Check: 11-5=6, 17-11=6
The number in the middle of 24 and 92 is (92+24)/2=116/2=58.
The positive difference between 58 and both 24 and 92 is :
58-24 = 34 & 92-58 = 34
Thus the height of a woman
x, can vary at most 34, from 58. That is the height of a woman can be 34 ft less or more than 58.
In absolute value notation this is expressed as :
|x-58|≤34
what this means is that
x-58≤34 or 58-x≤34
so x≤58+34 or -x≤34-58
x≤92 or -x≤-24, that is x≥24
Answer: |x-58|≤34 ; 24≤x≤92
A = L * W
A = 45
L = 2W + 1
45 = W(2W + 1)
45 = 2W^2 + W
2W^2 + W - 45 = 0
(2W - 9)(W + 5) = 0
W + 5 = 0
W = -5...not this one because it is negative
2W - 9 = 0
2W = 9
W = 9/2
W = 4.5 <=== the width is 4.5 ft
L = 2W + 1
L = 2(4.5) + 1
L = 9 + 1
L = 10 <=== the length is 10 ft
Answer:
Therefore m∠ B is 42.1°
Step-by-step explanation:
Given:
In Δ ABC
AB = 15 = c
AC = 18 = b
∠ C = 34°
To Find:
∠ B = ?
Solution:
In Δ ABC We have Sine Rule as
Substituting the given values we get
![\frac{b}{\sin B}= \frac{c}{\sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B%5Csin%20B%7D%3D%20%5Cfrac%7Bc%7D%7B%5Csin%20C%7D)
![\frac{18}{\sin B}= \frac{15}{\sin 34}\\\\\sin B=0.671\\\\\therefore B=\sin^{-1}(0.671)=42.14\°](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B%5Csin%20B%7D%3D%20%5Cfrac%7B15%7D%7B%5Csin%2034%7D%5C%5C%5C%5C%5Csin%20B%3D0.671%5C%5C%5C%5C%5Ctherefore%20B%3D%5Csin%5E%7B-1%7D%280.671%29%3D42.14%5C%C2%B0)
Therefore m∠ B is 42.1°
I think the first one is a simple as it gets
for the second one it could be simplified to 6x^6-4 because u combine the x terms and distribute the power