Answer:
Step-by-step explanation:
This equation is more intimidating than the problem you have to solve.
You know that the sine of everything is always between -1 and +1. So for the entire expression to be >= 0, the a*tan(pi/8) bit has to be 1 at least. Given this, we can forget about the sin(...) term of the equation for the remainder of solving it.
You already figured out that tan(pi/8) is sqrt(2)-1.
So what we're saying is a * (sqrt(2) - 1) has to be 1 at least.
If we solve a(sqrt(2)-1) >= 1 for a we get:
a = 1/(sqrt(2)-1)
Answer: ![\begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-\frac{2}{3}\quad \mathrm{or}\quad \:x\ge \:0\:\\ \:\mathrm{Decimal:}&\:x\le \:-0.66666\dots \quad \mathrm{or}\quad \:x\ge \:0\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-\frac{2}{3}]\cup \:[0,\:\infty \:)\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ax%5Cle%20%5C%3A-%5Cfrac%7B2%7D%7B3%7D%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax%5Cge%20%5C%3A0%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BDecimal%3A%7D%26%5C%3Ax%5Cle%20%5C%3A-0.66666%5Cdots%20%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax%5Cge%20%5C%3A0%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%28-%5Cinfty%20%5C%3A%2C%5C%3A-%5Cfrac%7B2%7D%7B3%7D%5D%5Ccup%20%5C%3A%5B0%2C%5C%3A%5Cinfty%20%5C%3A%29%5Cend%7Bbmatrix%7D)
Step-by-step explanation:
F(x) = 4 - 2x Domain = x = -4, 0, 5
f(x) = 4 - 2(-4) = 4 - (-8) = 12
f(x) = 4 - 2(0) = 4 - 0 = 4
f(x) = 4 - 2(5) = 4 - 10 = -6
f(x) = 12, 4, -6
The range is C.
Lets x is price of noble fir trees and y - is price for douglas fir trees
students got 5x+3y=420$ on friday
and 12x+9y=1080
now we need just solve the system of equations
5x+3y=420 - multiply by 3
12x+9y=1080
15x+9y=1260
12x+9y=1080
substract second equation from first
15x-12x=1260-1080
3x=180
x=60$ - the price of noble fir trees
put value x=60 in first equation 5x+3y=420
5*60+3y=420
300+3y=420
3y=120
y=40$ - price of Douglas fir trees
Answer: Noble fir trees cost $60 and Douglas fir trees cost $40
Step-by-step explanation:
the answer is -86 mark as brainliest or rate this if u found this helpful :)
