Answer:
A = 30°
x = 9·√3
Step-by-step explanation:
Part A
In the drawing, we are given;
The radius of the circle with center at point S = SA = 18
ΔAHA is a right triangle
One of the leg length of ΔASH = 9
The length of the hypotenuse side of ΔASH, AS = 18 The radius of the circle with center at the point 'S'
By Pythagoras's theorem, the length of the (radius) side, AS = √(SH² + AH²)
∴ AH = √(AS² - SH²)
AH = √(18² - 9²) = √(243) = 9·√3
AH = 9·√3
By circle theorem, SH bisects the line AH extended to the circumference of the circle
SH bisects the line with length AH + x
∴ AH = x
x = AH = 9·√3
x = 9·√3
Part B
By trigonometric ratios, we have;
∠A = arcsine (1/2) = 30°
Angle A = 30°
Step-by-step explanation:
As
so
x y
2 1
3 5
4 9
5 13
6 17
and so on
From the table:
As the slope-intercept form of the line is
putting m=4 and any point, let say (2, 1) to find y-intercept 'b'.
So putting and
in the slope-intercept form of the line
Therefore, the equation for the linear function will be:
Answer: Assuming the function is :
The x-intercept is .
The y-intercept is .
The horizontal asymptote is .
The vertical asymptote is .
Step-by-step explanation:
I'm going to assume the function is: and not
.
So we are looking at .
The x-intercept is when y is 0 (when g(x) is 0).
Replace g(x) with 0.
A fraction is only 0 when it's numerator is 0. You are really just solving:
Subtract 1 on both sides:
Divide both sides by 2:
The x-intercept is .
The y-intercept is when x is 0.
Replace x with 0.
.
The y-intercept is .
The vertical asymptote is when the denominator is 0 without making the top 0 also.
So the deliminator is 0 when x-3=0.
Solve x-3=0.
Add 3 on both sides:
x=3
Plugging 3 into the top gives 2(3)+1=6+1=7.
So we have a vertical asymptote at x=3.
Now let's look at the horizontal asymptote.
I could tell you if the degrees match that the horizontal asymptote is just the leading coefficient of the top over the leading coefficient of the bottom which means are horizontal asymptote is . After simplifying you could just say the horizontal asymptote is
.
Or!
I could do some division to make it more clear. The way I'm going to do this certain division is rewriting the top in terms of (x-3).
So you can think it like this what value will y never be here.
7/(x-3) will never be 0 because 7 will never be 0.
So y will never be 2+0=2.
The horizontal asymptote is y=2.
(Disclaimer: There are some functions that will cross over their horizontal asymptote early on.)