A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years w
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Answer:
y = 0
Step-by-step explanation:
The given sinusoidal equation is
The general form of the sin function is presented as follows;
y = A·sin(B·(x - C)) + D
Where;
A = The amplitude
The period, T = 2·π/B
The frequency, f = B/2·π
C = The horizontal shift
D = The vertical shift
By comparison with the given sine function, we have;
The amplitude, A = 2
The frequency, f = B/2·π = π/2/(2·π) = 1/4
The frequency, f = 1/4 Hz
C = The horizontal shift = 3/(π/2) = 6/π
The vertical shift, D = 0
Given that the mid line of the parent function, sin(x), is the line y = 0, and that the vertical shift is 0, the midline of the function, , is therefore, the line;
y = 0.
You're going to need to use Pythagoras' theorem to work this one out!
As you know, the perimeter of a triangle is just all the lengths of the sides added up.
We'll start with side AC first. We can see that A is (-8, -4) and C is (-6, -2). That means to get from A to C, we need to go 2 units to the right, and 2 units up. Which means we have our two sides to work out the length from Pythagoras' theorem. 2² + 2² = c², c = √8.
Now we'll move onto side AB. We already know A is (-8, -4) from above, and B is (-7, -8). That means to get from A to B, we have to go 4 units down, and 1 unit to the right. So once again: 4² + 1² = c², c = √17.
Lastly, we'll work out side BC. We know that B is (-7, -8) and C is (-6, -2). That means to get to C from B, we have to go 1 unit to the right and 6 units up. So, again: 1² + 6² = c², c = √37.
Now that we have all of our lengths, we simply just add them up!
√8 + √17 + √37 ≈ 13.03 units.
(I've also attached something to help you visualise how I worked it out.)
