F(xth) if f(x) = 4x2+4x - 1
1 answer:
You might be interested in
<u>Solution-</u>
A school has 1800 students and 1800 light bulbs, each with a pull cord and all in a row.
As all the lights start out off, in the first pass all bulbs will be turned on.
In the second pass all the multiples of 2 will be off and rest will be turned on.
In the third pass all the multiples of 3 will be off, but the common multiple of 2 and 3 will be on along with the rest. i.e all the multiples of 6 will be turned on along with the rest.
In the fourth pass 4th light bulb will be turned on and so does all the multiples of 4.
But, in the sixth pass the 6th light bulb will be turned off as it was on after the third pass.
This pattern can observed that when a number has odd number of factors then only it can stay on till the last pass.
1 = 1
2 = 1, 2
3 = 1, 3
<u>4 = 1, 2, 4</u>
5 = 1, 5
6 = 1, 2, 3, 6
7 = 1, 7
8 = 1, 2, 4, 8
9 = 1, 3, 9
10 = 1, 2, 5, 10
11 = 1, 11
12 = 1, 2, 3, 4, 6, 12
13 = 1, 13
14 = 1, 2, 7, 14
15 = 1, 3, 5, 15
16 = 1, 2, 4, 8, 16
so on.....
The numbers who have odd number of factors are the perfect squares.
So calculating the number of perfect squares upto 1800 will give the number of light bulbs that will stay on.
As, , so 42 perfect squared numbers are there which are less than 1800.
∴ 42 light bulbs will end up in the on position. And there position is given in the attached table.
You haven't provided a graph or equation so I will tell the simplified meaning of amplitude instead.
Amplitude, is basically a distance from midline/baseline to the maximum or minimum point.
For sine function, can be written as:
- A = amplitude
- b = period = 2π/b
- c = horizontal shift
- d = vertical shift
I am not able to provide an attachment for an easy view but I will try my best!
We know that amplitude or A is a distance from baseline/midline to the max-min point.
Let's see the example of equation:
Refer to the equation above:
- Amplitude = 2
- b = 1 and therefore, period = 2π/1 = 2π
- c = 0
- d = 0
Thus, the baseline or midline is y = 0 or x-axis.
You can also plot the graph on desmos, y = 2sinx and you will see that the sine graph has max points at 2 and min points at = -2. They are amplitude.
So to conclude or say this:
If Amplitude = A from y = Asin(x), then the range of function will always be -A ≤ y ≤ A and have max points at A; min points at -A.