Well the period of the tan(x) function is π. It means that when you add π on X axis you will get the same y axis value.
There is a little trick to find the period of functions like yours.
You just divide period of basic tan(x) function with, in your case 3.
So this mean you have
To = π/3
Function intercepts x axis when function is equal to 0.
tan(3x) = 0
3x = k * π
x = k * (π / 3)
There are only vertical asymptotes in tangent function.
You can easily see it if you look at the graph
tan(x) = ∞ , (π/2 + kπ)
tan(x) = -∞ (-π/2 + kπ).
x = π/2 + kπ
x = - π/2 + kπ
tan(3x) = ∞
3x = π/2 + kπ
x = π/6 + kπ/3
tan(3x) = -∞
3x = -π/2 + kπ
x = -π/6 + kπ/3
There are several ways, but the general format follows f(x) = ax2 + bx + c f(x) = ax² + bx + c, where A, B, and C are non-zero numbers. Another way of finding a quadratic equation is examining the graph of it, you'll notice a "U" shape called a parabola, which come in many shapes but they all retain a "U"-like curve.
Answer:
c. [70.30, 74.70]
Step-by-step explanation:
Confidence interval is a range of values in which there is a specified probability that the value of a parameter lies within that range.
The confidence interval of a statistical data can be written as.
x+/-zr/√n .......1
Given;
Mean gain x = 72.5 cm
Standard deviation r = 4.5 cm
Number of samples n = 16
Confidence interval = 95%
z (at 95% confidence) = 1.96 (from the table)
Substituting the values we have into equation 1;
72.5 +/- 1.96×4.5/√16
72.5 +/- 2.20 cm
[70.30, 74.70]
Therefore, the 95% confidence interval is
[70.30, 74.70] cm
Answer:
x = -2
Step-by-step explanation:
Given the point, (-2, 9) and the linear equation of a <u>horizontal line</u>, y = 6:
The linear equation of a horizontal line with a slope of zero (<em>m</em> = 0) is y = <em>b, </em>for which the y-intercept is (0, <em>b</em>). <u>Perpendicular lines</u> comprise of the intersection of two lines forming 90° angles.
Since we are given the equation of a horizontal line, then we can assume that <em>the line that intersects a horizontal line must be a </em><u><em>vertical line</em></u> in order to form perpendicular lines.
The linear equation of a <u>vertical line</u> with an undefined slope is <em>x</em> = <em>a</em>, for which the x-intercept is (<em>a</em>, 0). Vertical lines have an <u>undefined slope </u>because these lines do not have any horizontal change. Thus, when you try to solve for its slope, the denominator will have a difference of 0, making the mathematical operation undefined.
We can use the <u>x-coordinate</u> of the given point, (-2, 9), to formulate an equation for a vertical line: x = -2.
Therefore, the equation of the line that goes through y = 6 is x = -2.
Attached is a screenshot of the graph of both equations, y = 6 and x = -2, showing that their intersection form 90° angles, making them perpendicular lines.
69 plus 13 because 30 plus 13 is 43, 43 plus 13 is 56, and you know the rest
