Find the volume of a cylinder with a diameter of 16 mm and the height of 5.7mm
1 answer:
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Option A
-x + 6y = 42 is the standard form
<u>Solution:</u>
Given that we have to write in standard form
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers
Given equation is:
Let us convert the above equation into standard form
Make the denominator same in R.H.S
Solve the above equation
Move 6 from R.H.S to L.H.S
Bring all the terms to one side, leaving only constant on R.H.S
The above equation is of form Ax + By = C
Thus option A is correct
The function is divided in 2 parts:
For x<0, the function is
, which is a linear function, and its graph is a line.
For x≥0, the function is
, which is a quadratic function, and its graph is a parabola.
Note that y=x is the line containing the points (0, 0), (1, 1), (5, 5) etc, that is, it is the line passing through the origin, with an inclination of 45° with the positive x-axis.
The parabola is the parabola 
reflected with respect to the x-axis. It contains points like (0, 0), (-1, 1), (2, -4) etc...
The 2 graphs, with domain all real numbers, are shown in the first picture.
The second picture is the graph of the function described in our problem. We use the first picture, but restrict the domains.
That is, we delete the part of the line corresponding to x≥0, and the part of the parabola corresponding to x<0.
For x<0, the function is
For x≥0, the function is
Note that y=x is the line containing the points (0, 0), (1, 1), (5, 5) etc, that is, it is the line passing through the origin, with an inclination of 45° with the positive x-axis.
The parabola
The 2 graphs, with domain all real numbers, are shown in the first picture.
The second picture is the graph of the function described in our problem. We use the first picture, but restrict the domains.
That is, we delete the part of the line corresponding to x≥0, and the part of the parabola corresponding to x<0.