156 - n - 412 = 154,n =
1 answer:
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Answer:
Step-by-step explanation:
The complete exercise is: "The circumference of a circle is 47.1 and the diameter of the circle is 15. Which best represents the value of π? "
In order to solve this exercise, it is important to remember that the circle can be calculated with the following formulas:
1.
Where "C" is the circumference of the circle and "D" is the diameter of the circle.
2.
Where "C" is the circumference of the circle and "r" is the radius of the circle (Remeber that the diameter is twice the radius).
In this case, the exercise gives you the circumference of the circle and its diameter. These are:
Then, knowing those values, you can substitute them s into the first equation , as following:
The final step is to solve for :
Answer:
Step-by-step explanation:
To sketch a quadratic function we need two things:
1) Nature of the curve
2) Vertex
3) y-intercept
The completing square form of the quadratic equation is:
where,
a represents the nature of the graph it can be maximum or minimum , meaning, if a > 0 then minimum(u shaped curve/happy face) and if a < 0 then maximum(n shaped curve/sad face).
h represents the x-coordinate of the vertex.
k represents the y-coordinate of the vertex.
Now if we compare g(x) with our completing square form we get the following:
When we simply compare the following we get ,
a = 1 , which means a > 0 since 1 is greater than 0 the nature of the curve will be minimum(happy face/u shaped)
h = 4, which means the x-coordinate of the vertex is 4
k = 12, which means the y-coordinate of the vertex is 12
Now we have the nature of the curve, we have the vertex now all we need is the y-intercept.
For y-intercept:
For y-intercept meaning at which point will the graph cross the y-axis(0 , y)
For that we expand the formula and turn it into the standard quadratic equation form by using the formula (a - b)^2
now we compare with the standard quadratic form:
here c is the y-intercept and while comparing we can see that c = 28 ,
so the curve cuts the y-axis at (0 , 28)
So we have all the three things that we need to graph our function.
So we just plot the y-intercept , the vertex , and join the dots. Just a tip draw a dotted line on the x-coordinate of the vertex because the vertex point is also called as a turning point where the graph goes in the opposite direction just like a mirror reflection. I attached 2 images you can check them out. One is handmade(i know i suck at drawing but still xD) , one is sketched by online graphing calculator.
