The standard normal curve shown below is a probability density curve for a
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We can answer the first part of the question not taking intersecting function into account. The domain of is all the numbers, x∈(-∞, +∞) and the range is y∈(-∞, 36]. We can observe these results with the help of a graph, as well. Since we are talking about the rainbow, the values above the ground level will make sense. In this case, we will take into account the range as it changes between 0 and 36, included and the domain between -6 and 6. Here (0;36) is the y-intercept and (-6;0) and (6;0) are the x-intercepts of the parabola.
Since in our problem, the linear function that intersects parabola is not given, we have to provide it by ourselves according to the conditions of the problem. It could be any line intersecting parabola in two points. One important point is that the y-intercept has to be no more than 36. Considering these conditions, we can set our linear function to be . We can observe the points that we included in the table (they have been given with orange dots in the graph and the table is attached below). We can see that the values of the function (values of y) are positive. Indeed, we are discussing the part of the rainbow above the ground level.
The system of equations with linear and quadratic functions has got two solutions and we can observe that result from the graph. The solutions are (-5.823; 2.088) and (5.323; 7.662). The solutions are the intersection points.
We are given fractions and
.
In order to write them in simplest fractions, we need to find a common number that can divide both top and bottom.
Let us work on simplifying first fraction first.
We have 77672 on the top and 5548 in the bottom.
The greatest number 5548 can divide both 77672 and 5548 both.
Dividing 77672 by 5548, we get 14 and dividing 5548 by 5548 we get 1.
Putting quotent 14 on the top and 1 in the bottom, we get
. This is the answer for first part.
Let us work on simplifying second fraction .
Top number 288184 and bottom number 34, both can be divided by 34.
On dividing 288184 by 34, we get 8476 and dividing 34 by 34, we get 1.
Putting quotent 8476 on the top and 1 in the bottom, we get
. This is the answer for second part.