Which is greater?.75 or 3/5
2 answers:
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Answer:
a)
b)
c)
Step-by-step explanation:
In order to solve this problem we must start by sketching the graph of the function. This will help us visualize the problem better. (See attached picture)
You can sketch the graph of the function by plotting as many points as you can from x=0 to x=20 or by finding the vertex form of the quadratic equation by completing the square. You can also do so by using a graphing device, you decide which method suits better for you.
A)
So we are interested in finding the area under the curve, so we divide it into 5 rectangles taking a right hand approximation. This is, the right upper corner of each rectangle will touch the graph. (see attached picture).
In order to figure the width of each rectangle we can use the following formula:
in this case a=0, b=20 and n=5 so we get:
so each rectangle must have a width of 4 units.
We can now calculate the hight of each rectangle. So we figure the y-value of each corner of the rectangles. We get the following heights:
h1=64
h2=96
h3=96
h4= 64
h5=0
so now we can use the following formula to find the area under the graph. Basically what the formula does is add the areas of the rectangles:
which can be rewritten as:
So we go ahead and solve it:
so:
B) The same procedure is used to solve part B, just that this time we divide the area in 10 rectangles.
In order to figure the width of each rectangle we can use the following formula:
in this case a=0, b=20 and n=10 so we get:
so each rectangle must have a width of 2 units.
We can now calculate the hight of each rectangle. So we figure the y-value of each corner of the rectangles. We get the following heights:
h1=36
h2=64
h3=84
h4= 96
h5=100
h6=96
h7=84
h8=64
h9=36
h10=0
so now we can use the following formula to find the area under the graph. Basically what the formula does is add the areas of the rectangles:
which can be rewritten as:
So we go ahead and solve it:
so:
c)
In order to find part c, we calculate the area by using limits, the limit will look like this:
so we start by finding the change of x so we get:
next we find
so:
and we find
cand we do some algebra to simplify it.
we do some factorization:
and plug it into our formula:
And simplify:
And now we use summation formulas:
and simplify:
and solve the limit
Answer:
x-intercept= (3⅓, 0)
y-intercept= (0, 4²⁄₇)
Please see the attached picture for the graph.
Step-by-step explanation:
-9x -7y= -30
Let's simplify the equation by dividing both sides by -1.
9x +7y= 30
x- intercept occurs at y= 0.
When y= 0,
9x +7(0)= 30
9x= 30
x= 30 ÷9
Thus, x- intercept occurs at (3⅓, 0).
y-intercept occurs at x= 0.
When x= 0,
9(0) +7y= 30
7y= 30
y= 30 ÷7
Thus, y- intercept occurs at (0, 4²⁄₇).
_____
To graph the equation, draw the x and y axis on a graph paper. Use an appropriate scale to divide the line into equal parts. Next, plot the points (3⅓, 0) and (0, 4²⁄₇). Then, join the two points with a straight line.
Notes:
- x- intercept is the point at which the graph cuts through the x- axis. In this case, your x- axis is the horizontal line that runs from left to right of your graph paper. In order for a point to be on this horizontal line, look at the y- axis and notice that it sits at y= 0. The same reason applies for why the y- intercept occurs at x= 0. This has to do with the two axis cutting each other at the point (0,0), resulting in the x and y coordinates of 0 for the y and x intercepts respectively.
- Simplifying the equation in the first step is not necessary, but it is a good practice and might reduce carelessness.
