The volume generated by rotating the given region about OC is
Because the given region () has a look like a washer, we will apply the washer method to find the volume generated by rotating the given region about the specific line.
solution
We first find the value of x and y
A similar question about finding the volume generated by a given region is answered here: brainly.com/question/3455095
Answer:
Step-by-step explanation:
We have been given an equation . We are asked to find the zeros of equation by factoring and then find the line of symmetry of the parabola.
Let us factor our given equation as:
Dividing both sides by 2:
Splitting the middle term:
Using zero product property:
Therefore, the zeros of the given equation are .
We know that the line of symmetry of a parabola is equal to the x-coordinate of vertex of parabola.
We also know that x-coordinate of vertex of parabola is equal to the average of zeros. So x-coordinate of vertex of parabola would be:
Therefore, the equation represents the line of symmetry of the given parabola.
Answer:
See attached. (Both inequalities graph to the same region.)
Step-by-step explanation:
To graph an inequality, you first replace the inequality symbol by an equal sign. Then you graph the line (or curve) described by the equation. If the inequality symbol includes the "or equal to" case, then the line (or curve) is solid and is part of the solution set. If not, then the line (or curve) is dashed and is <em>not part of the solution set</em>.
Here, the line x+y=5, will bound the solution set, but is not part of it.
Note that the line -x -y = -5 (from the second inequality) is the same ilne.
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After you have graphed the boundary of the solution region, you need to determine which side of the boundary has the solutions. I find it easy to do this by locating an x- or y-term with a positive coefficient and seeing which side of the inequality symbol that lies on. Here, both the x-term and the y-term lie on the "is greater than" side of the symbol, so the half-plane is shaded above and to the right of the line, where x- and y-values are greater than they are on the line.
In the second inequality, you can multiply the whole thing by -1 to get
... x + y > 5 . . . . same as the first inequality
or you can add (x+y) to both sides to get
... 0 < -5 +x +y
Once again, the x- and y-values that satisfy this are greater than those that are on the boundary line.
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The graph seems to show only one equation. Both are there, but the dashed blue line sits on top of the dashed red line, so you can't see it. The purple shading indicates both red and blue shading in the same area.
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Of course you graph the boundary line the way you would any linear equation. In this form, it is not too difficult to see that both the x- and y-intercepts are 5. (When x=0, y=5; and when y=0, x=5 for the boundary line's equation x+y=5.) Draw the dotted line through these intercept points, add shading above, and you have your graph.
