Math Homework Number 49
2 answers:
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Answer:
b)
Step-by-step explanation:
b) set up equations so they are equal to each other,
this is when f(x)=g(x) so our approximation was close.
c)solving it graphically is nearly impossible because the solution can be any value around the intersection. only way to be sure is to solve it symbolically.
Answer:
Step-by-step explanation:
In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:
and
3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and
So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):
* and
and
so
** and, in standard form:
4y = -3x + 29 and
3x + 4y = 29***
* : point-slope form
** : slope-intercept form
*** : standard form
This is the equation of an upside down parabola, so the maximum height will be at the vertex. To find the vertex, we'll use the formula for the x-coordinate and then solve for the y-coordinate.
Plugging this into the given formula:
Since it asks us to round, the maximum height would be 20 yards. To find how far the football travels in total, we need to set the equation equal to 0 and find the roots:
Then by the zero product property (or the no zero divisors rule), we have:
(this is the x value where the ball is kicked from)
So the ball travels 51 yards in total.
Plugging this into the given formula:
Since it asks us to round, the maximum height would be 20 yards. To find how far the football travels in total, we need to set the equation equal to 0 and find the roots:
Then by the zero product property (or the no zero divisors rule), we have:
So the ball travels 51 yards in total.