Answer:
The skaters will collide at the points;
(2,28) and (4,24)
Step-by-step explanation:
The points they might collide will be the points when both y are equal;
-2x + 32 = -2x^2 + 18x
2x^2 -18x -2x + 32 = 0
2x^2 -20x + 32 = 0
2x^2 - 16x - 4x + 32 = 0
2x(x -8) -4( x -8) = 0
(2x -4)(x -8) = 0
2x = 4 or x = 8
x = 4/2 or x = 8
hence; x = 2 or 8
Now let’s get the y value
at x = 2, just substitute into any of the 2
y = -2x + 32
y = -2(2) + 32
y = -4 + 32 = 28
at x = 4
y = -2(4) + 32
y = -8 + 32
y = 24
The points that they will collide are;
(2,28) and (4,24)
Answer:
y = (-5/4)x + 5
Step-by-step explanation:
Slope-intercept form is y = mx + b
m is the slope and b is the y-intercept
To find m, we can use the plotted points on the graph
(0,5)(4,0)
Now, do delta y/ delta x
(0-5)/(4-0)
slope = -5/4
Now, the y-intercept is the point where the graph crosses the y-axis
This point is where x is 0. Here, when x is 0, y is 5.
Therefore, the y-intercept is 5
Finally, replace what you've found into the equation
y = (-5/4)x + 5
no it is not simplified because there are two y values
Integrating gives
To compute the integral, substitute 
, so that 
. Then
Since 
for all 
, we can drop the absolute value, so we end up with
Given that 
, we have
so that
For this case what you should do is follow the following steps:
1) factorize numerator and denominator of both expressions.
2) cancel similar terms
3) add both fractions by cross product
4) Rewrite the numerator and denominator.
Answer:
See attached image.
