The point P(9, −4) lies on the curve y = 4 / (8 − x).
If Q is the point (x, 4/(8 − x)) find the slope of the secant line PQ (correct to six decimal places) for the following values of x.
a) 9.1 b) 9.001
for a) I keep getting 3.636363 and for b) I keep getting 3.996003. I'm not sure what I'm doing wrong.
what makes you think you're wrong?
why do you not show your work?
(f(9..1)-f(9))/(9.1-9) = (-4-(-3.636363))/0.1 = -3.363636
Maybe you just misread your calculator ...
Show your work for the 2nd one
My online homework keeps marking both problems as wrong...
My work for the second one is [(4/(8-9.001) - (-4)]/(9.001 - 9) = [(4/-1.001) - (-4)]/(.001) = (-3.996003996 + 4)/(.001) = (0.003996004)/(.001) = 3.996003
I noticed when you showed your work for the second part, that you
were not consistent in the direction you subtracted .
If your points are,
(9, -4)
(9.001, k)
then you calculate either (k -(-4)) / (9.001 - 9)
or (-4 - k)/(9 - 9.001)
so should have been:
[(4/(8-9.001) - (-4)]/(9.001 - 9) = -3.996003996
= -3.996004 correct to 6 decimals or
[-4 - 4/(8-9.001)]/(9.001 - 9) = -3.996004 correct to 6 decimals
you did - ∆y / ∆x
Thanks so much for your responses. I appreciate it. Part of my error is that I was forgetting to round!
To find the slope of the secant line PQ, we need to calculate the difference in y-coordinates over the difference in x-coordinates between the points P and Q.
Let's start by finding the coordinates of point Q for the given values of x.
a) For x = 9.1:
Substitute x = 9.1 into the equation y = 4 / (8 − x):
y = 4 / (8 − 9.1)
Simplifying, we get:
y = 4 / (-1.1)
y = -3.636363636...
For x = 9.1, the coordinates of Q are (9.1, -3.636363636...).
b) For x = 9.001:
Substitute x = 9.001 into the equation y = 4 / (8 − x):
y = 4 / (8 − 9.001)
Simplifying, we get:
y = 4 / (-1.001)
y = -3.996003996...
For x = 9.001, the coordinates of Q are (9.001, -3.996003996...).
Now that we have the coordinates of both points P and Q, we can calculate the slope of the secant line PQ by using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
For point P(9, -4) and point Q(a, b) in general, the slope of the secant line PQ is:
slope = (b - (-4)) / (a - 9)
a) For x = 9.1:
slope = (-3.636363636... - (-4)) / (9.1 - 9)
slope = 0.363636...
b) For x = 9.001:
slope = (-3.996003996... - (-4)) / (9.001 - 9)
slope = 0.995004...
Therefore, the correct slopes of the secant lines PQ for a) and b) are approximately:
a) 0.363636...
b) 0.995004...
It seems like there might be an error in the calculations or rounding. Make sure you are using accurate decimal approximations and check your calculations again. You can also use a calculator or spreadsheet software to verify the results.