The point P(4, −2)lies on the curve y = 2/(3 − x).
(a) If Q is the point(x, 2/(3 − x)),use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.
1) 3.9 mPQ=
2) 3.99 mPQ=
3)3.999 mPQ=
4) 4.1 mPQ=
5) 4.01 mPQ=
im so confused! i just started this and my teacher really didn't explain it. can someone please break this down for me?
See my reply to your previous post
http://www.jiskha.com/display.cgi?id=1346202745
All 5 answers should be very close to -2
(the exact answer is -2 which will make sense in a couple more lessons )
Sure! I'd be happy to break it down for you.
Let's start by understanding what the problem is asking for. The problem gives you a point P(4, -2) that lies on a curve described by the equation y = 2/(3 - x). It also introduces another point Q, but its x-coordinate can vary. The task is to find the slope of the secant line PQ for different values of x.
To find the slope of a secant line, we need to calculate the slope between two points on the curve. In this case, we have the fixed point P(4, -2) and the variable point Q with the coordinates (x, 2/(3 - x)).
The slope formula for two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Now that we understand the problem, let's solve it step by step for each value of x given.
1) For x = 3.9:
- Plug in the values for x and y into the slope formula:
mPQ = (2/(3 - 3.9) - (-2)) / (3.9 - 4)
- Simplify the numerator and denominator:
mPQ = (-48 / 9) / (-0.1)
mPQ = 5.333333 (correct to six decimal places)
2) For x = 3.99:
- Repeat the same steps as above with x = 3.99:
mPQ = (2/(3 - 3.99) - (-2)) / (3.99 - 4)
mPQ = (-198 / 1) / (-0.01)
mPQ = 19800.000000 (correct to six decimal places)
3) For x = 3.999:
mPQ = (2/(3 - 3.999) - (-2)) / (3.999 - 4)
mPQ = (-1998 / 0.001) / (-0.001)
mPQ = 1998000.000000 (correct to six decimal places)
4) For x = 4.1:
mPQ = (2/(3 - 4.1) - (-2)) / (4.1 - 4)
mPQ = (-18 / 1.1) / (0.1)
mPQ = -163.636364 (correct to six decimal places)
5) For x = 4.01:
mPQ = (2/(3 - 4.01) - (-2)) / (4.01 - 4)
mPQ = (-200 / 0.01) / (0.01)
mPQ = -20000.000000 (correct to six decimal places)
So the answers to the respective values of x are:
1) mPQ = 5.333333
2) mPQ = 19800.000000
3) mPQ = 1998000.000000
4) mPQ = -163.636364
5) mPQ = -20000.000000
You can use a scientific calculator or an online calculator to perform the necessary calculations. Remember to be careful with parentheses and to double-check your work for accuracy.
I hope this explanation helps you understand the problem better! Let me know if you have any further questions.