Please solve this homeworkThis math equation needs to be solved 0.00 100.02 8.1870.04 6.7030.06 5.4880.08 4.4930.10 3.678SolutionIn the following figure we plot the data and use it to sketch a curve that approximates the graph of the function.Q(coulombs)108Q642OGiven the points P(0.04, 6.703) and R(0.00, 10) on the graph, we find that the slope of the secant line PR, rounded to two decimal places, is as follows.10-(x )80.00 -0.04The following table shows the results of similar calculations for the slopes of other secant lines.R60.02 0.04 0.05 0.08 0.104(0.00, 10)-82.43(0.02, 8.187)-74.20(0.06, 5.488)-60.75(0.08, 4.493)-55.25(0.10, 3.678) -50.42From this table we would expect the slope of the tangent line at t-0.04 to lie somewhere between -74.20 and -60.75. In fact, the average of the slopes of the two closest secant lines is as follows.(-74.20-60.75) -xt (seconds)mpst2So, by this method, we estimate the slope of the tangent line, rounded to the nearest integer, to be aboutxAnother method is to draw an approximation to the tangent line at P and measure the sides of the triangle ABC, as in the figure below.Q(coulombs)104xAP……………………………… (seconds)t0.02 0.04 0.05 0.08 0.10This gives an estimate of the slope of the tangent line asAMB]5.362-8.044-67.05.|BC|0.06 -0.02

Slope of the secant line is given slope, We have given point , Slope of secant line PR is given by:

Answered: Q 0.00 10 0.02 8.187 0.04 6.703 0.06…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

Please solve this homework

This math equation needs to be solved

0.00 10
0.02 8.187
0.04 6.703
0.06 5.488
0.08 4.493
0.10 3.678
Solution
In the following figure we plot the data and use it to sketch a curve that approximates the graph of the function.
Q(coulombs)
10
8
Q
6
4
2
O
Given the points P(0.04, 6.703) and R(0.00, 10) on the graph, we find that the slope of the secant line PR, rounded to two decimal places, is as follows.
10-(x )
8
0.00 -0.04
The following table shows the results of similar calculations for the slopes of other secant lines.
R
6
0.02 0.04 0.05 0.08 0.10
4
(0.00, 10)
-82.43
(0.02, 8.187)
-74.20
(0.06, 5.488)
-60.75
(0.08, 4.493)
-55.25
(0.10, 3.678) -50.42
From this table we would expect the slope of the tangent line at t-0.04 to lie somewhere between -74.20 and -60.75. In fact, the average of the slopes of the two closest secant lines is as follows.
(-74.20-60.75) -
x
t (seconds)
mpst
2
So, by this method, we estimate the slope of the tangent line, rounded to the nearest integer, to be about
x
Another method is to draw an approximation to the tangent line at P and measure the sides of the triangle ABC, as in the figure below.
Q(coulombs)
104
x
A
P
……………………………… (seconds)
t
0.02 0.04 0.05 0.08 0.10
This gives an estimate of the slope of the tangent line as
A
MB]
5.362-8.044-67.05.
|BC|
0.06 -0.02

Expert Solution

Step 1: Evaluation Slope of the secant line:

Slope of the secant line is given

slope, $m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction$

We have given point $P left parenthesis 0.04 comma space 6.703 right parenthesis comma space R left parenthesis 0.00 comma space 10 right parenthesis$ ,

Slope of secant line PR is given by:

$m subscript P R end subscript equals fraction numerator 10 minus bold 6 bold. bold 703 over denominator 0.00 minus 0.04 end fraction equals bold minus bold 82 bold. bold 425$