Which of the following are identities? Check all that apply.
1 answer:
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You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).
In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.
The result is
So, the second equation turned to be an equality, i.e. an equation where both sides are the same.
This implies that the system has infinitely many solutions, because every couple such that
is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.
Answer:
See the explanation for the answer.
Step-by-step explanation:
Given function:
The n-th order Taylor polynomial for function f with its center at a is:
As n = 3 So,
= 3 + 0.0092592593 (x - 81) + 1/2 ( - 0.000085733882) (x - 81)² + 1/6
(0.0000018522752) (x-81)³
= 0.0092592593 x - 0.000042866941 (x - 81)² + 0.00000030871254
(x-81)³ + 2.25
Hence approximation at given quantity i.e.
x = 94
Putting x = 94
= 0.0092592593 (94) - 0.000042866941 (94 - 81)² +
0.00000030871254 (94-81)³ + 2.25
= 0.87037 03742 - 0.000042866941 (13)² + 0.00000030871254(13)³ +
2.25
= 0.87037 03742 - 0.000042866941 (169) +
0.00000030871254(2197) + 2.25
= 0.87037 03742 - 0.007244513029 + 0.0006782414503 + 2.25
= 3.113804102621
Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Compute as
using calculator
Exact value:
(94) = 3.113737258478
Compute absolute error:
Err = | 3.113804102621 - 3.113737258478 |
Err (94) = 0.000066844143
If you round off the values then you get error as:
|3.11380 - 3.113737| = 0.000063
Err (94) = 0.000063
If you round off the values up to 4 decimal places then you get error as:
|3.1138 - 3.1137| = 0.0001
Err (94) = 0.0001
