Louisa biked 50 4/5 miles in 4 hours how many miles did she bike per hour
2 answers:
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ANSWERS
(5) Graph:
(6) Solutions: (-1, -5) and (-2, -7)
Not solutions: (1, 1) and (-4, -3)
EXPLANATION
(5) To graph this system, first, we have to graph each of the inequalities. Both are linear, so we have to graph each line with a dashed line - this is because they are "less than" the line, so the line is not included, and shade the area below each of them.
The first inequality is y < -3x-4,
The second inequality is y < 2x - 1,
The graph of the system is the area shared by both graphs,
(6) Any point that is inside the shaded area is a solution of the system. For example, points (-1, -5) and (-2,-7) are solutions to the system.
On the other hand, any point outside that area, or on the dashed lines is not a solution. For example, points (1, 1) and (-4, -3) are not solutions
Answer:
The values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0
The explanation of the answer is now provided as follows:
Given:
f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0 …………….. (1)
= (x) = (e^z /4!)x^4
Since the aim is (x) < 0.001, this implies that:
(e^z /4!)x^4 < 0.0001 ………………………………….. (2)
Multiply both sided of equation (2) by (1), we have:
e^4x^4 < 0.024 ……………………….......……………. (4)
Taking 4th root of both sided of equation (4), we have:
|xe^(z/4) < 0.3936 ……………………..........…………(5)
Dividing both sides of equation (5) by e^(z/4) gives us:
|x| < 0.3936 / e^(z/4) ……………….................…… (6)
In equation (6), when z > 0, e^(z/4) > 1. Therefore, we have:
|x| < 0.3936 -----> 0 < x < 0.3936
Therefore, the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.