Answer:
Step-by-step explanation:
we have
Equate to zero
The formula to solve a quadratic equation of the form
is equal to
in this problem we have
so
substitute in the formula
Remember that
so
The table lists the results from a survey (of questionable accuracy) of adults and how much they spend on a night out.
2 answers:
The <em>correct answer</em> is:
The correct scatter plot is attached.
There appears to be a negative correlation between a person's age and the amount they spend on a night out.
Explanation:
Age will be the independent variable, along the x-axis, and the cost of a night out will be the dependent variable, along the y-axis.
The ages range from a low of 20 to a high of 45. We will start our graph at 0 and use a scale of 5s along the x-axis, going to 45.
The amounts for a night out range from a low of 38 to a high of 58. We will start our graph at 0 and use a scale of 5s along the x-axis, going to 60.
We then plot each point as a coordinate of (age, amount spent).
Once we get the graph plotted, we see there is a negative trend in the data. As the age increases, the amount spent out decreases.
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<h3>Answer:</h3>
- using y = x, the error is about 0.1812
- using y = (x -π/4 +1)/√2, the error is about 0.02620
The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.
If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...
... x -sin(x) @ x=π/3
... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812
You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.
___
If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...
... (x+1-π/4)/√2 -sin(x) @ x=π/3
... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620