Table to Exponential Function
1 answer:
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Given:
f(x) = sin(x)
g(x) = cos(x).
Note that because sin²x + cos²x = 1, the value for f²+g² should be equal to 1.
Create the table shown below.
x f² g² f² + g²
-------- ---------- ----------- ------------
-π 0 1 1
-0.8π 0.3455 0.6545 1
-0.6π 0.9045 0.0955 1
-0.4π 0.9045 0.0955 1
-0.2π 0.3455 0.6545 1
0 0 1 1
0.2π 0.3455 0.6545 1
0.4π 0.9045 0.0955 1
0.6π 0.9045 0.0955 1
0.8π 0.3455 0.6545 1
π 0 1 1
A sketch is shown in the figure below.
f(x) = sin(x)
g(x) = cos(x).
Note that because sin²x + cos²x = 1, the value for f²+g² should be equal to 1.
Create the table shown below.
x f² g² f² + g²
-------- ---------- ----------- ------------
-π 0 1 1
-0.8π 0.3455 0.6545 1
-0.6π 0.9045 0.0955 1
-0.4π 0.9045 0.0955 1
-0.2π 0.3455 0.6545 1
0 0 1 1
0.2π 0.3455 0.6545 1
0.4π 0.9045 0.0955 1
0.6π 0.9045 0.0955 1
0.8π 0.3455 0.6545 1
π 0 1 1
A sketch is shown in the figure below.
Using linear function concepts, the slope of -1 means that when one of the length/width is increased by 1, the other is decreased by 1.
<h3>What is a linear function?</h3>A linear function is modeled by:
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
In this problem:
- The lengths and the widths are interchangeable, that is, either can be considered as the input or as the output.
- The slope of -1 means that when the input in increased by 1, the output is decreased by -1, that is, when one of the length/width is increased by 1, the other is decreased by 1.
You can learn more about linear function concepts at brainly.com/question/24808124
Answer:
The estimate for the number of students who took the test is 23.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 78
Standard deviation = 6
Since the normal distribution is symmetric, 50% of the students had scores above the mean and 50% had scores below the mean.
Proportion of students who scored between 72 and 90:
72 = 78 - 6
So 72 is one standard deviation below the mean.
Of the 50% of the students who scored below the mean, 68% scored above 72.
90 = 78 + 2*6
So 90 is two standard deviations above the mean.
Of the 50% of the students who scored above the mean, 95% scored below 72.
Then
0.68*0.5 + 0.95*0.5 = 0.815
81.5% of the students scored between 72 and 90.
Nineteen students had test scores between 72 and 90. Estimate the number of students who took the test.
19 is 91.5% = 0.815 of the total number of students.
How much is 100% = 1?
19 - 0.815
x - 1
Rounding to the nearest whole number
The estimate for the number of students who took the test is 23.