This table shows a linear relationship. x: 6 12 18 24 30 y: 252 504 756 1008 1260 Based on the information in this table, which
1 answer:
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Answer:
End points of the this segment are (9,1) and (2,3).
Step-by-step explanation:
The given function is
End points of the this segment are (1,9) and (3,2).
If a function is defined as
then
It means, we have to interchange x and y-coordinates of the end points.
So, end points of the this segment are (9,1) and (2,3).
Plot these point and join them by a line segment.
To give you a context on the problem, a tangent line is a line that intersects the parabola only at one single point. A parabola is a curve that forms an arc-shaped figure. A tangent line to a parabola is shown in the attached picture.
Now, we apply the concepts in calculus and analytical geometry. The first derivative of the equation is equal to the slope at the point of intersection. This slope must be equal to the slope of the tangent line.
y = x² - 5x + 7
dy/dx = slope = 2x -5
Since tangent lines must have the same slope with what they intersect with, we can determine the slope from the equation: y = 3x + c. This is already arranged in a slope-intercept form, where 3 is the slope and c is the y-intercept. So, we can equate the equation above to 3.
2x - 5 = 3
x = 4
Now, we substitute x=4 to the original equation of the parabola:
y = (4)² - 5(4) + 7
y = 3
Therefore, the point of intersection is at (4,3). Now, we use it to the equation of the tangent line to find c.
y = 3x + c
3 = 3(4) + c
c = -9
Now, we apply the concepts in calculus and analytical geometry. The first derivative of the equation is equal to the slope at the point of intersection. This slope must be equal to the slope of the tangent line.
y = x² - 5x + 7
dy/dx = slope = 2x -5
Since tangent lines must have the same slope with what they intersect with, we can determine the slope from the equation: y = 3x + c. This is already arranged in a slope-intercept form, where 3 is the slope and c is the y-intercept. So, we can equate the equation above to 3.
2x - 5 = 3
x = 4
Now, we substitute x=4 to the original equation of the parabola:
y = (4)² - 5(4) + 7
y = 3
Therefore, the point of intersection is at (4,3). Now, we use it to the equation of the tangent line to find c.
y = 3x + c
3 = 3(4) + c
c = -9
Answer:
15.39%
Step-by-step explanation:
Step 1
Find the z-value associated to the given datum x, in this case x = 28 mpg
<em>z is given by the formula </em>
where is the mean of the distribution and
is the standard deviation. In this case,
Step 2
Locate the z-value in the table of z-values of the normal distribution.
(See table attached) and read the number corresponding to this z-value. In this case is highlighted in the table and its value is 0.34614.
<em>This numbers gives us the % of vehicles with a mpg between 0 and 28. </em>
Step 3
As we know that the total area under the curve for z > 0 is 0.5, then we have to subtract 0.34614 from 0.5 to obtain the % of cars with a mpg greater than 28 mpg.
0.5 - 0.34614 = 0.15386
so, the % of 2016 vehicles that have better gas mileage than the Beetle's gas mileage is 15.39 % (rounded to two decimals)
