Write a linear equation that intersects y = x2 at two points. then write a second linear equation that intersects y = x2 at just one point, and a third linear equation that does not intersect y = x2. explain how you found the linear equations.

Step-by-step explanation:

1. Any linear equation that describes a line with non-zero slope through the vertex of the parabola will intersect the parabola at two points (the vertex being one of them). A simple equation for such a line is y=x.

__

2. Differentiating the equation, you find that the slope of the curve y = x^2 is 2x, so if we choose a line with a slope of 1, it will go through the point on the curve with x-value equal to 1/2. The y-value at that point is y = (1/2)^2 = 1/4, so the y-intercept of the line must be -1/4.

The line that intersects the curve at one point (1/2, 1/4) is tangent at that point. It has equation y = x -1/4.

__

3. Any line with the same slope as the tangent line, but a more negative y-intercept, will not intersect the parabola at all. Such a line is y = x -1/2.

_____

Truth be told, I found the line y = x -1/2 did not intersect the parabola at all when I thought I was writing the equation for the tangent line. It was an answer to part of your question, just not the part I originally intended.

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

related questions

it has changed from the width and the height.

step-by-step explanation: