Answer:
You can drive at 53 miles per day.
Step-by-step explanation: Hope this helped )(-:
The reflection is
<h3>What is reflection over axis?</h3>
A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.
For reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
and, for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y value the same.
So, by considering the above value rules the reflection of the given points as follows over respective axis.
E(7, 1) ⇒ (7, -1)
Here, the reflection is over x-axis because the y value is changing
F(-3, 5) ⇒ (-3, -5)
Here, the reflection is over x-axis because the y value is changing
G(6, -2) ⇒ (-6, -2)
Here, the reflection is over y-axis because the x value is changing.
Learn more about this concept here:
brainly.com/question/15175017
#SPJ1
Answer:
Step-by-step explanation:
The motion of the dolphin is quadratic
i.e y=-16t²+20t
To get the maximum height the dolphin will reach
We need to find the point of inflexion. i.e dy/dt=0
dy/dt=-32t+20
Then set dy/dt=0
0=-32t+20
Then, -32t=-20
t=0.625
Let find d²y/dt²
d²y/dt²=-32. Since this is negative then the point t=0.625 is the maximum point the dolphin can reach
Then substitute t=0.625 into y
y=-16t²+20t
y=-16(0.625)²+20(0.625)
y=6.25ft
Then the maximum height the dolphin can reach is 6.25ft
Using discriminant
Formular method
y=-16t²+20t
So the dog height y<7
y=-16t²+20t <7
-16t²+20t-7<0
a=-16, b= 20. c=-7
t=(-b±√b²-4ac)/2a
Using the a, b and c direct for the discriminant
D=b²-4ac
D=20²-4×-16×-7
D=-48
Which is a complex number
Then the dolphin can reach the height
Then we need to model the D to be greater than 0
Therefore,
D>0
b²-4ac>0
We cannot do anything to a and b it is already given
a=-16, b=20
(20)²-4(-16c)>0
400+64c>0
64c>-400
Then
c>-6.25
Divide both side by - and the inequality sign will change
Therefore -c<6.25
So the dog height y<6.25
y=-16t²+20t <6.25
Therefore the maximum height is 6.25.
If it is greater than that then, we are going to have a complex root movement which is not possible for the dolphin .
Answer:
4.5
Step-by-step explanation:
Answer:
- vertical scaling by a factor of 1/3 (compression)
- reflection over the y-axis
- horizontal scaling by a factor of 3 (expansion)
- translation left 1 unit
- translation up 3 units
Step-by-step explanation:
These are the transformations of interest:
g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k
g(x) = f(x) +k . . . . vertical translation by k units (upward)
g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis
g(x) = f(x-k) . . . . . horizontal translation to the right by k units
__
Here, we have ...
g(x) = 1/3f(-1/3(x+1)) +3
The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:
- vertical scaling by a factor of 1/3 (compression) . . . 1/3f(x)
- reflection over the y-axis . . . 1/3f(-x)
- horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
- translation left 1 unit . . . 1/3f(-1/3(x+1))
- translation up 3 units . . . 1/3f(-1/3(x+1)) +3
_____
<em>Additional comment</em>
The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.
The horizontal transformations could also be described as ...
- translation right 1/3 unit . . . f(x -1/3)
- reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)
The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.
