Answer:
a. D'(p) = -10p - 6
b. There is a decrease of 96 units of demand for each dollar increase
Step-by-step explanation:
The demand function is:
(a) The derivate of the demand function with respect to price gives us the rate of change of demand:
(b) When p = $9, the rate of change of demand is:
This means that, when p = $9, there is a decrease of 96 units of demand for each dollar increase.
It is convenient to start with the 2-point form of the equation for a line.
... y - y1 = (y2 - y1)/(x2 - x1)×(x - x1)
Either point can be (x1, y1), and the other can be (x2, y2). If we take them in order, we get
... y - 4 = (16 - 4)/(5 - 3)×(x - 3) . . . . . fill in the two points
... y = 12/2(x -3) +4 . . . . . . . . . . . . . . add 4, simpliffy a bit
... y = 6x -18 +4 . . . . . . . . . . . . . . . . . eliminate parentheses
... y = 6x -14 . . . . . . . . . . . . . . . . . . . . put in slope-intercept form
Answer:
The coordinates of the vertices of the reflected figure are :
R' is (5 , -2) , S' is (3 , 5) , T' is (-7 , 6) ⇒ the right answer is (d)
Step-by-step explanation:
* When you reflect a point across the line y = x, the x-coordinate
and y-coordinate change their places.
- If the point is (x , y) then its image is (y , x)
* If you reflect over the line y = -x, the x-coordinate and y-coordinate
change their places and their signs
- If the point is (x , y) then its image is (-y , -x)
* Lets study the matrix of the reflection about the line y = x
- The matrix of the reflection about the line y = x is
- Because the x-coordinate and y-coordinate change places.
* Now lets solve the problem
- We will multiply the matrix of the reflection about y = x
by each point to find the image of each point
- The dimension of the matrix of the reflection about y = x
is 2×2 and the dimension of the matrix of each point is 2×1,
then the dimension of the matrix of each image is 2×1
∵ The point R is (-2 , 5)
∴
∴ R' is (5 , -2)
∵ The point S is (5 , 3)
∴
∴ S' is (3 , 5)
∵ The point T is (6 , -7)
∴
∴ T' is (-7 , 6)
* Lets look to the figures to find the right answer
∵ The R' is (5 , -2) , S' is (3 , 5) , T' is (-7 , 6)
∴ The right answer is (d)