Given:
The function is
![f(x)=\dfrac{8\sqrt[3]{x}-8}{9}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B8%5Csqrt%5B3%5D%7Bx%7D-8%7D%7B9%7D)
To find:
The inverse function 
.
Solution:
We have,
Step 1: Putting f(x)=y, we get
![y=\dfrac{8\sqrt[3]{x}-8}{9}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B8%5Csqrt%5B3%5D%7Bx%7D-8%7D%7B9%7D)
Step 2: Interchange x and y.
![x=\dfrac{8\sqrt[3]{y}-8}{9}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B8%5Csqrt%5B3%5D%7By%7D-8%7D%7B9%7D)
Step 3: Isolate variable y.
![9x=8\sqrt[3]{y}-8](https://tex.z-dn.net/?f=9x%3D8%5Csqrt%5B3%5D%7By%7D-8)
![9x+8=8\sqrt[3]{y}](https://tex.z-dn.net/?f=9x%2B8%3D8%5Csqrt%5B3%5D%7By%7D)
![\dfrac{9x+8}{8}=\sqrt[3]{y}](https://tex.z-dn.net/?f=%5Cdfrac%7B9x%2B8%7D%7B8%7D%3D%5Csqrt%5B3%5D%7By%7D)
Taking cube on both sides, we get
Step 4: Putting 
, we get
Therefore, the correct option is C.
Answer:
$3200
Step-by-step explanation:
The total area of land is 30 acre. Let x represent the area in acre that corn is planted and y represent the area in acre that wheat is planted. Therefore:
x + y = 30 (1)
Also, the farmer can spend at most $750 on seeds. Corn cost $15 per acre, maize cost $30 per acre. Hence:
15x + 30y ≤ 750 (2)
Also, x and y > 0
The profit is given by the function:
Profit = 100x + 110y
Graphing equation 1 and equation 2 and solving, we get the points:
(10, 20)
Hence the maximum profit is at:
Max profit = 100(10) + 110(20) = $3200
Answer:
Step-by-step explanation:
3x + x + 60 = 180.
first, we add the x's together.
4x + 60 = 180
then we see if they all have a common multiple. in this case, they do. they are all divisible by 4, so we can use that.
x + 15 = 45
then, just subtract 15 from both sides, that way we get the variable by itself.
x = 30
also, it is a right triangle. the top angle (3x) multiplied by 3 is 90. any triangle that has a 90 degree angle is automatically a right triangle.
Answer:
The length is 2.5 units
Step-by-step explanation:
Before we find the value of the length of the side, we need the measure of the coordinates after dilation
B’ = 1/2 B = 1/2(3,2) = (1.5, 1)
C’ = 1/2 C = 1/2( 0,-2) = (0,-1)
The measure of the length is the distance between the two points
Mathematically, that would be;
D = √(x2-x1)^2 + (y2-y1)^2
D = √(0-1.5)^2 + (-1-1)^2
D = √(2.25 + 4)
D = √6.25
D = 2.5 units
Answer:
15 pages
Step-by-step explanation:
45/15=3
3x5=15
