Answer:
yes
Step-by-step explanation:
Let us find the inverse of g(x)
To find the inverse, exchange x and y and then solve for x
y = x^3 -1
Exchange x and y
x = y^3 -1
Solve for y
Add 1 to each side
x+1 = y^3-1+1
x+1 = y^3
Take the cube root of each side
(x+1) ^ (1/3) = y
The two functions are inverses of each other
The total time taken by Clem Shirestock to reach the gate is given by the equation 7 = 4√(x²+1)+ 8 - 2 x
Let the point P is at a distance of x miles from the toll gate.
Hence when Clem reaches the point P he rows in the form of right angled triangle. and we know that the width of the river is 1 mile.
So by using Pythagoras Theorem we can infer that the distance covered by Clem is the hypotenuse which is equal to √(x²+1).
Time taken to complete this route is 4√(x²+1) .
Now he has only to walk 4-x distance along the river.
His speed is 2 mph
Time taken = 2(4-x) = 8-2x
Hence we can conclude that the total time is 7 hours. so the equation to represent this is 7 = 4√(x²+1)+ 8 - 2 x .
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Answer: 402.124 inches²
Step-by-step explanation:
What is a cylinder?
A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.
The surface area of a cylinder is the sum of the area of the base and the lateral area of the curved cylinder.
Given that the diameter of the cylinder is 8 inches, while the height of the cylinder is 12 inches. Since the radius is half the length of the diameter. Therefore, the radius of the given cylinder is 4 inches.
Now, the surface area of the cylinder is,
Surface area of the cylinder = Area of the bases + Area of the curved surface
= 2(πr²) + 2πrh
= 2(π × 4²) + (2 × π × 4 × 12)
= 2(50.265) + 301.5928
= 100.5309 + 301.5928
= 402.124 inches²
Hence, the surface area of the cylinder is 402.124 inches².
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Answer:2.24
Step-by-step explanation: