Answer:
Step-by-step explanation:the first one
Formula for distance between two points:
d = √( (x₂ -x₁)² + (y₂ - y₁)²)
x₁ = -2, y₁ = 4, x₂ = 0, y₂ = -6
d = √( (x₂ -x₁)² + (y₂ - y₁)²)
d = √( (0 - -2)² + (-6 - 4)²)
d = √( (0 + 2)² + (-10)²)
d = √( (2)² + (-10)²)
d = √(4 + 100)
d = √104 Use a calculator
d ≈ 10.1980
d ≈ 10.20 units to the nearest hundredth.
Answer:
The volume of the Rubik's Cube is 27 in^3
Step-by-step explanation:
Each face of a Rubik's Cube has 3x3 cubes, then each face has 9 small cubes.
We can think of a Rubik's Cube as 3 pieces, such that each piece has 9 small cubes on it, and the 3 pieces are: Front side, middle part, back part.
Then the total number of small cubes on a Rubik's cube is 9*3 = 27 small cubes.
Now we know that each one of these small cubes has a volume of 1 in^3
Then the volume of 27 of these cubes is 27 times the volume of a single smaller cube, then the volume of the Rubik's Cube is:
V = 27*( 1 in^3) = 27 in^3
To get the function y = <span>-2+5sin(pi/12(x-2)), the maximum value can be determined by differentiating the function and equating it to zero. The value of x will give the maximum value of the function.
dy/dx = 5 cos (pi/12 (x-2)) (pi/12)
dy/dx = 5 pi/12 cos(pi/12 (x-2))
Equate to zero</span>:
<span>5 pi/12 cos(pi/12 (x-2)) =0
pi/12 (x-2) = 3pi/2
x = 8
Substituting,
y= -2 + 5sin( pi/12 (8-2)
y = -1.86
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