A yoga instructor earns $80 for teaching 4 classes. The instructor receives a 15% raise. Enter
1 answer:
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Answer:
Step-by-step explanation:
Given that a rock is thrown vertically upward from the surface of an airless planet. It reaches a height of
where t is expressed in seconds
The rock goes upto a height where the velocity becomes 0 and then it starts falling down by gravity
Velocity at time t = s'(t) =
This becomes 0 when t =15 seconds
Hence at 15th second the rock starts falling and upto
s(15) = metres high it goes
The time taken to reach highest point is = 15 seconds.
Answer:
For least material to be used lengths of square base and sides = 10 units.
Step-by-step explanation:
Let the lengths of the square base and the sides = x feet, x feet and y feet
Area of the square base = x² feet
Volume of the rectangular prism = Area of the square base × Height
= x²y cubic feet
1000 = x²y
y = -------(1)
Material used in the prism = Surface area of the rectangular prism
= 2(lb + bh + hl)
Here, h = height of the prism
l = length of the base
w = Width of the base
Material to be used (S) = 2(xy + x² + xy) - Area of lid
S = 2(x² + 2xy) - x²
S = x² + 2xy
Now by substituting the value of y from equation (1),
S = x² +
= x² +
For least amount of material used,
We will find the derivative of the given function and equate it to zero.
S' = 2x -
2x - = 0
2x³ = 2000
x³ = 1000
x = 10 feet
From equation (1),
y =
y = 10 feet
Therefore, for least amount of the material used lengths of square base and sides will be 10 feet.