Michael’s haircut was 14.00 he gave a tip of 3.50 what percentage did Michael leave as a tip
1 answer:
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Answer:
Trapezoid 1 (left side):
Base 1 = 2
Base 2 = 5
Trapezoid 2 (right side):
Base 1 = 6
Base 2 = 8
Step-by-step explanation:
<u>1st trapezoid:</u>
b_1 = x
b_2 = x + 3
h = 4
Hence, area (from formula) would be:
<u>2nd trapezoid:</u>
b_1 = 3x
b_2 = 4x
h = 2
Putting into formula, we get:
Let's equate both equations for area and find x first:
We can plug in 2 into x and find length of each base of each trapezoid.
Trapezoid 1 (left side):
Base 1 = x = 2
Base 2 = x + 3 = 2 + 3 = 5
Trapezoid 2 (right side):
Base 1 = 3x = 3(2) = 6
Base 2 = 4x = 4(2) = 8
The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
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Complete Question
(Image Attached)
Cubic polynomial
Binomial
By vertical method of multiplication we get,
