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icang [17]
3 years ago
13

The smiths counted 11 riders and 26 wheels passing by. There were no unicycles, only bicycles and tricycles with only one rider.

How many more bicycles than tricycles did they see?
Mathematics
1 answer:
zimovet [89]3 years ago
6 0
I only one person rode a tricycle - that would leave 23 wheels and you cannot make a complete number of bicycles
If 2 people rode tricycles that would leave 20 wheels which would seat 10 bicyclists.
But that totals up to 12 people

3 people riding tricyles leaves 15 wheels which will not complete a number of bicycles

4 people riding tricycles (4 x 3) leaves 14 wheels for 7 bicyclist and is the answer

4 trike riders (12 wheels) + 7 bike riders (14 wheels) = 11 people and 26 wheels

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Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, \frac{2}{3}

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

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Width of the box = (8 - 2x) = 8 - 1.34

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Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

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