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Digiron [165]
3 years ago
5

Javier works in a photo lab and needs to make a reduced copy of a photograph that is 8 inches long. The customer wants the copy

to have a length of 4.5 inches. Each time he presses the reduce button on the copier, the copy is reduced by 12%. Javier and his boss had an argument, because Javier claimed that pressing the button 5 times would be enough to fulfill the customer's request. His boss said that pressing the button 5 times would result in a length less than the desired 4.5 inches. Which of the following conclusions can be made?
Mathematics
2 answers:
Scrat [10]3 years ago
5 0

Answer:

Javier should not press the button five time.

Step-by-step explanation:

The given scenario says that Javier claimed that pressing the button 5 times would be enough to fulfill the customer's request. So, lets check that.

We will start at 8 inches.

Press once, 8-0.12*8=7.04 inches.

Pressing again, we get 7.04-.12*7.04=6.1952 inches.

Again pressing we get 6.1952-.12*6.1952 = 5.451776 inches.

Again we get 5.451776-.12*5.451776 =4.79756288 inches.

Again we get 4.79756288-.12*4.79756288= 4.221855334 inches.

We can clearly see here that pressing 4 or 5 times does not get 4.5 inches exactly as claimed by Javier.

Therefore, Javier claim is not right and his boss is right.

REY [17]3 years ago
5 0

Answer:

Javier should not press the button five time.

Step-by-step explanation:

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Find the arc-length parametrization of the curve that is the intersection of the elliptic cylinder x 2 + y 2/2 = 1 and the plane
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f(\theta) = (cos(\frac{\theta}{\sqrt2}), \sqrt2 sin(\frac{\theta}{\sqrt2}), cos(\frac{\theta}{\sqrt2})-2)

0 ≤ Ф ≤ 4π.

Step-by-step explanation:

since x²+y²/2 = 1, then x²+s² = 1, with s = (y/√2)². Hence, (x,s) = (cos(Ф),sin(Ф)) and (x,y,z) = (cos(Ф),√2 sin(Ф), cos(Ф)-2). This expression evaluated in zero gives as result (1,0,-1). The derivate of this function is (-sin(Ф),√2 cos(Ф), -sen(Ф))

the norm of the derivate is √(sin²(Ф) + 2cos²(Ф)+sin²(Ф)) = √2. In order to make the norm equal to 1, i will divide Ф by √2, so that a √2 is dividing each term after derivating.

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f(\theta) = (cos(\frac{\theta}{\sqrt2}), \sqrt2 sin(\frac{\theta}{\sqrt2}), cos(\frac{\theta}{\sqrt2})-2)

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Whose square norm is 1/2cos²(Ф/2)+sen²(Ф/2)+1/2cos²(Ф/2) = 1. This is te parametrization that we wanted.

The values from Ф range between 0 an 4π, because the argument of the sin and cos is Ф/2, not Ф, Ф/2 should range between 0 and 2π.

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