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3 years ago

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The pressure P (in pounds per square foot), in a pipe varies over time. Ten times an hour, the pressure oscillates from a low of

40 to a high of 280 and then back to a low of 40. The pressure at time t = 0 is 40. Let the function P = f(t) denote the pressure in pipe at time t minutes. Find the formula for the function P=f(t),

1 answer:

Vedmedyk [2.9K]3 years ago

6 0

<span>Pressure oscillating ten times every hour. So period n = 6 min. So the negative cos is represented in the graph and since it datrt at time 0, P = f(t) = Acos(Bt) + D Amplitude A = (Ph - Pl) / 2 = (280 - 40) / 2 = 240 / 2 = 120 Period B = 2xpi / 6 = pi /3 D = (Ph + Pl) / 2 = (280 + 40) / 2 = 320 / 2 = 160 Subtituting the equation we get f(t) = 120cos (pi x t ) / 3 + 160.</span>

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Step-by-step explanation:

The first question is written in standard form like this:

Standard Form: 315 x 64 = 20,160

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The second question is written like this:

Standard Form: 940 x 40 = 37,600

Algebraically/Logical Reasoning: 940 students x 40 letters = 37,600 letters written to students in a different country.

Note: This question has a random P 240, That will be erased so that is why the equation is 940 x 40

The third question is written like this:

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Approximate form: 36 x 7 = 252

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Which relationship is a direct variation?

Setler79 [48]

Option A is the relationship which shows a direct variation.

Step-by-step explanation:

The direct variation is a relationship between two variables in which one is the multiple of the other. It is given by the relation

$\frac{y}{x}=k$

Option A:

For $x=2$ and $y=1$ ,

$\frac{y}{x}=\frac{1}{2}$

For $x=4$ and $y=2$ ,

$\frac{y}{x}=\frac{2}{4}= \frac{1}{2}$

Since, the constant k is equal for all the values of x and y in the table, this relationship is a direct variation.

Option B:

For $x=2$ and $y=4$ ,

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For $x=4$ and $y=16$ ,

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Option C:

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For $x=2$ and $y=5$

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Option D:

For $x=1$ and $y=-1$

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For $x=2$ and $y=2$

$\frac{y}{x} =\frac{2}{2} =1$

Since, the values of constant k is not equal for all the values of x and y in the table, this relationship is not a direct variation.

Thus, Option A is the relationship which shows direct variation.

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