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Lera25 [3.4K]
3 years ago
11

Don works in home construction. He determined that the function t(A)=144A/9.252 gives the total number of 9 in. tiles needed to

cover an area of A square feet, when spacing the tiles a quarter inch apart. Find t(400) and explain what it means.
__________________________________________________________________

Your response needs to include the following:

Response needs to be at least 4 statements – math explanations or sentences.
Response states the question in your terms.
Response answers all parts of the question
Explanation is thorough for solving the problem or answering the question.
Sentence starters:
For instance, .....
For example, .....
I solve this problem by …
In order to solve this problem, I need to …
The problem could also be solved by…
The specific math words that I would use in this situation are …
Mathematics
1 answer:
Drupady [299]3 years ago
7 0

Answer:

Step-by-step explanation:

It’s easy

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Answer:

5a.  approximately 6 grams remain after 2 seconds

5b.  The graph shown cannot be a solution. The solution has negative slope everywhere.

5c.  y = 50/(t+5)

5d.  The amount is changing at a decreasing rate. (As y gets smaller, so does the magnitude of dy/dt.)

Step-by-step explanation:

5a. The tangent line has the equation ...

  y = f'(0)t +f(0)

Here, that is

  y = -0.02·10²·t +10 = 10 -2t

Then at t=2, the value is ...

  y = 10 -2·2 = 6 . . . . grams remaining

__

5b. y² is always positive (or zero), so -0.02y² will be negative. This is dy/dt, the slope of the curve with respect to time, so any curve with positive slope somewhere cannot be a solution.

__

5c. The equation is separable so can be solved by integrating ...

  ∫y^-2·dy = -0.02∫dt

  -y^-1 = -0.02t +c . . . . for some arbitrary constant c

Multiplying by -50 gives ...

  50/y = t + c . . . . for some constant c

We can find the value of c by invoking the initial condition. At t=0, y=10, so we have ...

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Then, solving for y, we get ...

  y = 50/(t+5)

__

5d. As noted above (and as described by the differential equation), the magnitude of the rate of change is proportional to the square of y. As y decreases, its rate of change will also decrease (faster). You can see that the curve for y flattens out as t increases. The amount of the substance is changing at a decreasing rate.

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What is the measure of angle S?
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132 + 56 + 79 = 267

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answer is 93 degrees

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