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TEA [102]
3 years ago
7

Describe a relationship modeled by the function f(x) = 4x3 − 72x2 + 320x

Mathematics
1 answer:
solmaris [256]3 years ago
7 0

Answer:

  • A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.

Explanation:

To find a relationship modeled by the given function it is recommendable to factor it.

The function is:

  • f(x)=4x^3-72x^2+320x

The first step to factor it is to extract common factor 4x:

  • f(x)=4x(x^2-18x+80)

The second step is to factor the quadratic trinomial.

That is made by writting it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is:

  • f(x)=(4x)(x-10)(x-8)

Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.

  • x is the desired (unknown) length
  • 4x is 4 times the desired length
  • x - 10 is 10 less than the desired length
  • x - 8 is 8 less than the desired length

Thus, the volume of the prism is the product of the three factors:

  • Volume = (4x)(x-10)(x-8)
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How do you right 0.0001 in expanded form
kirza4 [7]

The expanded form of the number 0.0001 is \bold{\frac{1}{10000}}.

<u>SOLUTION: </u>

Given that, we have to write 0.0001 in expanded form.

Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression.

Now, take the given number 0.0001

As there are no other digits except 0 in front of 1 our work is simplified.

Expanded form will be \frac{1}{10000}

Hence, the expanded form of the number 0.0001 is \frac{1}{10000}.  

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