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Eduardwww [97]
3 years ago
6

An open box of maximum volume is to be made from a square piece of material 24 cm on a side by cutting equal squares from the co

rners and turning up the sides (see figure).
a. Write volume V as a function of x, the length of the corner squares.







b. What is the domain of the function?

​
Mathematics
1 answer:
mr Goodwill [35]3 years ago
5 0

Answer:

V = x(24 - x)^2 cm^3.

Domain = (0, 24).

Step-by-step explanation:

a. Let the lengths of the sides of the squares be x cm.

Then the lengths of the sides of the base of the box will be  (24 - 2x) cm.

The height of the box will be x cm.

So the required volume

= height * area of base

So V = x(24 - x)^2

b. The domain of this function is (0, 24).

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The values of x for which the rational expression is undefined are -6 and -8.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a rational function:

\rm f(x) = \dfrac{3x+20}{x^2+14x+48}

As we know in the rational function denominator cannot be zero:

The values of x for which the rational expression is undefined.

x² + 14x + 48 = 0

\rm x_{1,\:2}=\dfrac{-14\pm \sqrt{14^2-4\cdot \:1\cdot \:48}}{2\cdot \:1}

\rm x_1=\dfrac{-14+2}{2\cdot \:1},\:x_2=\dfrac{-14-2}{2\cdot \:1}

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Thus, the values of x for which the rational expression is undefined are -6 and -8.

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brainly.com/question/5245372

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6 0
1 year ago
Mike deposited $6500 into two saving accounts bearing simple interest. One of the accounts has an interest rate of 3% while the
ololo11 [35]
0.03x+0.06 (6500-x)=225
Solve for x
0.03x+390-0.06x=225
0.03x-0.06x=225-390
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The equation F equals 9/5C + 32 relates temperature measured in degrees Celsius, C, to degrees F, Fahrenheit. Determine whether
muminat

Answer: There is none.

Step-by-step explanation:

There is no proportional relationship between Celsius and Fahrenheit because for a proportional relationship to exist, the two variables need to have an equivalent ratio between them which would ensure that their values vary constantly when they are either divided or multiplied.

In other words, only the arithmetic operations of multiplication and division should be present. In the above there is an additive operation which renders the two variables being Fahrenheit and Celsius, non-proportional.

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Answer:

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Step-by-step explanation:

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