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Levart [38]
2 years ago
13

the amount of food a dog should eat depends on the weight of the dog. 1. identify the independent and dependent variables in thi

s situation. 2. write the dependency relationship using the word "function." 3. write the dependency relationship using function notation​
Mathematics
1 answer:
fomenos2 years ago
5 0

Here, we are required to identify the dependent and independent variables, the dependency relationship in the situation.

  1. The independent and dependent variables are the weight of the dog and the amount of food it should respectively.
  2. The dependency relationship is thus; The amount of food a dog should eat is a function of the weight of the dog
  3. The dependency relationship using the function notation is; f(x) = {function of x}.

  • The independent variable in this situation is the weight of the dog while the amount of food the dog should eat is the dependent variable. The above is evident from the statement; <em>T</em><em>he amount of food a dog should eat depends on the weight of the </em><em>dog</em><em>.</em>

  • <em>According</em><em> </em><em>to </em><em>the </em><em>premise</em><em> </em><em>given </em><em>in </em><em>the </em>question, it is evident that the dependency relationship is;. The amount of food a dog should eat is a function of the weight of the dog

  • The dependency relationship can be written mathematically using the function notation as;. f(x) = {function of x}.

Read more:

brainly.com/question/11239214

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Answer:

13) (5x)^{-\frac{5}{4} ⇒ \frac{1}{\sqrt[4]{(5x)^5}}

15) (10n)^{\frac{3}{2} ⇒ \sqrt{(10n)^3}

Step-by-step explanation:

Given expression:

13) (5x)^{-\frac{5}{4}

15) (10n)^{\frac{3}{2}

Write the expressions in radical form.

Solution:

For an expression with exponents as fraction like

(x)^{\frac{m}{n}

the numerator m represents the power it is raised to and the denominator n represents the nth root of the expression.

For an expression with exponents as negative  fraction like

(x)^{-\frac{m}{n}

We take the reciprocal of the term by rule for negative exponents.

So it is written as:

\frac{1}{(x)^{\frac{m}{n}}}

using the above properties we can write the given expressions in radical form.

13) (5x)^{-\frac{5}{4}

⇒ \frac{1}{(5x)^{\frac{5}{4}}}   [Using rule of negative exponents]

⇒ \frac{1}{\sqrt[4]{(5x)^5}}    [writing in radical form]

15) (10n)^{\frac{3}{2}

⇒ \sqrt{(10n)^3}     [Since 2nd root is given as \sqrt{} in radical form]

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