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ASHA 777 [7]
3 years ago
11

A model of a famous statue is 2 1/2 inches tall. The actual statue is 3 1/3 feet tall. What is the ratio of the height of the mo

del to the height of the actual statue in simplest form?
Mathematics
1 answer:
Gekata [30.6K]3 years ago
4 0

1. A model of a famous statue is 2\dfrac{1}{2} inches tall that is

\dfrac{2\cdot 2+1}{2}=\dfrac{5}{2} in.

2. The actual statue is 3\dfrac{1}{3} feet tall that is

\dfrac{3\cdot 3+1}{3}=\dfrac{10}{3}\ ft=\dfrac{10}{3}\cdot 12=40\ in.

3. The ratio of the height of the model to the height of the actual statue in simplest form is

\dfrac{\dfrac{5}{2}}{40}=\dfrac{5}{2}\cdot \dfrac{1}{40}=\dfrac{1}{16}.

Answer: \dfrac{1}{16}.

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Given f(x)=3x+12, find f(f^-1(0))
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Answer:

<h2>0</h2>

Step-by-step explanation:

METHOD 1.

We know:

f\bigg(f^{-1}(x)\bigg)=x

Therefore

f\bigg(f^{-1}(0)\bigg)=0

METHOD 2.

\text{Find}\ f^{-1}(x)

f(x)=3x+12\to y=3x+12

exchange x to y and vice versa:

x=3y+12

solve for y:

3y+12=x          <em>  subtract 12 from both sides</em>

3y=x-12        <em>divide both sides by 3</em>

y=\dfrac{x-12}{3}\to f^{-1}(x)=\dfrac{x-12}{3}

f\bigg(f^{-1}(x)\bigg)\to    replace x in f(x) with the expression\dfrac{x-12}{3}

f\bigg(f^{-1}(x)\bigg)=3\cdot\dfrac{x-12}{3}+12=x-12+12=x

f\bigg(f^{-1}(0)\bigg)\to put x = 0 to f\bigg(f^{-1}(x)\bigg)=x

f\bigg(f^{-1}(0)\bigg)=0

METHOD 3.

\text{Find}\ f^{-1}(x)

f^{-1}(x)=\dfrac{x-12}{3}

Calculate the value of <em>f</em> ⁻¹(x) for x = 0:

f^{-1}(0)=\dfrac{0-12}{3}=\dfrac{-12}{3}=-4

Calculate the value of <em>f(x)</em> for x = -4:

f(4)=3(-4)+12=-12+12=0

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