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ser-zykov [4K]
3 years ago
11

What is the answer to this problem 1/2=q 2/3?

Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
6 0
3/2 = 2q
q = 3/2 ÷ 2
q = 3/2 × 1/2
q = 3/4
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Given the following functions below,

\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}\text{ and} \\ g(x)=\frac{4x^2-16x+16}{4x+48} \end{gathered}

Factorising the denominators of both functions,

Factorising the denominator of f(x),

\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}=\frac{x+12}{x^2+6x-2x-12}=\frac{x+12}{x(x+6)-2(x+6)}=\frac{x+12}{(x-2)(x+6)} \\ f(x)=\frac{x+12}{(x-2)(x+6)} \end{gathered}

Factorising the denominator of g(x),

\begin{gathered} g(x)=\frac{4x^2-16x+16}{4x+48}=\frac{4(x^2-4x+4)}{4(x+12)} \\ \text{Cancel out 4 from both numerator and denominator} \\ g(x)=\frac{x^2-4x+4}{x+12}=\frac{x^2-2x-2x+4}{x+12}=\frac{x(x-2)-2(x-2)}{x+12}=\frac{(x-2)^2}{x+12} \\ g(x)=\frac{(x-2)^2}{x+12} \end{gathered}

Multiplying both functions,

undefined

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Step-by-step explanation:

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Find the linear approximation of the function g(x) = 3 1 + x at a = 0. g(x) ≈ Correct: Your answer is correct. Use it to approxi
EleoNora [17]

Answer:

3.296x+3

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Step-by-step explanation:

g(x) = 3^{1+x}

Let the linear approximation be L(x) at a = 0. This is given by

L(x) = g(a) + g'(a)(x-a)

g'(x) is the derivative of g(x). To find this, we use the form

If f(x) = a^x, then f'(x) =a^x\ln a

By doing this and applying chain rule for the power (which is a function of x), we have

g'(x) = 3^{1+x}\ln 3

Then

g'(0) = 3^{1+0}\ln 3 = 3.296

Also g(0) = 3^{1+0} = 3

Hence L(x) = 3+(x-0)\times3.296 = 3.296x + 3

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Using this in L(x),

3^{0.95} = 3.296(-0.05) + 3 = 2.835

For 3^{1.1}, 1+x = 1.1 and x=0.1

Using this in L(x),

3^{1.1} = 3.296(0.1) + 3 = 3.330

7 0
3 years ago
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