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3 years ago

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Question 20 please thank hou

1 answer:

Mekhanik [1.2K]3 years ago

8 0

$\dfrac{9mn-6m}{25-m^2}\div\dfrac{12mn}{5+m}=\dfrac{3m(3n-2)}{5^2-m^2}\cdot\dfrac{5+m}{3m\cdot4n}\\\\=\dfrac{3n-2}{(5-m)(5+m)}\cdot\dfrac{5+m}{4n}=\dfrac{3n-2}{4n(5-m)}\to\boxed{C.}$

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Answer:

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Step-by-step explanation:

Slope refers to the steepness of the line.

Slope is equal to change in value of y divided by change in value of x.

The slope of the secant line is given by $\frac{f(x)-f(a)}{x-a}$ .

Given points are $P\left ( 5,-4 \right )\,,\,Q\left ( x,\frac{4}{4-x} \right )$

So, slope of the secant line is $\frac{\frac{4}{4-x}+4}{x-5}=\frac{4+4(4-x)}{(x-5)(4-x)}=\frac{20-4x}{(x-5)(4-x)}=\frac{-4(x-5)}{(x-5)(4-x)}=\frac{-4}{4-x}=\frac{4}{x-4}$

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$\frac{4}{4.9-4}=\frac{4}{0.9}=4.444444$

(ii) At x = 4.99,

$\frac{4}{4.99-4}=\frac{4}{0.99}=4.040404$

(iii) At x = 4.999,

$\frac{4}{4.999-4}=\frac{4}{0.999}=4.004004$

(iv) At x = 4.9999,

$\frac{4}{4.9999-4}=\frac{4}{0.9999}=4.0004$

(v) At x =5.1,

$\frac{4}{5.1-4}=\frac{4}{1.1}=3.636364$

(vi)

At x = 5.01,

$\frac{4}{5.01-4}=\frac{4}{1.01}=3.960396$

(vii) At x = 5.001,

$\frac{4}{5.001-4}=\frac{4}{1.001}=3.996004$

(viii) At x = 5.0001,

$\frac{4}{5.0001-4}=\frac{4}{1.0001}=3.9996$

(b)

Slope of the tangent line is 4.

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