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Brums [2.3K]
3 years ago
6

Mathematics puzzle from my calculus text book.

Mathematics
1 answer:
xenn [34]3 years ago
4 0

Answer:

{ \tt{g(x) = a {x}^{2} + bx + c = 0 }} \\ { \tt{f(x) =  {a'x}^{2} + b 'x + c' = 0}} \\ { \boxed{ \bf{f(g(x)) = g(f(x))}}} : \\ { \tt{ =(  \frac{a}{a'})x {}^{2}   + ( \frac{b}{b'}) x} +  \frac{c}{c'} } = 0

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Find the slope from the two points (-4,-1) (-3,-3)
kicyunya [14]

The slope is -2_________

8 0
3 years ago
What is the equation of the line that passes through (-1, 5) and (3, -7)?
enyata [817]

Answer:

3x + y = 2

Step-by-step explanation:

y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)

y - 5 = \dfrac{-7 - 5}{3 - (-1)}(x - (-1))

y - 5 = \dfrac{-12}{4}(x + 1)

y - 5 = -3(x + 1)

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3 0
3 years ago
Prove the formula for (d/dx)(cos−1(x)) by the same method as for (d/dx)(sin−1(x)). Let y = cos−1(x). Then cos(y) = and 0 ≤ y ≤ π
gtnhenbr [62]

Answer:

\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }

Step-by-step explanation:

Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;

let;

y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\

\frac{dy}{dx} = \frac{-1}{sin y}  \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}

Therefore;

\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }

Since x = cos y from the above substitute;

\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }

Hence, \frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} } gives the required proof

5 0
4 years ago
I don't know how to do it
Alex
Is it number 6 or 8 cause I'm little bit confused
5 0
4 years ago
I need the answer plzzz I really need it plzz help me
aleksklad [387]
I honestly don’t know good day
5 0
3 years ago
Read 2 more answers
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