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JulijaS [17]
3 years ago
13

What is the equation of the line that passes through the points (1, 1) and (7, -5)?

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
6 0

Answer:

y = -1x+2

Step-by-step explanation:

(1,1)(7,-5)

y2-y1/x2-x1 = slope

-5-1/7-1 = -6/6= -1

y-y1 = slope(x-x1) // equation formula

y-1=-1(x-1)

y = -1x + 1 +1

y = -1x+2

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\frac{d}{dx}[f(x)+g(x)+h(x)] = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}} - 81\cdot x^{80}-2\cdot x

Step-by-step explanation:

This derivative consist in the sum of three functions: f(x) = 81\cdot \sin^{-1} x^{9}, g(x) = - x^{81} and h(x) = - x^{2}. According to differentiation rules, the derivative of a sum of functions is the same as the sum of the derivatives of each function. That is:

\frac{d}{dx} [f(x)+g(x) + h(x)] = \frac{d}{dx} [f(x)]+\frac{d}{dx} [g(x)] +\frac{d}{dx} [h(x)]

Now, each derivative is found by applying the derivative rules when appropriate:

f(x) = 81\cdot \sin^{-1} x^{9} Given

f'(x) = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}} (Derivative of a arcsine function/Chain rule)

g(x) = - x^{81} Given

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h(x) = - x^{2} Given

h'(x) = -2\cdot x (Derivative of a power function)

\frac{d}{dx}[f(x)+g(x)+h(x)] = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}} - 81\cdot x^{80}-2\cdot x (Derivative for a sum of functions/Result)

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