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Mathematics

1 answer:

hodyreva [135]3 years ago

6 0

Answer:

Step-by-step explanation:

x = 8

y = 40

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Consider the cartesian equation of a circle, y=-2+- sqrt 36-(x-1)^2 , verses the parametric equations of the same circle: x=1+6

hjlf

What are the advantages of the parametric equations

Answer:

Step-by-step explanation:

Parametric equations shows the relation between a group of quantities by expressing the coordinates of points of a curve and function as one or more independent variables.

From the question given; the advantages of parametric equations given

x = 1 + 6 cos t

y= -2 + 6 sin t

are :

1) For a given value of the independent variable the parametric equation is used exactly one point on the graph

2) the parametric equations have a finite domain

3) the parametric equation is easier to enter into a calculator for graphic

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3 years ago

Find the derivative of y=sin^(2)(x)cos^(2)(x)

wariber [46]

$sin^{2}x \ cos^{2} x= \frac{1}{2} (1-cos2x) \times \frac{1}{2} (1+cos2x) \\ = \frac{1}{4} (1- cos^{2} 2x) \\ = \frac{1}{4} ( sin^{2} 2x +cos^{2} 2x- cos^{2} 2x) \\ = \frac{1}{4} ( sin^{2} 2x) \\ = \frac{1}{4} ( \frac{1}{2} (1-cos2(2x))) \\ = \frac{1}{8} (1-cos4x) \\ \frac{d}{dx} (sin^{2}x \ cos^{2} x)= \frac{1}{8} \frac{d}{dx} (1-cos4x) \\ = \frac{1}{8} [-4(-sin4x) \\ \frac{1}{2} sin4x$