The following two sets of parametric functions both represent the same ellipse. explain the difference between the graphs.

x = 3 cos t and y = 8 sin t
x = 3 cos 4t and y = 8 sin 4t

Answer with explanation:

The two parametric equation of the same ellipse is

x = 3 cos t and y = 8 sin t

x = 3 cos 4 t and y = 8 sin 4 t

This is the equation of same ellipse, having different Parametric forms.

→The function involving , 3 cos t and 8 sin t has maximum value, 3 and 8,respectively , and a period of π  , whereas, the function  3 cos 4 t and , 8 sin 4 t , has also same maximum value, 3 and 8,respectively , but period changes , the period after which cycle of trigonometric function  sin 4 t and cos 4 t  repeats is, .

→x = 3 cos t and y = 8 sin t

→x = 3 cos 4 t and y = 8 sin 4 t

Also, these are equation of two lines having different slopes both passing through the origin.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

what