Mathematics, 30.07.2019 17:10 cherryice68

Aferris wheel has a diameter of 191 feet and sits 12 feet above the ground. it rotates in a counterclockwise direction, making one complete revolution every 25 minutes. place your coordinate system so that the origin of the coordinate system is on the ground below the bottom of the wheel. find the equation of the ferris wheel.

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Answer from: haileyhale5

The equation of the Ferris wheel is $y=-95.5\cos (\frac{2\pi}{25}x)+107.5$ .

Step-by-step explanation:

The general form of cosine function is

$y=A\cos (Bx+C)+D$ .... (1)

where, A is amplitude, period is $\frac{2\pi}{B}$ , C is phase shift and D is midline.

It is given that a Ferris wheel has a diameter of 191 feet and sits 12 feet above the ground. So, the minimum value of the function is 12 and the maximum value of the function is 191+12=203.

The midline of the function is

$D=Midline=\frac{Maximum+Minimum}{2}=\frac{203+12}{2}=107.5$

It makes one complete revolution in every 25 minutes.

Period =25

$\frac{2\pi}{B}=25$

On cross multiplication we get

$\frac{2\pi}{25}=B$

Phase shift is not given, So C=0.

Substitute $B=\frac{2\pi}{25}$ , C=0 and D=107.5 in equation (1).

$y=A\cos (\frac{2\pi}{25}x+0)+107.5$

$y=A\cos (\frac{2\pi}{25}x)+107.5$ .... (2)

It is given that the origin of the coordinate system is on the ground below the bottom of the wheel. It means the graph passes through the point (0,12).

Put x=0 and y=12 in equation (2) to find the value of A.

$12=A\cos (\frac{2\pi}{25}(0))+107.5$

12=A(1)+107.5

12-107.5=A

-95.5=A

Substitute A=-95.5 in equation (2).

$y=-95.5\cos (\frac{2\pi}{25}x)+107.5$

Therefore the equation of the Ferris wheel is $y=-95.5\cos (\frac{2\pi}{25}x)+107.5$ .

Answer from: Quest

Ithink if im not mistaking b is -3 but im not a 100% sude
Can someone and explain this problem to me? : d

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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Aferris wheel has a diameter of 191 feet and sits 12 feet above the ground. it rotates in a counterc...

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