Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 3θ

The graph is symmetric about x- axis.

Step-by-step explanation:

We are given that an equation

We have to find the graph is symmetric  about x- axis , y-axis or origin.

We taking r along y-axis and [tex\theta [/tex] along x- axis

When the graph is symmetric about x= axis then (x,y)=(-x,y)

is replaced by and r remain same then we get

We know that cos (-x)=cos x

Therefore,

Hence, the graph is symmetric about x- axis.

When the graph is symmetric about y- axis then (x,y)=(x,-y)

Now, r is replaced by -r then we get

Therefore, the graph is not symmetric about y-axis.

When the graph is symmetric about y- axis then (x,y)=(x,-y)

Now, r is replaced by -r then we get

Therefore, the graph is not symmetric about y-axis.

When the graph is symmetric about origin then (-x,-y)=(x,y)

Replaced r by -r and by-

Then we get

Because cos(-x)=cos x

Hence, the graph is not symmetric about origin.

is it 35

step-by-step explanation:

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 =.

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

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

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

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

slope of the solid line would be =.

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