Car is moving on a circle on a plane. at time t (seconds), its x-coordinate is given by x(t) = 10 sin(200t + 3) + 30 while its y-coordinate is given by y(t) = 10 cos(200t + 3) + 40. what is the center and radius?

we have centre of circle as (30,40) and radius = 1

Step-by-step explanation:

Given that a car is moving on a circle on a plane.

At time t (seconds),

and

when we square and add both the equations we get

(since sin square + cos square = 1 always)

i.e. we have centre of circle as (30,40) and radius = 1

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.