Acar wheel has a 13-inch radius. through what angle does the wheel turn when the car rolls forward 3 ft?

158.7°

Step-by-step explanation:

Data:

r = 13 in

s = 3 ft

Calculations:

(a) Convert feet to inches

s = 3 ft × (12 in/1 ft) = 36 in

(b) Calculate the angle

Let θ = the angle subtended by the arc.

s = rθ

θ = s/r  = 36/13  ≈ 2.7692 rad

Convert radians to degrees

2.7692 rad × (360°/2π rad) = 158.7°

The wheel travels through an arc of 158.7°.

Step-by-step explanation:

Givens:

refers to the length of the circumference, which is the same distance rolled.

So, to find the angle, we have to use this definition:

; which is the relation between arc, angle and length.

Before, replacing all values, we have to transform 13 inches in feet. We know that 1 feet is 12 inches. So,

Now, we find the angle.

Therefore, the angle is 2.78 radians.

To have it in degrees, we have to transform.

y=mx+

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.