Answer:
a). Graph attached
b). 20 ft
c). 20 ft
d). 1 : 1
e). 28.28 feet
f). 5.66 feet per second
g). (0, 0)
Step-by-step explanation:
A robot crosses (10, 10) at 1 second and (30, 30) at 6 seconds with a constant speed.
a). As shown in the figure attached.
b). Change in x-coordinates = 30 - 10 = 20 feet
c). Change in the y-coordinates = 30 - 10 = 20 feet
d). Ratio of change in y to change in x coordinates = [tex]\frac{20}{20}[/tex]
= 1 : 1
e). Distance traveled by robot between these points = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]
= [tex]\sqrt{(30-10)^{2}+(30-10)^{2}}[/tex]
= [tex]\sqrt{400+400}[/tex]
= [tex]20\sqrt{2}[/tex] feet
= 28.28 ft
f). Speed of the robot = [tex]\frac{\text{Distance covered}}{\text{Time taken to cover the distance}}[/tex]
= [tex]\frac{20\sqrt{2}}{(6-1)}[/tex]
= [tex]\frac{20\sqrt{2}}{5}[/tex]
= [tex]4\sqrt{2}[/tex]
= 5.66 feet per second
g). Robot stared from the origin (0, 0).
