Duke starts at the base of a ramp and walks up it at a constant rate. his elevation increases by 3 ft. every second. just as duke starts walking up the ramp, shirley starts at the top of the same 25 ft. high ramp and begins walking down the ramp at a constant rate. her elevation decreases 2 ft. every second.

a. sketch two graphs on the same set of elevation-versus-time axes to represent duke’s and shirley’s motions.
b. what are the coordinates of the point of intersection of the two graphs? at what time do duke and shirley pass each other?
c. write down the equation of the line that represents duke’s motion as he moves up the ramp and the equation of the line that represents shirley’s motion as she moves down the ramp. show that the coordinates of the point you found in the question above satisfy both equations.

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step-by-step explanation:

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm