Priya and han are biking in the same direction on the same path.

han is riding at a constant speed of 16 miles per hour. write an expression that shows how many miles han has gone after hours.

priya started riding a half hour before han. if han has been riding for hours, how long has priya been riding?

priya is riding at a constant speed of 12 miles per hour. write an expression that shows how many miles priya has gone after han has been riding for hours.

use your expressions to find when han and priya meet.

I copy the complete questions again to make them clearer:

Priya and Han are biking in the same direction on the same path.

a. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after         hours.

b. Priya started riding a half hour before Han. If Han has been riding for         hours, how long has Priya been riding?

c. Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for         hours.

d. Use your expressions to find when Han and Priya meet.

Explanation:

a. Since Han is riding at a constant speed of 16 miles per hour, the number of miles that he has gone is proportional to the number of hours, t, that he has been riding, the constant of variation is 16, and the expression for the number of miles he has gone is:

Where, H is the number of miles Han has gone, and t is the number of hours.

b. Since Priya started riding a half hour before Han, you have to add 1/2 or 0.5 to the time of Han, which is t, to express how long Priya has been riding:

c. Since, Priya is riding at a constant speed of 12 miles per hour, the number of miles that she has gone is proportional to the number of hours, t + 0.5, that she has been riding, the constant of variation is 12, and the expression for the number of miles she has gone is:

Where P is the number of miles Priya has gone, and t is the number of hours since Han is riding.

d. To find when Han and Priya meet, you just need to solve the sytem of equations, making H = P, which means that the number of miles that both Han and Priya rides is equal:

Which means that they meet when it has passed 1.5  hours since Han started riding.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

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