Dalam suatu 6 km larian amal, beza masa yang digunakan
antara juara dengan pemenang yang ke-15 ialah 30 minit.
jika beza laju antara mereka ialah 2 km cari laju bagi
juara itu.

The speed of the champion (v1) = 6 km/h.

Step-by-step explanation:

v1: velocity of the champion

t1: the amount of time the champion completed the race

v2: velocity of the 15th winner

t2: the amount of time the 15th winner completed the race

S: the distance

We have the equation: S = v1.t1 = v2.t2 (1)

The champion ran 2 km/h faster than the 15th winner, so:

v2 = v1 - 2 (2)

The champion finished the race 30 minutes (or half an hour) before the 15th winner, so:

t2 = t1 + 0.5 (3)

From (1), (2) and (3), we have:

v1×t1 = (v1-2)×(t1+0.5)

<=> v1×t1 = v1×t1 + 0.5×v1 - 2×t1 - 2×0.5

<=> 0.5×v1 - 2×t1 - 2×0.5 = 0

<=> 0.5×v1 = 2×t1 + 1

<=> 0.5×v1 - 1 = 2×t1

<=> t1 = (0.5×v1 - 1)/2            [4]

As S  = v1×t1 = 6 and t1 = (0.5×v1 - 1)/2, we have:

v1×(0.5×v1 - 1)/2 = 6

<=> v1×(0.5×v1 - 1) = 2×6 = 12

<=> 0.5 v1^2 - v1 = 12

<=> v1^2 - 2×v1 = 24

<=> (v1^2 - 2×v1 + 1) = 25

<=> (v1 - 1)^2 = 25

<=> v1 - 1 = 5

=> v1 = 5 + 1 = 6 (km/h)

da freeck kinda math is this just drop out

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: