Suppose a five minute overseas call costs $5.91 and a 10 minute call costs $10.86. What is the equation and how long can you talk on the phone if you have $12 to spend?

Step-by-step explanation:

let x represent the number of minutes of call made.

Let y represent the cost for x minutes of call.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (10.86 - 5.91)/(10 - 5)

m = 4.95/5 = 0.99

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 10, y = 10.86 and m = 0.99 into y = mx + c. It becomes

10.86 = 0.99 × 10 + c = 9.9 + c

c = 10.86 - 9.9

c = 0.96

The linear function becomes

y = 0.99x + 0.96

Therefore, for $12, the number of minutes would be

12 = 0.99x + 0.96

0.99x = 12 - 0.96

0.99x = 11.04

x = 11.04/0.99

x = 11.15 minutes

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