# Tutor profile: Taha B.

## Questions

### Subject: Trigonometry

The London Eye is a large Ferris wheel located on the banks of the Thames River in London, England. Each sealed and air-conditioned passenger capsule holds about 25 passengers. The diameter of the wheel is 135 m, and the wheel takes about half an hour to complete one revolution. a) Determine the exact angle, in radians, that a passenger will travel in 5 min. b) How far does a passenger travel in 5 min? c) How long would it take a passenger to travel 2 radians? d) What is the angular velocity of a passenger, in radians per second? e) What is the angular velocity of a passenger, in degrees per second?

a) 1 rev. in 0.5 hour = 360° in 0.5 hour = 360 degrees in 30 minutes = 2π radians in 30 minutes 2π rad / 30 min = x rad / 5 min x = 5(2π)/30 rad = π/3 radians b) s = rθ = (67.5 m)(π/3 rad) = 70.5 m (to 1 d.p.) c) ω = Δθ/Δt Δt = Δθ/ω Δt = 2 rads / (2π rad / 30 min) = 9,5 min (to 1 d.p.) d) 2π rad / 30 min = 2π rad / 30(60) sec = π/900 rad/s e) π/900 rad/s = π/900 × (180°/π) °/s = 0.2°/s = (1/5)°/s

### Subject: Geometry

If the formula to convert a Fahrenheit temperature to a Celsius temperature is C = (5/9)(F - 32), then the formula to convert a Celsius temperature to a Fahrenheit temperature is F = (9/5)C + 32. Write a two-column proof to verify this conjecture.

STATEMENTS REASONS _________________________________________________________________ 1. C = (5/9)(F - 32) 1. Given 2. (9/5)C = (9/5)(5/9)(F - 32) 2. Multiplication Property of Equality 3. (9/5)C = F - 32 3. Substitution Property of Equality 4. (9/5)C + 32 = F - 32 + 32 4. Addition Property of Equality 5. (9/5)C + 32 = F 5. Substitution Property of Equality 6. F = (9/5)C + 32 6. Symmetric Property of Equality

### Subject: Algebra

Find: a) The slope of the line 3x + 2y = 5 algebraically. b) The equation of the line that is perpendicular to the line in part a) and passes through (3,5).

a) Step 1: Re-arrange the equation of the line so that it is expressed in the y = mx + b form (a.k.a., "slope-intercept-form"): 3x + 2y = 5 2y = -3x + 5 y = (-3/2)x + 5/2 Step 2: The slope of the line is the coefficient of x. In this case, the slope of the line is -3/2 or -1.5. b) Step1: Find the nagative reciprocal of the slope of the line in part a), since two lines that are perpendicular have negative reciprocal slopes. Negative reciprocal of -3/2 is 2/3. Step 2: Use the obtained slope value (m), and the given point to calculate the y-intercept (b). y = mx + b 5 = (2/3)(3) + b 5 = 2 + b b = 3 Step 3: Write the equation of the line using the obtained m and b values. y = (2/3)x + 3

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