B. Write an equation for each of the following statements of variation:
(use k as the constant of variation)
1. The circumference C of a circle varies directly as the radius r.
2. At constant temperature the resistance R of a given size of wire varies
directly as the length l.
3. Mila’s commission C varies as the number n of dresses sold.
4. The interest I earned by a fixed deposit of P2,000 at 6% rate of interest is
related to the length of time t of deposit.
(use k as the constant of variation)
1. The circumference C of a circle varies directly as the radius r.
2. At constant temperature the resistance R of a given size of wire varies
directly as the length l.
3. Mila’s commission C varies as the number n of dresses sold.
4. The interest I earned by a fixed deposit of P2,000 at 6% rate of interest is
related to the length of time t of deposit.
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Answer:
1.C = 2πr, where C is the circumference of a circle with radius r. The circumference of a circles varies directly as its radius, or the circumference is directly proportional to its radius. ... r = ( d⁄t ), where r is the speed when travelling d miles in t hours.
2.The resistance R of a wire varies directly as its length L and inversely as the square of its diameter d. (a) Write an equation that expresses this joint variation. (b) Find the constant of proportionality if a wire 1.2 m long and 0.005 m in diameter has a resistance of 140 ohms. (c) Find the resistance of a wire made of the same material that is 3 m long and has a diameter of 0.008 m. (d) If the diameter is doubled and the length is tripled, by what factor is the resistance changed?