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Basic Algebra and Equations Flashcards

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  1. An elevator control system requires 3 resistors connected in series. The values of the resistors are R1, R2, and R3. The total resistance (RT) is 150 ohms. If R1 = 45 ohms and R2 is twice the value of R1, what is the value of R3 in ohms?

    Answer: 15 ohms

    The formula for total resistance in a series circuit is RT = R1 + R2 + R3. First, calculate R2: R2 = 2 * R1 = 2 * 45 ohms = 90 ohms. Next, plug the known values into the formula: 150 ohms = 45 ohms + 90 ohms + R3. Simplify the equation: 150 ohms = 135 ohms + R3. To solve for R3, subtract 135 from both sides: R3 = 150 - 135 = 15 ohms.

  2. A technician is installing a new traveling cable that weighs 2.5 pounds per foot. The total length of the cable needed is 'L' feet. The total weight of the cable must not exceed 180 pounds. Which of the following inequalities correctly represents the maximum length of the cable that can be used?

    Answer: 2.5 * L <= 180

    Let 'L' be the length of the cable in feet. The total weight is the weight per foot (2.5 lbs) multiplied by the length (L). The problem states the total weight must not exceed 180 pounds, which means it must be less than or equal to 180. Therefore, the correct inequality is 2.5 * L <= 180.

  3. Solve for x in the following equation: 4(x + 3) - 10 = 2(x + 5)

    Answer: x = 4

    First, use the distributive property on both sides: 4x + 12 - 10 = 2x + 10. Simplify both sides: 4x + 2 = 2x + 10. Next, get the 'x' terms on one side by subtracting 2x from both sides: 2x + 2 = 10. Then, isolate the 'x' term by subtracting 2 from both sides: 2x = 8. Finally, divide by 2 to solve for x: x = 4.

  4. An elevator motor runs at a speed that is dependent on the input voltage (V). The relationship is given by the formula S = 15V + 20, where S is the speed in RPM. If the motor is running at 500 RPM, what is the input voltage (V)?

    Answer: 32 volts

    Start with the given formula: S = 15V + 20. Substitute the known speed (S = 500) into the equation: 500 = 15V + 20. To solve for V, first subtract 20 from both sides: 480 = 15V. Then, divide both sides by 15: V = 480 / 15. 480 / 15 = 32. So, the input voltage is 32 volts.

  5. A maintenance schedule requires that for every 3 elevators inspected (E), a technician must complete 5 pages of paperwork (P). Which equation correctly describes the relationship between elevators inspected and pages of paperwork?

    Answer: 5E = 3P

    The ratio of elevators to paperwork is 3 to 5 (E/P = 3/5). To express this as an equation without fractions, we can cross-multiply. This gives us 5 * E = 3 * P, or 5E = 3P. This equation maintains the correct ratio; for example, if E=3, then 5(3) = 15, so 3P = 15 and P = 5, which matches the initial condition.

  6. A wire's resistance (R) in ohms is directly proportional to its length (L) in meters and inversely proportional to its cross-sectional area (A) in square millimeters. If a 50-meter wire with an area of 2 mm² has a resistance of 10 ohms, what is the resistance of a 100-meter wire of the same material with an area of 4 mm²?

    Answer: 10 ohms

    The relationship is R = k(L/A), where k is the proportionality constant. First, find k using the initial data: 10 = k(50/2), which simplifies to 10 = k(25), so k = 10/25 = 0.4. Now, use this constant to find the new resistance: R = 0.4 * (100/4). This simplifies to R = 0.4 * 25, which equals 10 ohms. The doubling of the length (which doubles resistance) is exactly offset by the doubling of the area (which halves the resistance).