The rule that compares two quantities where the second quantity has a value of 1 is known as the unit rate. This is calculated by dividing the first quantity by the second quantity, yielding a value that represents how much of the first quantity corresponds to a single unit of the second. For example, if you have 60 miles driven in 2 hours, the unit rate would be 60 miles divided by 2 hours, resulting in a rate of 30 miles per hour.
In your statement of the quantities, I don't see the word "equals" anywhere. Without that, all you have is an expression that stands for a number. The number depends on the values of 'x' and 'y', and it changes as soon as one of them changes. You don't have an equation, no question is asked, and no answer is required.
You can add or subtract any quantity on both sides of an equation, without changing the equation's solution set. Just make sure you add or subtract the same thing on both sides.
"30 mph west" is an example of a vector quantity, as it includes both a magnitude (30 mph) and a direction (west). In physics, vector quantities are important because they provide information about both how much and in which direction something is moving. In contrast, a scalar quantity would only provide a magnitude, such as "30 mph" without specifying a direction.
If it is purely a Venn diagram problem then you cannot. Venn diagrams offer a way of solving certain types of problems graphically.
Absolute values represent the distance of a number from zero on the number line, regardless of its direction, making them useful for describing quantities in various mathematical contexts. For instance, in measuring physical distances, temperature differences, or financial losses, the absolute value provides a clear indication of magnitude without concern for the sign. This allows for consistent comparisons and calculations, emphasizing the size of a quantity rather than its direction. Thus, absolute values help to convey meaningful information about quantities in both theoretical and practical applications.
The square of a vector quantity is the vector magnitude times itself without a change in the orientation.
No, a quantity cannot have units and still be dimensionless. The dimensions of a quantity are determined by its units, so if a quantity has units, it has dimensions. Dimensionless quantities are those without any units.
Scalar quantity is a physical quantity that has magnitude only, without any direction. It is often represented by a number with a unit. There is no specific formula for scalar quantity as it is independent of directions. Examples of scalar quantities include mass, temperature, and speed.
In physics, a scalar is a quantity that has only magnitude, without a direction. For example, temperature is a scalar quantity because it only has a value (e.g., 25 degrees) without needing a direction.
Vectors include information about their direction, and are incomplete without it. Examples are displacement, velocity, acceleration, momentum, magnetic field. (Velocity is speed with direction.) Scalars are complete without stating any direction. Examples are temperature, cost, mass, speed. (Speed is velocity without direction.)
When quantities are plentiful the price lowers; when quantities are scarce the price rises. Also called supply and demand. Whether or not it right or wrong, it's just the way it is and we have to accept it or do without that particular commodity.
No, a dimensionless quantity does not have a unit because it represents a pure number without any physical dimension. Examples of dimensionless quantities include ratios, proportions, and mathematical constants.
A human being is not a measurement. You can measure a human's height, mass, weight, albedo, loudness when he shouts, or whatever, and each of these can be expressed as a measurement, but the human being itself is not a measurement. In general, you have to distinguish an object from its properties.
A size but no direction. Mass is a scalar but the force we call weight is a vector: it always points down.
Scalar. Scalars are quantities that are described by magnitude only, without any direction. Examples include distance, speed, and temperature.
The smallest quantity that is divisible by two or more given quantities without a remainder: 12 is the lowest common multiple of 2, 3, 4, and 6.
Scalar quantities are measurements which have no specific physical direction. Two fundamental scalar quantities are mass and time. Mass and time simply exist without any directionality whatsoever. By way of comparison, distance is a fundamental vector quantity and not a scalar quantity. You cannot travel any distance without going in a specific physical direction: up or down, left or right, north or south, forward or backward, etc.