State the name of the unit and the type of measurement indicated for each ofthe following quantities: a. \(0.8 \mathrm{~L}\) b. \(3.6 \mathrm{~cm}\) c. \(4 \mathrm{~kg}\) d. \(35 \mathrm{lb}\) e. \(373 \mathrm{~K}\)
Short Answer
Expert verified
0.8 L is volume, 3.6 cm is length, 4 kg is mass, 35 lb is weight/mass, 373 K is temperature.
The unit 'L' stands for liter, which is a unit of volume. Therefore, 0.8 L indicates a measurement of volume.
02
Identify quantity in 3.6 cm
The unit 'cm' stands for centimeter, which is a unit of length. Therefore, 3.6 cm indicates a measurement of length.
03
Identify quantity in 4 kg
The unit 'kg' stands for kilogram, which is a unit of mass. Therefore, 4 kg indicates a measurement of mass.
04
Identify quantity in 35 lb
The unit 'lb' stands for pound, which is a unit of weight/mass. Therefore, 35 lb indicates a measurement of weight/mass.
05
Identify quantity in 373 K
The unit 'K' stands for Kelvin, which is a unit of temperature. Therefore, 373 K indicates a measurement of temperature.
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Volume Measurement
Volume measurement refers to the amount of space that a substance or object occupies. In chemistry, the liter (L) is a common unit used to measure volume. For instance, in the exercise, 0.8 L refers to a volume measurement. Understanding the concept of volume is crucial for various chemical experiments, especially when preparing solutions or mixing reagents. Volumes can also be expressed in milliliters (mL), where 1 L is equal to 1000 mL. Other units like cubic centimeters (cc or cm³) can also describe volume, especially for smaller quantities. Precise volume measurements ensure accurate results in chemical reactions.
Length Measurement
Length measurement determines the linear distance between two points. The centimeter (cm) is frequently used in chemical settings to measure the size of objects or distances. In the exercise, 3.6 cm is given as a length measurement. Length units can vary, including meters (m) for larger distances and millimeters (mm) for smaller ones - with 1 m equating to 100 cm and 1 cm equal to 10 mm. Accurate length measurements are vital for laboratory procedures such as measuring the dimensions of containers or the distance traveled by a substance during chromatography.
Mass Measurement
Mass measurement refers to the quantity of matter in an object, typically measured in kilograms (kg) or grams (g). In the provided exercise, 4 kg describes a mass measurement. Mass is distinct from weight, which is the force exerted by gravity on an object. Commonly, chemists use balances to determine mass, and it's critical for preparing chemical solutions, determining reaction yields, and calculating reagent quantities. Precision in mass measurement ensures reactions proceed as expected. For smaller amounts, mass can be measured in grams (1 kg = 1000 g), allowing for fine-tuned accuracy in experiments.
Weight Measurement
Weight measurement accounts for the force exerted by gravity on an object, commonly recorded in pounds (lb) or newtons (N). In the exercise, 35 lb indicates a weight measurement. While mass and weight are related, they are not interchangeable; weight varies depending on gravity, while mass remains constant. In chemistry, understanding weight is essential, especially when dealing with forces acting on substances or when converting between different units of force. For conversion, remember that 1 lb is approximately 4.448 N. Although mass is more frequently used in chemistry, knowing weight measurements underpins a comprehensive understanding of material properties.
Temperature Measurement
Temperature measurement is crucial in chemistry to understand how heat affects substances. The Kelvin (K) is the SI unit for temperature, shown in the exercise by 373 K. Temperature impacts reaction rates, solubility, and states of matter. Besides Kelvin, degrees Celsius (°C) and Fahrenheit (°F) are also used, with specific conversion formulas: \((K = °C + 273.15)\). Accurate temperature measurements ensure consistency in experimental conditions and reproducibility of results. Using thermometers or digital sensors, scientists can achieve precise temperature control, critical for both routine laboratory work and advanced research.
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Answer: There are various methods by which you can solve a quadratic equation such as: factorization, completing the square, quadratic formula, and graphing. These are the four general methods by which we can solve a quadratic equation.
The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations.
In math, we define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x^2 + 3x + 1.
As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b [ 2 ] - 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.
Step 1: Using inverse operations, move all terms to one side of your equal sign. Step 2: Simplify your equation, and move terms around so that your equation is in the standard form of a quadratic function. Step 3: Now that your equation is in standard form, you can determine the values for a, b, and c.
The terms a, b and c are also called quadratic coefficients. The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations.
Answer: A quadratic equation is the equation of the 2nd degree. This means that it comprises at least one (1) term that is squared. One of the standard formulas for solving quadratic equations is 'ax² + bx + c = 0' here a, b, and c are constants or numerical coefficients. 'X' here is an unknown variable.
The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The important condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term (a ≠ 0).
If the quadratic equation involves a SQUARE and a CONSTANT (no first degree term), position the square on one side and the constant on the other side. Then take the square root of both sides.
The discriminant determines the nature of the roots of a quadratic equation. The word 'nature' refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.
We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal. If we subtract the same number from both sides of an equation, both sides will remain equal.
Step 2: Factorise the product of the coefficient of and the constant term of the given quadratic equation. Step 3: Express the coefficient of the middle term as the sum or difference of the factors obtained in Step 2. Step 4: Use zero product property i.e., put each linear factor equal to 0.
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