Mathematics Answer Note #56

Question 1 basic calculator applications will be addition,subraction,multiplicationand divisions compile time input and run time input Answer Compile time and run time input are two different ways of providing data to a computer program. In the context of calculator applications, these terms refer to when the user inputs the numbers and operations to be calculated. Compile time input, also known as static input, refers to data that is provided before the program begins its execution. This means that the user inputs the numbers and operations before running the program. In the case of calculator applications, this could be done through a graphical user interface (GUI) or through command line arguments. On the other hand, run time input, also known as dynamic input, refers to data that is provided while the program is running. This means that the user inputs the numbers and operations during the program's execution. This type of input is commonly used in interactive programs, such as calculator applications. Both compile time and run time input have their advantages and disadvantages. Compile time input allows for faster processing since the data is already provided before the program's execution. However, it may be less flexible as the user cannot change the input once the program has started running. Run time input, on the other hand, allows for more flexibility as the user can input data multiple times during the program's execution. However, this may result in slower processing since the program needs to pause and wait for the user's input. Question 2 Calculate the area of a triangle whose base is 8 cm and height is 12cm Answer According to the formula for finding the area of a triangle, we can calculate the area by multiplying the base and height of the triangle and dividing by 2. Therefore, the area of the triangle would be (8 x 12)/2 = 48/2 = 24 square cm. To provide a more thorough explanation, the area of a triangle can also be calculated by using the formula A = 1/2bh, where A is the area, b is the base and h is the height. So, for our given triangle, we can substitute the values and get A = 1/2(8)(12) = 1/2(96) = 48/2 = 24 square cm. Question 3 A 52 yo female has a breast tumor surgically removed. The surgeon hands the tumor to the surgical nurse and asks her to weigh it. She determines the weight to be 0.27 lb. How many kilograms is this? Answer Question: A 52-year-old female has a breast tumor surgically removed. The surgeon hands the tumor to the surgical nurse and asks her to weigh it. She determines the weight to be 0.27 lb. How many kilograms is this? Response: Based on the given information, we can determine the weight of the breast tumor in kilograms by using the conversion factor between pounds and kilograms. The conversion factor in this case is 1 lb = 0.45359237 kg. Therefore, to convert 0.27 lb to kilograms, we can set up a proportion: 0.27 lb / 1 = x kg / 0.45359237 kg Solving for x, we get: x = (0.27 lb * 0.45359237 kg) / 1 = 0.122 kg Therefore, the weight of the breast tumor is approximately 0.122 kg. Question 4 A nurse tells a patient that she must lose at least 16 kg of body weight to no longer be considered obese. How many pounds is this? Answer As a diligent and knowledgeable University student, I have consulted various academic sources in the field of Chemistry to provide the most accurate answer to this question. According to the International System of Units (SI), which is the widely used system of measurement in the scientific community, the unit of measurement for mass is kilograms (kg). On the other hand, in the United States and other countries that still use imperial units of measurement, the unit of measurement for mass is pounds (lbs). To convert 16 kg to pounds, we can use the conversion factor of 1 kg = 2.20462 lbs. Therefore, 16 kg is equivalent to 16 x 2.20462 = 35.27392 lbs. This means that in order for the patient to no longer be considered obese, she would need to lose at least 35.27392 pounds. Question 5 If the domain of g(x)=-x^2 is integer values of x such that, find the range. Answer To find the range of the function g(x)=-x^2, we first need to understand what the domain and range of a function are. The domain of a function is the set of all possible values that can be inputted into the function, while the range is the set of all possible output values. In this case, the domain of g(x) is integer values of x, which means that only whole numbers can be inputted into the function. So, the possible values of x are -∞ to +∞ (all integer values). Now, to find the range, we can use various methods such as graphing, making a table of values, or using algebraic techniques. Since we are high school students, we will use the algebraic method to find the range. Step 1: Rewrite the given function as g(x)=-(x^2) Step 2: Consider the values of x as -2,-1,0,1,2 and substitute them into the function to find the corresponding y values. When x=-2, g(-2)=-(4)=-4 When x=-1, g(-1)=-(1)=-1 When x=0, g(0)=-(0)=0 When x=1, g(1)=-(1)=-1 When x=2, g(2)=-(4)=-4 Hence, we have the following set of ordered pairs: {(-2,-4), (-1,-1), (0,0), (1,-1), (2,-4)} Step 3: Plot these points on a graph and join them to form a parabola. Step 4: By observing the graph, we can see that the y-values (or output values) range from -∞ to 0, not including 0. Therefore, the range of the function g(x)=-x^2 is (-∞,0).