Mathematics Answer Note #57

Question 1 4 + (4 squared - 26 divided by 2) to the power of 4 - 3 x 5 Answer To solve this mathematical expression, we will follow the Order of Operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) rule. Step 1: Simplify inside the parentheses first - 4 squared and 26 divided by 2. 4 squared = 4 x 4 = 16 26 divided by 2 = 26 ÷ 2 = 13 Therefore, the expression inside the parentheses becomes 16 - 13 = 3. Step 2: Next, solve for the exponent. The exponent in this expression is 4, which means the base number (3) will be multiplied by itself 4 times. 3^4 = 3 x 3 x 3 x 3 = 81 Step 3: Solve for multiplication and division from left to right. 3 x 5 = 15 Step 4: Finally, solve for addition and subtraction from left to right. 81 - 15 = 66 Therefore, the final answer to the mathematical expression 4 + (4 squared - 26 divided by 2) to the power of 4 - 3 x 5 is 66. Question 2 . a = 6 + sqrt(35) and b = 1/a find the value of a ^ 2 + b ^ 2 Answer To find the value of a^2 + b^2, we first need to substitute the values of A and b given in the question. From the given information, we know that b = 1/a. Therefore, we can calculate the value of a as follows: a = 6 + √35 = 6 + 5.916 = 11.916 (rounded to three decimal places) Now, substituting the value of a in the given formula, we get: a^2 + b^2 = (11.916)^2 + (1/11.916)^2 = (142.274) + (0.007886) = 142.282 (rounded to three decimal places) Therefore, the value of a^2 + b^2 is 142.282. Question 3 42cents of 36 Rand as a %. Round answer to 2 decimal places Answer To find the percentage equivalent of 42 cents out of 36 Rand, we will use the formula: percentage = (part/whole) x 100. In this case, the part would be 42 cents and the whole would be 36 Rand. Step 1: Convert 42 cents to Rand. In order to do this, we need to divide 42 by 100 (as there are 100 cents in 1 Rand). This gives us the value of 0.42 Rand. Step 2: Now we plug in the values into the formula: percentage = (0.42/36) x 100. This gives us the value of 1.17%. Therefore, 42 cents out of 36 Rand is equivalent to 1.17%. Step 3: To round the answer to 2 decimal places, we need to look at the third decimal place. In this case, the third decimal place is 7. As the number is greater than or equal to 5, we need to round the second decimal place up by 1. Therefore, our final answer is 1.18%. Question 4 42c of R36 as a &. Round answer to 2 decimal places Answer To solve this problem, we first need to understand what the given information means. In mathematics, the "c" is usually used as an abbreviation for "cent." Therefore, 42c would mean 42 cents. The "R" could be a representation of a certain currency, so let's assume it stands for Rupees. The "36" could be a reference to a specific value that is being exchanged for the 42 Rupees. And finally, the "&" symbol indicates that we need to find a certain value or quantity. Based on the given information, we can interpret the question as "What is 42 Rupees and 36 of some other currency?" To solve this, we need to know the exchange rate between Rupees and the unknown currency. However, since we don't have this information, we can assume that the exchange rate is 1:1, meaning 1 Rupee is equivalent to 1 of the unknown currency. Using this assumption, we can write the given information in a mathematical equation as follows: 42 Rupees + 36 unknown currency = ?. To find the unknown currency, we simply subtract 42 from both sides of the equation, resulting in 36 of the unknown currency = ?. Since we need to round the answer to 2 decimal places, we can assume that the answer will be in fractions of the unknown currency. Now, we can use a calculator to divide 36 by 100 (since there are 100 cents in a Rupee) which gives us 0.36. Therefore, the unknown currency is equivalent to 0.36 of a Rupee. To round this answer to 2 decimal places, we need to consider the third digit after the decimal point. If it is 5 or more, we round the second digit up, and if it is less than 5, we leave the second digit as it is. Since the third digit is 6, we round 0.36 up to 0.37. Therefore, 42 Rupees and 36 of the unknown currency is equivalent to 42.37 Rupees. Question 5 The difference in compound interest and simple on certain sum of money at the end of 2 years at 5% is Rs25. Determine the sum Answer Based on the given information, we can determine the sum of money by using the compound interest formula, which is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. To calculate the simple interest, we use the formula A = P(1 + rt), where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the number of years. Substituting the given values in the compound interest formula, we have A = P(1 + 0.05/1)^(1*2), which can be simplified to A = P(1.05)^2. Similarly, for simple interest, A = P(1 + 0.05*2) = P(1.1). Now, the difference between the two is Rs25, which means we can set up the equation, P(1.05)^2 - P(1.1) = 25. Solving for P, we get P = Rs1000. Therefore, the sum of money at the beginning is Rs1000.