This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
a) Let the two numbers be x and y. The sum of the two numbers is 18: x + y = 18 (1) Their difference is 2: x - y = 2 (2) The set of simultaneous equations is: x + y = 18 \\ x - y = 2 b) Step 1: Add equation (1) and equation (2). (x + y) + (x - y) = 18 + 2 2x = 20 Step 2: Solve for x. x = (20)/(2) x = 10 Step 3: Substitute the value of x into equation (1). 10 + y = 18 Step 4: Solve for y. y = 18 - 10 y = 8 The two numbers are 10 and 8. x=10, y=8 Step 1: Identify the given values for the sector. Radius r = 15 cm Angle = 60^ Step 2: Use the formula for the area of a sector. A = ()/(360^) r^2 Step 3: Substitute the values into the formula. A = (60^)/(360^) (15 cm)^2 A = (1)/(6) (225 cm^2) Step 4: Calculate the area. A = (225)/(6) cm^2 A = (75)/(2) cm^2 A = 37.5 cm^2 Using ≈ 3.14159: A ≈ 37.5 × 3.14159 cm^2 A ≈ 117.81 cm^2 The area of the sector is 37.5 cm^2 or approximately 117.81 cm^2. Step 1: Identify the dimensions of the bar soap (cuboid). Length L = 12 cm Width W = 4 cm Height H = 3 cm Step 2: Use the formula for the surface area of a cuboid. SA = 2(LW + LH + WH) Step 3: Substitute the dimensions into the formula. SA = 2((12 cm)(4 cm) + (12 cm)(3 cm) + (4 cm)(3 cm)) Step 4: Calculate the products inside the parentheses. SA = 2(48 cm^2 + 36 cm^2 + 12 cm^2) Step 5: Sum the areas inside the parentheses. SA = 2(96 cm^2) Step 6: Calculate the total surface area. SA = 192 cm^2 The surface area of the bar soap is 192 cm^2. Send me the next one 📸