devyy To find the value of k such that the polynomial x² + kx + 6x² + 2kx + 1 has the sum of its zeroes equal to half of their product, we start by rewriting the polynomial in its standard form. First, combine like terms: x² + 6x² + kx + 2kx + 1 = … Read more
Calculating Mark’s Net Pay To find Mark’s net pay for the week, we need to subtract his total deductions from his gross pay. Here’s the step-by-step calculation: Gross Pay: Mark’s gross pay for the week is 95,000. Total Deductions: His total deductions amount to 11,854. Net Pay Calculation: To calculate the net pay, we use … Read more
The graphs of the equations y = 8x² + 1 and y = 8x² are both parabolas that open upwards because their leading coefficient, 8, is positive. However, there are key differences between them that affect their positioning on the Cartesian plane. 1. Vertical Shift: The main difference between the two graphs is the vertical … Read more
To demonstrate that (f o g)(g o f)(x) holds true for the functions f(x) = 2x + 1 and g(x) = x + 12, we first need to understand what the composition of functions means. The notation f o g represents the function f applied to the output of the function g. Similarly, g o … Read more
To find the number of ways to select 3 bananas from a group of 9, we can use the concept of combinations. The formula for combinations is given by: C(n, r) = n! / [r! * (n – r)!] Where: C(n, r) = number of combinations n = total number of items to choose from … Read more
To find the area of a trapezoid, you can use the formula: Area = (Base1 + Base2) / 2 * Height In this case, we have: Base1: 8 cm Base2: 16 cm Height: 10 cm Now, plug the values into the formula: Area = (8 cm + 16 cm) / 2 * 10 cm Calculating … Read more
Finding the HCF and LCM To find the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of the numbers 12, 15, 18, and 27, we can follow these steps: Step 1: Prime Factorization First, we will perform the prime factorization for each number: 12: 2 x 2 x 3 = 22 x 31 … Read more
To find the value of f(g(8)), we will first need to compute g(8) and then use that result to compute f(g(8)). 1. **Calculate g(8)**: The function g(x) is defined as g(x) = x + 5. Now we substitute x = 8: g(8) = 8 + 5 = 13. 2. **Calculate f(g(8))**: We found that g(8) … Read more
Understanding the Formula for sin-1(x) and sin-1(y) The formula for the sine inverse (or arcsine) of two variables is essential in trigonometry, particularly in applications where angles are involved. The sine inverse function, denoted as sin-1(x) or arcsin(x), is the inverse of the sine function, and it provides the angle whose sine is the given … Read more
To find the general solution of the given differential equation x dy/dx = 6y + x3 – x, we start by rewriting the equation in a more manageable form. First, let’s rearrange the equation: dy/dx = (6y + x3 – x)/x This simplifies to: dy/dx = 6(y/x) + x2 – 1 Now, we can use … Read more