The volume of a sphere can be calculated using the formula: V = \frac{4}{3} \pi r^3 In this formula, V represents the volume, \pi is a constant approximately equal to 3.14159, and r is the radius of the sphere. Given the radius of the sphere is 48 cm, we can substitute r in the formula: … Read more
The cosine function is a periodic function that oscillates between -1 and 1. To analyze the specific function given, y = 3cos(4x), we can break it down into its components: amplitude, period, and range. Amplitude The amplitude of a cosine function y = A * cos(Bx) is determined by the coefficient A. In this case, … Read more
To find the value of f(16) for the function f(x) = 0.34x, we need to substitute 16 into the equation in place of x. So, we start with: f(x) = 0.34x Now, we substitute: f(16) = 0.34 * 16 Next, we perform the multiplication: f(16) = 5.44 Thus, the value of f(16) is 5.44.
To find the quotient of the polynomials represented by the coefficients 6, 15, 10, 10, and 4 at varying powers of x, we need to divide the first polynomial by the second polynomial. Let’s assume the two polynomials are: Numerator: 6×4 + 15×3 + 10×2 + 10x + 4 Denominator: 3×2 + 2 We will … Read more
To find the point on the line y = 3x + 5 that is closest to the origin (0, 0), we can use the concept of distance in coordinate geometry. The distance D from any point (x, y) on the line to the origin is given by the distance formula: D = √(x2 + y2) … Read more
The function f(x) = 6x is a linear function, where ‘x’ represents the independent variable. In this case, the coefficient of ‘x’ is 6, which indicates the growth factor of the function. The growth factor is essentially the rate at which the function’s value increases as ‘x’ increases. For this function, every time ‘x’ increases … Read more
To solve the problem, let’s define the current ages of Michael and Brandon. Let B be Brandon’s current age. According to the information provided: Michael is three times as old as Brandon: M = 3B. 18 years ago, Michael was nine times as old as Brandon: M – 18 = 9(B – 18). Now, we … Read more
Holly’s expression contains a combination of terms involving the variables m and n, but it seems she might have overlooked the rules of combining like terms in algebra. To understand Holly’s error, let’s break down the expression: 11m: This represents 11 times the variable m. 13n: This signifies 13 times the variable n. 6mn: This … Read more
To find the missing value from Samuel’s solution, we need to first combine the like terms of the polynomials involved in his calculation. The polynomials given are: 15x² + 11y² + 8x – 7x² – 5y² – 2x – x² – 6y² – 6x Now, let’s rearrange and group the similar polynomial terms: x² terms: … Read more
The equation x2 = 2x can be solved by first rearranging it into a standard quadratic form. To do this, we can subtract 2x from both sides: x2 – 2x = 0 Next, we can factor the left-hand side: x(x – 2) = 0 This product is equal to zero when either factor is equal … Read more