What is true about the sum square root of 50 square root of 18?
To find the sum of the square roots of 50 and 18, we first need to calculate each square root separately. The square root of 50 can be simplified as follows: √50 = √(25 × 2) = √25 × √2 = 5√2 Next, we can simplify the square root of 18: √18 = √(9 × […]
Describe Minors and Cofactors
In linear algebra, minors and cofactors are important concepts related to matrices, particularly when calculating determinants and working with inverses. A minor of a matrix is the determinant of a smaller matrix that you obtain by deleting one row and one column from the original matrix. For instance, if you have a 3×3 matrix, the […]
Find sin2x, cos2x, and tan2x from the given information: cscx = 8, tanx = 0
To find the values of sin2x, cos2x, and tan2x from the given information that cscx = 8 and tanx = 0, we start by interpreting these functions. Cosecant is the reciprocal of sine. Thus, if cscx = 8, we have: sinx = 1/cscx = 1/8 Now, knowing that sinx = 1/8 lets us find cosx […]
Which statements are true for the functions g(x) = x² and h(x) = x²? Check all that apply.
To determine which statements are true for the functions g(x) = x² and h(x) = x², we need to first recognize that both functions are identical. They represent the same mathematical relationship where the output is the square of the input. Both functions are even functions: True. An even function is defined as a function […]
List the first five terms of the sequence an = 1n + 16n
To find the first five terms of the sequence given by an = 1n + 16n, we need to substitute the values of n starting from 1 to 5 into the expression. For n = 1: a1 = 11 + 161 = 1 + 16 = 17 For n = 2: a2 = 12 + […]
In circle O, AE and FC are diameters. Arc ED measures 17; what is the measure of arc EFC?
To find the measure of arc EFC, we can use the fact that the entire circle measures 360 degrees. Since AE and FC are diameters, they split the circle into two semicircles. Given that arc ED measures 17 degrees, we can determine the measure of arc EFC by considering the arc that complements it. The […]
How to Differentiate log₁(x) x² Function
To differentiate the function log₁(x) x², we first need to understand how logarithms and derivatives work. The function log₁(x) can actually be simplified, as log base 1 is technically undefined for all positive numbers except at the value of 1. However, if we interpret the query as differentiating log(x) · x² instead, we can proceed […]
For what values of m does the graph of y = 3x² + 7x + m have two x intercepts?
To determine the values of m for which the graph of the quadratic function y = 3x² + 7x + m has two x-intercepts, we need to analyze the discriminant of the quadratic equation. The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are […]
What is the set of all real numbers x for which x² – x – 2 = 0?
To solve the equation x² – x – 2 = 0, we can factor it. We are looking for two numbers that multiply to -2 (the constant term) and add up to -1 (the coefficient of x). These two numbers are -2 and +1. Thus, we can factor the equation as follows: x² – x […]
How to Find All Solutions to the Equation 2sin(2x)sin(4x) = 0 in the Interval [0, 2π]
To find all solutions to the equation 2sin(2x)sin(4x) = 0 in the interval [0, 2π], we first recognize that the product is zero when either factor is zero. This gives us two separate equations to solve: 1. 2sin(2x) = 0 2. sin(4x) = 0 Solving 2sin(2x) = 0: We divide both sides by 2 (noting […]