If Robert buys a candy bar for 78 cents, how much change does he get back from a one dollar bill?
To determine how much change Robert receives after buying a candy bar for 78 cents with a one dollar bill, we first need to convert everything into the same unit, which is cents. One dollar is equal to 100 cents. Now, we simply subtract the cost of the candy bar from the total amount paid: […]
Multiply and Simplify the Product 2i and 5i. Select the Product.
To multiply the complex numbers 2i and 5i, we follow the basic rules of multiplication. First, multiply the coefficients and the imaginary unit separately: Coefficients: 2 * 5 = 10 Imaginary units: i * i = i² Now, we know that i² is equal to -1. Therefore, we can substitute: 10 * i² = 10 […]
Find the Arc Length Function for the Curve y = 2x^3/2 with Starting Point P(0, 36) and Ending Point (4, 32)
To find the arc length function for the curve defined by y = 2x^(3/2), we first need to use the arc length formula. The arc length L from point a to b for a curve y = f(x) is given by: L = ∫(a to b) √(1 + (dy/dx)²) dx First, we need to compute […]
Solve the equation on the interval: 0 ≤ x ≤ 2π for 2 cos(x) – 2 cos(x) sin(x) = 0
To solve the equation 2 cos(x) – 2 cos(x) sin(x) = 0, we can start by factoring: Factor out 2 cos(x): 2 cos(x) (1 – sin(x)) = 0 This gives us two cases to consider: 2 cos(x) = 0 1 – sin(x) = 0 For the first case, 2 cos(x) = 0: Dividing by 2, […]
Find the Length of the Curve r(t) = (3t, 3cos(t), 3sin(t))
To find the length of the curve represented by the vector function r(t) = (3t, 3cos(t), 3sin(t)), we need to compute the arc length using the formula: L = ∫ab ||r'(t)|| dt First, we differentiate the vector function r(t) with respect to t: r'(t) = (3, -3sin(t), 3cos(t)) Next, we find the magnitude of the […]
What is the value of the discriminant for the quadratic equation 3x² + 2x?
To find the value of the discriminant for the quadratic equation, we first need to put it in the standard form, which is ax² + bx + c = 0. The given equation is 3x² + 2x = 0, where: a = 3 b = 2 c = 0 The discriminant D is calculated using […]
How many ways can a committee of four students be selected from a 15 member club?
To determine how many ways we can select a committee of four students from a club consisting of 15 members, we need to use the concept of combinations. Combinations are used when the order of selection does not matter. The formula for combinations is given by: C(n, r) = n! / (r!(n – r)!) Where: […]
Select the Equations of the Lines that are Parallel to the Line Whose Equation is y = 3x + 5
To determine the equations of the lines that are parallel to the given line, we first need to identify the slope of that line. The standard form of a linear equation is y = mx + b, where m represents the slope and b is the y-intercept. In the equation y = 3x + 5, […]
Find the HCF of 1008 and 1080 by Prime Factorization Method
To find the Highest Common Factor (HCF) of 1008 and 1080 using the prime factorization method, we first need to break down both numbers into their prime factors. Step 1: Prime Factorization of 1008 We start with 1008: 1008 is even, so we start dividing by 2. 1008 ÷ 2 = 504 504 ÷ 2 […]
Segments RT and SU are Diameters of Circle O. What is m of ∠SRT?
In a circle, when you have two diameters, like segments RT and SU, they intersect at the center of the circle, which we’ll call point O. This forms several angles, including angle SRT. First, let’s note that since RT and SU are both diameters, they divide the circle into four equal parts. This means that […]