devyy To express the complex number (5/2) * (cos(150°) + i sin(150°)) in the form a + bi, we first need to evaluate the trigonometric functions involved. The angle 150° is located in the second quadrant of the unit circle. Its cosine and sine values are: cos(150°) = -√3/2 sin(150°) = 1/2 Next, we can substitute … Read more
The area of a triangle can be easily calculated using the following formula: Area = (Base × Height) / 2 In this case, you have a base of 8 units and a height of 6 units. Let’s plug these numbers into the formula: Area = (8 × 6) / 2 = 48 / 2 = … Read more
To derive the equation of the parabola with a given focus and directrix, we can use the definition of a parabola: it is the set of all points that are equidistant from the focus and the directrix. In this case, we have: Focus (F): (0, 5) Directrix (D): y = 5 The first step is … Read more
The interest rate used to compute the present value of future cash flows is known as the discount rate. This rate reflects the time value of money, which is a core principle in finance and investment decisions. Essentially, the discount rate serves as a crucial factor when determining how much future cash flows are worth … Read more
To rewrite the inequality 6x + 2y < 42 in slope-intercept form, follow these steps: Start with the original inequality: 6x + 2y < 42 Isolate the term with the variable y on one side. First, subtract 6x from both sides: 2y < -6x + 42 Next, divide every term in the inequality by 2
To determine whether the system of equations has solutions, we need to analyze the given equations. The initial expressions you provided seem to represent lines: Equation 1: y = 2x Equation 2: y = 4x Both of these equations are in the slope-intercept form (y = mx + b), where m represents the slope and … Read more
To graph the parametric equations x = 7 sin(t) sin(7t) and y = 7 cos(t) cos(7t), follow these steps: 1. Understanding the Parametric Equations The equations define a curve in the XY-plane where the position of each point is determined by the parameter t. The x and y values oscillate between -7 and 7 based … Read more
To find the value of m, we start with the given information. We know: n = 8 162m = 4n Now, we can substitute the value of n into the equation: 162m = 4(8) Calculating the right-hand side: 4(8) = 32 So, we now have: 162m = 32 Next, to isolate m, we divide both … Read more
The slope of a line is a measure of its steepness and is calculated using the formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, we are given the points (7, 1) and (1, 10). Let’s designate: (x1, y1) = (7, 1) (x2, y2) = (1, 10) Now, we can … Read more
Let the denominator of the fraction be d. According to the problem, the numerator is d – 4. So, the fraction can be represented as: Fraction = (d – 4) / d When 1 is added to both the numerator and the denominator, the fraction becomes: ((d – 4) + 1) / (d + 1) … Read more