If y varies directly as x and y is 180 when x is n and y is n when x is 5 what is the value of n?
To solve this problem, we begin with the understanding that if y varies directly as x, it can be represented mathematically as: y = kx where k is the constant of variation. From the question, we have two scenarios: When x = n, y = 180 When x = 5, y = n From the […]
How many triangles can be made if one angle is 95 and another angle is obtuse?
To determine how many triangles can be formed when one angle is 95 degrees and another angle is obtuse, we first need to understand the properties of triangles and the characteristics of angles. In any triangle, the sum of the interior angles must equal 180 degrees. An obtuse angle is defined as an angle that […]
Determine Whether the Geometric Series is Convergent or Divergent: 10, 2, 0.4, 0.08. If It Is Convergent, Find Its Sum.
To determine whether the given geometric series is convergent or divergent, we start by identifying the first term and the common ratio. The series is: 10, 2, 0.4, 0.08. The first term (a) of the series is 10. To find the common ratio (r), we can divide the second term by the first term: r […]
Use the Laplace Transform to Solve the Given Initial Value Problem: y’ = 5y + e^(4t), y(0) = 2
To solve the initial value problem using the Laplace transform, we start by applying the Laplace transform to both sides of the equation. The given first-order linear differential equation is: y’ = 5y + e^(4t) Taking the Laplace transform of the left-hand side, we have: L{y’} = sY(s) – y(0) where Y(s) is the Laplace […]
What is the solution set of 2x² + 15?
To find the solution set of the equation 2x² + 15 = 0, we start by isolating x². First, we subtract 15 from both sides: 2x² = -15 Next, we divide both sides by 2: x² = -7.5 At this point, we can see that x² is equal to a negative number. Since the square […]
Which of the following is a complex number: 7, 2, 3, 4, 9i, p?
A complex number is defined as a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which satisfies the equation i² = -1. In the options provided: 7, 2, 3, and 4 are all real numbers. 9i is a complex […]
Find the Curved Surface Area of a Cone of Slant Height l and Radius r
The curved surface area (CSA) of a cone can be calculated using the formula: Curved Surface Area (CSA) = πrl Where: π is a mathematical constant approximately equal to 3.14159. r is the radius of the base of the cone. l is the slant height of the cone. To understand why we use this formula, […]
How to Draw the Graph of y = x² and Solve x² – 1 = 0
To draw the graph of the function y = x², start by plotting a few key points. The function is a parabola that opens upwards. You can calculate the value of y for different values of x: If x = -2, then y = (-2)² = 4 If x = -1, then y = (-1)² […]
What is the 7th term of the geometric sequence 4, 20, 100?
To find the 7th term of the geometric sequence given by 4, 20, 100, we first need to determine the common ratio of the sequence. A geometric sequence is defined by a starting term and a common ratio, which is the factor by which we multiply each term to get to the next term. In […]
How do you solve for x in the equation 23x^2 = 14?
To solve the equation 23×2 = 14, you need to isolate x. Here’s how you can do it step by step: Start with the equation: 23×2 = 14. Next, divide both sides of the equation by 23 to isolate x2: x2 = 14 / 23. Now, simplify the right side: x2 = 14/23. The next […]