What is the value for fx 42x 100 when x = 2?
To find the value of fx 42x 100 when x = 2, we first need to replace x with 2 in the expression. We have: fx = 42x * 100 Substituting x = 2: fx = 42 * 2 * 100 Now we can calculate: 42 * 2 = 84 Next, we multiply 84 by […]
How do you find an explicit solution of the initial value problem x^2 dy/dx = y(xy + 1) – 5?
To solve the initial value problem given by the equation x2 dy/dx = y(xy + 1) – 5, we first rearrange the equation into a more workable form. We can rewrite the equation as: dy/dx = (y(xy + 1) – 5)/x2 This is a first-order differential equation. We can attempt to separate variables or apply […]
Find the slope of 9x + 3y = 15
To find the slope of the equation given, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m represents the slope. The equation provided is: 9x + 3y = 15 First, we’ll solve for y: Subtract 9x from both sides: 3y = -9x + 15 Now, divide […]
How do I write the quadratic function in the form f(x) = a(x – h)² + k and find the vertex of the graph f(x) = x² – 8x – 20?
To write the quadratic function in the form f(x) = a(x – h)² + k, we need to complete the square for the given function. The original function is: f(x) = x² – 8x – 20. Step 1: Organize the quadratic and linear terms. We can rewrite the function as: f(x) = (x² – 8x) […]
How to Write an Equation of the Line That Passes Through the Given Points
To write the equation of a line that passes through two given points, you need to follow a few steps. First, identify the coordinates of the two points. Let’s say these points are (x1, y1) and (x2, y2). For example, consider the points (2, 3) and (4, 7). Next, calculate the slope (m) of the […]
Find the Exact Values of the Six Trigonometric Ratios of the Angle 8 in the Triangle
To find the exact values of the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, and cotangent) for an angle of 8 degrees, we can use the definitions of these ratios in relation to a right triangle. First, we recall the definitions: Sine (sin): Ratio of the length of the opposite side to the hypotenuse. […]
Ramesh bought 2 boxes for Rs 1300: What is the cost of each box?
To find the cost of each box, let’s denote the cost price of the first box as C1 and the second box as C2. According to the problem, we know: C1 + C2 = 1300 Additionally, Ramesh sold one box at a profit of 20% and another at a loss of 12%. The selling prices […]
Find the height of a square pyramid that has a volume of 12 cubic feet and a base length of 3 feet
To find the height of a square pyramid, we can use the formula for the volume of a pyramid: Volume = (1/3) × Base Area × Height In this case, the base of the pyramid is a square. The area of the base (A) can be calculated as: Base Area = Side Length × Side […]
How many solutions will this system of equations have: y = 3 + 5x and y = 3 + 5x?
To determine how many solutions this system of equations has, we first need to analyze the two equations given: 1. y = 3 + 5x 2. y = 3 + 5x Both equations are identical, which means they represent the same line on a graph. Since they are the same line, any point on this […]
HCF of two numbers a and b is 5 and their LCM is 200. Find the product of a and b.
To find the product of two numbers a and b when given their HCF (Highest Common Factor) and LCM (Lowest Common Multiple), we can use the relationship: Product of a and b = HCF(a, b) × LCM(a, b) In this case, we know that the HCF of a and b is 5, and their LCM […]