devyy To find the terminal point (px, y) on the unit circle for the angle t = 3π/4, you can follow these steps: Understand the Unit Circle: The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system. Any point on this circle can be … Read more
To solve for the value of v in the inverse variation equation given by p = 8/v, we first need to set p equal to the value provided, which is 4. So, we substitute p with 4: 4 = 8/v Next, to isolate v, we can multiply both sides of the equation by v to … Read more
To identify the values that create ordered pairs satisfying the equation 3x + 5y = 205y + x2, we first need to rearrange the equation into a more standard form. Starting with the original equation: 3x + 5y = 205y + x2 We can move all terms to one side of the equation: x2 – … Read more
When we say that the ratio of the length to the breadth of a rectangle is 53, we are essentially indicating how the two sides of the rectangle relate to each other in terms of their size. This ratio can be expressed mathematically as: Length : Breadth = 53 : 1 This means that for … Read more
The classification of the expression 3×4 + 9×3 + 3×2 + 6 involves examining its terms and determining its degree and leading coefficient. This expression is a polynomial since it is a sum of terms, each composed of a constant coefficient and a variable raised to a non-negative integer exponent. The polynomial can be classified … Read more
To determine the fraction of prime numbers among the natural numbers from 2 to 12, we first need to identify which of these numbers are prime. The natural numbers between 2 and 12 are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Next, we identify the prime numbers in this range. … Read more
To find the inverse of the function f(x) = x² – 25, we will follow a systematic approach. Step 1: Replace f(x) with y. We start by rewriting the function as: y = x² – 25 Step 2: Swap x and y. To find the inverse function, we swap the roles of x and y: … Read more
Proving the Derivative of csc(x) * csc(x) * cot(x) To prove that the derivative of the function y = csc(x) * csc(x) * cot(x) is computed correctly, we will use the product rule and the chain rule of differentiation. The derivative of the product of multiple functions can be calculated using the general product rule. … Read more
Determining the Surface Area of an Open Box An open box with a square base means that it has four vertical sides and one top, but no bottom. To find the surface area as a function of the side length of the base, denoted as x, we’ll follow a few steps to derive the formula. … Read more
The quadratic equation 2×2 + 4x + 12 = 0 has several important characteristics that can be analyzed using the properties of quadratic equations. 1. **Standard Form**: The equation is in the standard form of a quadratic equation, which is ax2 + bx + c = 0, where: a = 2 b = 4 c … Read more