devyy To find the derivative dy/dx for the given equation, we first need to rewrite the expression in terms of known variables. The function provided is y(t) = sin(t) + t2 + 3t. This means we need to differentiate y with respect to t. The process of differentiation involves applying the rules of calculus: Derivative of … Read more
To determine the surface area of a cube when you know its volume, you can follow these straightforward steps: The volume of a cube is given by the formula: Volume (V) = side³ In this case, we have a volume of 8 cubic units: V = 8 To find the length of one side (s) … Read more
To find the answer, we need to break down the question into smaller steps. Let’s tackle it step by step: Calculate one ninth of 900: To find one ninth of 900, we divide 900 by 9: 900 ÷ 9 = 100 Calculate one fourth of the result: Now, we take the result from the previous … Read more
The given sequence is 58, 47, 36, 25. To find the next term in this sequence, we need to analyze the pattern or rule governing the changes between the terms. Let’s look at the differences between the terms: 47 – 58 = -11 36 – 47 = -11 25 – 36 = -11 We can … Read more
A quadratic function is typically expressed in the form of: f(x) = a(x – r1)(x – r2) where r1 and r2 are the roots (or zeros) of the function, and a is a non-zero constant that affects the vertical stretch or compression of the graph. In your case, the real zeros are given as x … Read more
The volume of a rectangular prism can be calculated using a simple formula. The formula is: Volume (V) = Length (L) × Width (W) × Height (H) In this formula, you will need to know three dimensions of the prism: Length (L): This is one side of the base of the prism. Width (W): This … Read more
To calculate the volume of a cylinder, you can use the formula: V = πr²h Where: V is the volume of the cylinder, r is the radius of the base, h is the height of the cylinder, and π (Pi) is approximately 3.14159. In this case, you’re given that the height h is twice the … Read more
Determining Values of m for f(x) = x^m To find the values of m for which the function f(x) = x^m is a solution to the given equations, we need to analyze each equation separately. We will perform this by substituting f(x) into each equation and simplifying to see under what conditions the equations hold … Read more
To determine the potential roots of the polynomial function 6x³ + 19x² + 15x – 28, we can utilize a few mathematical tools and techniques. One common approach is the Rational Root Theorem, which suggests that any rational solution, or root, of a polynomial equation can be expressed as \\frac{p}{q}\, where: p is a factor … Read more
Applying the properties of rational numbers can greatly enhance our ability to solve mathematical problems and real-world scenarios efficiently. There are several properties to consider, including: Addition of Rational Numbers: When adding two rational numbers, such as \/frac{a}{b} + \/frac{c}{d}, you can find a common denominator (bd) to simplify the process. Thus, the sum can … Read more