devyy To express x as a function of y when we know that x is 7 more than y, we can start by understanding the relationship between the two variables. The statement “x is 7 more than y” can be translated into a mathematical equation. We can represent this relationship as: x = y + 7 … Read more
To simplify the expression 7 log3 k + 6 log3 m + 9 log3 n, we can make use of the properties of logarithms. The key properties we will use are: Product Rule: logb (xy) = logb x + logb y Power Rule: logb (xn) = n logb x First, we can apply the Power … Read more
To simplify the expression cos(21°) tan²(2°), we start by breaking it into its components. Let’s first recall the definition of the tangent function: tan(θ) = sin(θ) / cos(θ) Therefore, we can write: tan²(2°) = (sin(2°) / cos(2°))² = sin²(2°) / cos²(2°) Now, substitute this into the original expression: cos(21°) tan²(2°) = cos(21°) * (sin²(2°) / … Read more
Calculating the Surface Area of a Rotated Curve To find the surface area obtained by rotating the curve defined by the equation y = 8x² about the x-axis from x = 0 to x = 8, we will use the formula for the surface area of a revolution: A = 2π × ∫ab y × … Read more
To find the formula for the nth term of an arithmetic sequence, we need to determine its first term and the common difference. An arithmetic sequence is one where each term after the first is generated by adding a constant (the common difference) to the previous term. Given: a20 = 240 a15 = 170 The … Read more
To solve the equation 15 – 4 – 7x + 9 = 0, we start by simplifying the left side. First, perform the arithmetic operations: Combine the constant terms: 15 – 4 + 9 This simplifies to 20. The equation now looks like: 20 – 7x = 0 Next, isolate the variable x: Subtract 20 … Read more
Finding the Exact Values of Trigonometric Functions To find the exact values of the given trigonometric functions, let’s calculate each one step by step: 1. Calculate sin(4π/3) The angle 4π/3 radians is in the third quadrant. To find sin(4π/3): The reference angle is: 4π/3 – π = π/3. In the third quadrant, the sine value … Read more
To solve the equation їx/4 + 2x = 14 – 4ї, we first simplify the right side of the equation: Step 1: Simplify the right side: 14 – 4 = 10 So the equation becomes: x/4 + 2x = 10 Step 2: Eliminate the fraction by multiplying the entire equation by 4: 4 * (x/4) … Read more
Solving the Equation: 3x + 4 = 4x + 1 + 2 To solve the equation 3x + 4 = 4x + 1 + 2, follow these steps: First, simplify the right side of the equation: 4x + 1 + 2 = 4x + 3 Now, your equation looks like this: 3x + 4 = … Read more
To find the general solution to the differential equation xdydx = 4y + x3 + x, we can begin by rearranging the terms and separating the variables. First, we rewrite the equation: xdydx – 4y = x3 + x. This can be reorganized as: xdydx = 4y + x3 + x. Next, we divide both … Read more