devyy To find the equation of the tangent plane to the given surface at the specified point, we can follow these steps: 1. Identify the surface function: The surface is given by the equation z = 3y² – 2x² + x + 2. 2. Compute the partial derivatives: We need the partial derivatives of the function … Read more
To tackle the expression find a b 9a 7b a and a b a 9i 8j 7k b 7i 9k, we need to break it down into manageable pieces. First, let’s understand what a and b signify. These often represent variables in algebra, standing in for unknown values. In various contexts within mathematics, they could … Read more
In an isosceles right triangle, by definition, two sides are of equal length, and the angle opposite these sides is the right angle, measuring 90 degrees. The other two angles in the triangle must be equal since it is isosceles. To find the measure of these base angles, we can use the property that the … Read more
To rewrite the quadratic equation y = 3x² + 22x + 52 in vertex form, we need to complete the square. The vertex form of a quadratic equation is expressed as y = a(x – h)² + k, where (h, k) is the vertex of the parabola. Here’s a step-by-step process on how to complete … Read more
When we say that two scalene triangles are similar with a scale factor of 52, it means that all their corresponding angles are equal, and their sides are proportional to each other by a ratio of 52:1. This implies several important properties and characteristics about these triangles. Firstly, the fact that the triangles are scalene … Read more
Finding the Length of the Curve y = ln(1 + x2) from x = 0 to x = 1.6 The length of a curve defined by a function y = f(x) from x = a to x = b can be calculated using the formula: L = ∫ab √(1 + (f'(x))2) dx Step 1: Define … Read more
To find the remainders when dividing the polynomials ax³ + 3x² + 3 and 2x³ + 5x by x – 4, we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial f(x) by x – c is simply f(c). Step 1: Calculate for the first polynomial … Read more
To find the equation of a line that is perpendicular to the given line xy = 7 and passes through the point (1, 1), we can follow these steps: Determine the slope of the given line: First, we need to rewrite the equation xy = 7 in a more familiar slope-intercept form (y = mx … Read more
The smallest 5-digit number is 10000. To express this number using its prime factors, we can break it down systematically. First, we start by finding the prime factorization of 10000. The process involves continuously dividing the number by the smallest prime numbers until we reach 1. Here’s how the prime factor tree diagram for 10000 … Read more
To solve for tan(60) * tan(60), we first need to determine the value of tan(60 degrees). The tangent of 60 degrees is a well-known value in trigonometry: tan(60 degrees) = √3 or approximately 1.732. Now, if we calculate tan(60) * tan(60): tan(60) * tan(60) = (√3) * (√3) This simplifies to 3. Therefore, tan(60) * … Read more