devyy

To find the two consecutive positive integers whose product is 812, we can define the integers as n (the lesser integer) and n + 1 (the greater integer). The equation representing their product can be expressed as: n(n + 1) = 812 This expands to: n2 + n – 812 = 0 This is a … Read more

To find the remainder when the polynomial 6x² + 11x + 7 is divided by 2x + 1, we can use the Remainder Theorem, which states that the remainder of the division of a polynomial f(x) by a linear divisor ax + b is equal to f(-b/a). In our case, we have: Polynomial: f(x) = … Read more

To find the approximate perimeter of the right triangle given the angles, we first need to determine the lengths of the sides of the triangle. We know that in a right triangle, the angles add up to 180 degrees. Therefore, we can find angle C: Angle A (90 degrees) + Angle B (25 degrees) + … Read more

To determine the acceleration of the car, we can use the formula for acceleration, which is defined as the change in velocity divided by the time taken. The initial velocity (u) of the car is 0 km/h, and the final velocity (v) is 60 km/h. The time (t) taken for this change is 10 seconds. … Read more

To determine the convergence or divergence of the series S = ∑n=1∞ 1/(n² + 5n + 6), we first need to analyze the behavior of the terms of the series as n approaches infinity. Step 1: Simplifying the Expression The denominator can be factored as follows: n² + 5n + 6 = (n + 2)(n … Read more

To find the equation of the line that passes through the points (1, 0) and (3, 4), we can follow these steps: Determine the slope (m): The slope formula is given by: m = (y2 – y1) / (x2 – x1) Here, we have the points: (x1, y1) = (1, 0) (x2, y2) = (3, … Read more

Understanding the Function f(x) = 3 tan(4x) To analyze the function f(x) = 3 tan(4x), we need to identify its period and phase shift. This function is a transformation of the basic tangent function. 1. Period of the Function The period of the basic tangent function, tan(x), is π. However, when the tangent function is … Read more

To find the general solution of the differential equation dy/dx = 2y e^(3x), we can begin by recognizing that this is a first-order linear ordinary differential equation. The equation can be rearranged to separate the variables: dy/y = 2 e^(3x) dx Now, we can integrate both sides. The left side, dy/y, integrates to ln|y|, and … Read more

To find the product of two prime numbers whose sum is 85, let’s first identify those prime numbers. The sum of two prime numbers, say p1 and p2, is given by: p1 + p2 = 85 By analyzing the primes less than 85, we find pairs of primes that add up to 85. Notably, one … Read more

To solve the differential equation y” + 14y’ + 4y = e^{x^2} using the method of undetermined coefficients, we should follow these steps: 1. Find the Complementary Solution (yc) The complementary solution is found by solving the associated homogeneous equation: y” + 14y’ + 4y = 0 We can start by finding the characteristic equation: … Read more