devyy

To find the ratio of the radii of two spheres given that their volumes are in a ratio of 18, we can use the formula for the volume of a sphere: Volume of a sphere: V = \frac{4}{3} \pi r^3 Let the volumes of the two spheres be V_1 and V_2. According to the problem: … Read more

Understanding the Problem: We need to find the rate of increase of the radius of a spherical ball whose volume is growing at a constant rate. Given are: Volume increase rate: 4π cc/sec Volume at the point of interest: 288π cc Volume of a Sphere: The volume V of a sphere is given by the … Read more

To find the point on the line y = 2x + 1 that is closest to the point (5, 2), we can follow several steps: 1. Understanding the Problem We need to minimize the distance between a point (x, y) on the line and the point (5, 2). The distance D between two points is … Read more

To solve the system of equations given by: Equation 1: 2y + 6 = 6y + x Equation 2: x = 18 We start by substituting the value of x from Equation 2 into Equation 1. Substituting x = 18 into Equation 1: 2y + 6 = 6y + 18 Now, we will simplify this … Read more

Solving the System of Equations Let’s solve the given system of equations step-by-step: Equation 1: 2x + 3y + z = 1 Equation 2: 3x + y + 2z = 12 Equation 3: x + 2y + 3 = 5 Step 1: Simplify Equation 3 First, let’s simplify Equation 3: x + 2y = 5 … Read more

To find the sum of the arithmetic sequence given the first few terms (3, 9, 15) and the total number of terms (36), we can follow a simple process. An arithmetic sequence is defined by a starting number (the first term) and a common difference between consecutive terms. First, let’s identify the first term and … Read more

To calculate the distance covered by a wheel after a certain number of revolutions, we can use the formula: Distance = Number of Revolutions × Circumference of the Wheel. First, we need to calculate the circumference of the wheel. The circumference (C) of a circle is given by the formula: C = π × D … Read more

To find the area of the circle given its circumference, we can follow a few straightforward steps. The formula for the circumference (C) of a circle is: C = 2πr where r is the radius of the circle. In this case, we know that: 5π = 2πr Next, we can simplify this equation by dividing … Read more

To solve the system of equations y = x + 2 and y = 2x + 7, you can use either graphing or creating a table of values. Here’s how to do both: Method 1: Graphing 1. **Graph the first equation**: For the equation y = x + 2, you can easily find two points. … Read more

To find the height of a pile of 25 books, we first need to determine the thickness of each book in a consistent unit, preferably in centimeters or meters. The thickness of each book is given as 3 cm and 5 mm. To convert everything into centimeters: 1 cm = 10 mm, so 5 mm … Read more