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To determine how far a man has run in an hour and a half at a speed of 8 miles per hour, we can use the formula for distance: Distance = Speed × Time In this case: Speed = 8 miles per hour Time = 1.5 hours (which is equivalent to 1 hour and 30 … Read more

The volume of a cone is calculated using the formula: V = \frac{1}{3} \pi r^2 h Where: V = Volume of the cone r = Radius of the base of the cone h = Height of the cone In this scenario, both the radius (r) and the height (h) are increasing at a constant rate … Read more

To use the chain rule to find dz/dt for the function z = xy3 + x2y + xt2y(t2 + 1), we must first identify all the dependent variables and how they relate to t. In this function, z depends on x and y, both of which are functions of t. 1. **Identify the Variables:** We … Read more

To find the probability of getting between 40 and 60 heads when flipping a fair coin 100 times, we can use the normal approximation to the binomial distribution. Since the number of flips (n) is large, this approximation is quite effective. 1. **Understanding the Binomial Distribution**: Each flip of the coin has two possible outcomes: … Read more

To solve the quadratic equation 2x² + 16x + 34 = 0, we can use the quadratic formula, which is: x = (-b ± √(b² – 4ac)) / (2a) In our equation, the coefficients are: a = 2 b = 16 c = 34 Let’s plug these values into the quadratic formula step by step: … Read more

To write the number 7452283 in the international system of numeration, we can break it down into its place values. The international system, also known as the place value system, helps us understand the significance of each digit in a number based on its position. 7,000,000 – This digit (7) is in the millions place. … Read more

To find the x and y intercepts of the graph of the equation y = x² + 3x + 10, we can follow these steps: X-Intercepts The x-intercepts occur where the graph crosses the x-axis. At these points, the value of y is zero. To find the x-intercepts, we set y to zero and solve … Read more

To solve the quadratic equation 3x² + 2x + 7 = 0, we will use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a) In our equation, the coefficients are: a = 3 b = 2 c = 7 Now, we will first calculate the discriminant, which is b² – 4ac: b² … Read more

To determine the intervals where a function f is concave up or concave down, you need to follow a few mathematical steps that involve analyzing the second derivative of the function. Here’s a step-by-step guide: Find the first derivative: Start by calculating the first derivative of the function f, denoted as f’. This will give … Read more