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To find the radius of a circle where the area and circumference are equal, we can start with the formulas for area and circumference: Area (A) = πr² Circumference (C) = 2πr We want to set these two equations equal to each other: A = C πr² = 2πr Next, we can simplify by dividing … Read more

To find the quotient of x³ divided by 8x², we need to simplify the expression. Here’s the step-by-step breakdown of the process: Write the expression: We start with the expression x³ ÷ 8x². Divide the coefficients: The coefficient of x³ is 1 (since it’s not explicitly written), and the coefficient of 8x² is 8. Therefore, … Read more

To find the area of a triangle, you can use the following formula: Area = (base × height) / 2 In this case, you have: Base = 9 inches Height = 14 inches Now, plug in the values: Area = (9 inches × 14 inches) / 2 Calculating this: Area = (126 inches²) / 2 … Read more

To evaluate the double integral d = ˆ{x^2 + 6y} dA, where the region of integration is bounded by y = x, y = x^3 and x = 0, we first need to determine the limits of integration by finding the points of intersection of the curves. 1. **Finding Points of Intersection:** To find where … Read more

The area of a trapezoid can be calculated using the following formula: Area = (1/2) * (b1 + b2) * h Where: b1: Length of the first base (the top side of the trapezoid). b2: Length of the second base (the bottom side of the trapezoid). h: Height of the trapezoid (the perpendicular distance between … Read more

To find the angles M1 and M3 in a kite, even when the diagram is not drawn to scale, you need to apply some basic properties of kites and the geometric relationships that apply to them. Here’s how you can do it step by step: Understand the Properties of a Kite: A kite is a … Read more

To calculate the sales tax rate, you can use the following formula: Sales Tax Rate = (Sales Tax / Cost of Item) x 100% In this case, the cost of the shirt is $3,499, and the sales tax is $210. Plugging these values into the formula gives us: Sales Tax Rate = ($210 / $3,499) … Read more

When reflecting a point across the x-axis, we only change the sign of the y-coordinate. The x-coordinate remains the same. For the point (1, 6): The x-coordinate is 1. The y-coordinate is 6. After reflection, it becomes -6. Thus, the new coordinates after reflection across the x-axis will be: (1, -6) So, the coordinates of … Read more

Finding the x-coordinates of the solutions To solve for the x-coordinates of the solutions to the system of equations given by: x² + y² = 36 y = x + 6 we can substitute the second equation into the first. Here are the steps: Start with the first equation: x² + y² = 36. Next, … Read more

To find the equation of a line that is perpendicular to the given line and passes through the specified point, follow these steps: Step 1: Determine the slope of the original line The given line’s equation is in the slope-intercept form: y = mx + b, where m is the slope. Here, the slope of … Read more