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To find an equivalent equation for w, we start with the initial equations provided. We know: Initial equation: 2x²y + 24 = w Another form provided: w = 8x²y + 2 To find an equivalent equation, we can set 2x²y + 24 equal to 8x²y + 2. So, we will rewrite the equation: 2x²y + … Read more

To solve the expression log4y + 9 log4(4) + log4(64), we’ll break it down step by step: Step 1: Simplifying Each Term 1. The term log4(4) is equal to 1 because any logarithm of a number to itself is 1. Therefore: log4(4) = 1 2. We can now simplify the expression: 9 log4(4) = 9 … Read more

When the circumcenter of a triangle lies inside the triangle, it indicates that the triangle is an acute triangle. To understand this better, let’s explore the concepts of circumcenter and the types of triangles. Circumcenter Explained: The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is also … Read more

To determine how many boxes of medicine weighing 4 kg 500 g can be loaded onto a can that can carry a maximum of 800 kg, we need to start by converting the box weight into a uniform measurement (either kg or g) for ease of calculation. 1. **Convert the box weight:** – 4 kg … Read more

A horizontal line is a line that runs parallel to the x-axis. The defining characteristic of a horizontal line is that it has a constant y-coordinate for all points along the line. In the case of the point (8, 7), the y-coordinate is 7. This means that for every x-value, the y-coordinate will always remain … Read more

The total differential of a function gives us insights into how the function changes with respect to its variables. In this case, we will find the total differential of the function z = x * cos(y) * cos(x). The total differential, denoted as dz, can be calculated using the following formula: dz = ∂z/∂x * … Read more

To construct a parallelogram given diagonals and the angle between them, follow these steps: Understanding dimensions: The diagonals of the parallelogram are 54 cm and 62 cm. Setting up your tools: You will need a ruler, a compass, and a protractor. Drawing the first diagonal: Use your ruler to draw a line segment of 54 … Read more

To find the equation of a quadratic graph defined by its focus and directrix, we can utilize the definition that the set of all points on the graph is equidistant from the focus and the directrix. Given: Focus: (6, 0) Directrix: y = 10 Let’s denote a point on the parabola as (x, y). The … Read more

To divide x to the 3/4 power by x to the 1/6 power, you can use the laws of exponents. According to the law of exponents, when you divide two numbers with the same base, you subtract their exponents. So, in this case, you have: x^(3/4) / x^(1/6) = x^(3/4 – 1/6) Next, you need … Read more

To determine whether the relation {1, 3, 4, 0, 3, 1, 0, 4, 2, 3} is a function, we need to understand what a function is in mathematical terms. A relation is considered a function if every input (or ‘x’ value) is associated with exactly one output (or ‘y’ value). In other words, for each … Read more