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To approximate the value of y in the equation 10y = 6 using the graph of fx = log10(x), we first need to isolate y in the equation. 1. **Rearranging the Equation:** We start by dividing both sides by 10. This gives us: y = 6 / 10 which simplifies to y = 0.6. 2. … Read more

Calculating the Surface Area To find the surface area of a rectangular solid (also known as a rectangular prism), you can use the formula: Surface Area = 2(ab + bc + ac) Where: a = length = 6 cm b = width = 8 cm c = height = 10 cm Now, we can calculate … Read more

Finding the Unit Tangent Vector To find the unit tangent vector t at a specific point defined by a parameter t using the given parametric equations, follow these steps: Step 1: Identify the Parametric Equations The curve is defined by the position vector: r(t) = (t^2, 2t, 1 + 3t + 13t^3 + 12t^2) Step … Read more

To find the sum of the first six terms of the geometric series given by the numbers 2, 6, 18, and 54, we first need to identify the first term and the common ratio of the series. The first term ( a) in this series is 2. To find the common ratio ( r), we … Read more

To determine for which values of x the series Σ (x * (3^n) / (2^n)) converges, we can rewrite the expression inside the summation. The series can be expressed as: Σ (x * (3^n) / (2^n)) = x * Σ (3/2)^n Now, we analyze the series Σ (3/2)^n. This is a geometric series with a … Read more

To determine the ratio of x to y, let’s start with the information provided. We know that the ratio of 2x to 5y is given as: 2x : 5y = 3 : 4 This can be expressed as the equation: 2x/5y = 3/4 Now we can cross-multiply to eliminate the fractions: 4(2x) = 3(5y) This … Read more

Multiplying two 2-digit numbers might seem daunting at first, but with a systematic approach, it can be quite straightforward! Here’s a step-by-step guide to help you through the process. Step 1: Write the Numbers Vertically Start by writing the two numbers you want to multiply one above the other, just like you would with standard … Read more

A gallon is a unit of volume that is commonly used in the United States and other countries. The conversion between gallons and liters is important for various applications, such as cooking, automotive, and scientific contexts. To answer your question, there are approximately 3.78541 liters in a US gallon. This means that if you have … Read more

To find a vector that has the same direction as another vector but with a different magnitude, we follow these steps: Identify the original vector: Here, we are given the vector (2, 4, 2). Calculate the magnitude of the original vector: The magnitude (length) of a vector is calculated using the formula: Magnitude = √(x² … Read more