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The number 78 x 1012 can initially seem a bit confusing when it comes to determining the significant figures. Let’s break it down step by step. First, we need to notice that in the number 78, both of the digits (7 and 8) are considered significant because: All non-zero digits are always significant. There are … Read more

To determine the center, vertices, and foci of the ellipse given by the equation 2x² + 9y² = 18, we need to first rewrite it in the standard form of an ellipse equation. 1. **Standard Form Conversion**: Start by dividing all terms in the equation by 18 to make the right side equal to 1: … Read more

To graph the first six terms of a sequence where the first term ( a1) is 3 and the common difference (d) is 10, you will first need to identify the sequence itself. This type of sequence is known as an arithmetic sequence, which is defined by the formula: an = a1 + (n – … Read more

To find the value of x in the equation y = 192 + x, we can substitute y with 32. So the equation becomes: 32 = 192 + x Next, we want to isolate x. To do this, we need to move 192 to the left side of the equation. We can do this by … Read more

To determine a factor of the polynomial function f(x) given its roots, we start by recognizing the relationship between roots and factors of a polynomial. A root of a polynomial f(x) is a value of x that makes the polynomial equal to zero. If r is a root, then (x – r) is a factor … Read more

To evaluate the expression 2r² + 3s³ + 2r⁴ + 2r given the values r = 2, s = 3, and t = 5, we can follow these steps: First, substitute the value of r into the expression: 2(2)² + 3(3)³ + 2(2)⁴ + 2(2) Next, calculate each term: 2(2²) = 2(4) = 8 3(3³) … Read more

To find a vector that has the same direction as the given vector (6, 6, 2) but with a different length (specifically, a length of 6), you can follow these steps: Calculate the length (magnitude) of the original vector: The formula for the magnitude of a vector (x, y, z) is: Magnitude = √(x² + … Read more

To identify the three whole numbers that occur just before 10001, we simply need to subtract one from 10001 repeatedly. The first number before 10001 is: 10000 The second number before that is: 9999 The third number before that is: 9998 Therefore, the three whole numbers occurring just before 10001 are 10000, 9999, and 9998.

To find the value of the expression 42x 100 when x = 2, we first need to substitute the value of x into the expression. We start with the expression: 42x 100 Substituting x = 2 into the expression gives: 42(2) 100 Next, we perform the multiplication: 42 * 2 = 84 Now we incorporate … Read more

To solve the initial value problem given by the equation: x² rac{dy}{dx} + yxy = 1 we start by rearranging the equation to isolate the derivative: rac{dy}{dx} = rac{1 – yxy}{x²} This is a first-order differential equation and can be simplified further. To solve it, we can use the method of separation of variables. First, … Read more