How to Find a Vector in the Same Direction as (2, 4, 2) with Length 6?
To find a vector that has the same direction as the vector (2, 4, 2) and a specified length of 6, we need to follow a few steps involving vector normalization and scaling. First, we determine the length (or magnitude) of the original vector (2, 4, 2). The magnitude is calculated using the formula: Magnitude […]
Multiply and Simplify the Product 3, 5i, 2, 4i
To multiply and simplify the expression 3, 5i, 2, and 4i, we will first multiply the real numbers together, and then the imaginary parts separately. 1. First, let’s look at the real numbers: 3 and 2. When we multiply these, we get: 3 * 2 = 6 2. Next, we will multiply the imaginary numbers: […]
A rectangular solid has sides of 6 cm, 8 cm, and 10 cm. What is its surface area?
The surface area of a rectangular solid (also known as a rectangular prism) can be calculated using the formula: Surface Area = 2(lw + lh + wh) where l is the length, w is the width, and h is the height. In this case, we have: Length (l): 10 cm Width (w): 6 cm Height […]
How do you find the unit tangent vector at a given point for the parametric function r(t)?
To find the unit tangent vector at a given point for the parametric function r(t) = (t^2, 2t, 1 + 3t^3 – 12t^2), we follow these steps: First, we need to compute the derivative of the vector function r(t) with respect to t, denoted as r'(t). Next, we evaluate r'(t) at the specific value of […]
If the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?
To find the ratio of x to y given that the ratio of 2x to 5y is 3 to 4, we can set up the equation based on the given ratio: We start by writing the ratio as: 2x / 5y = 3 / 4 Now, we can cross-multiply to eliminate the fraction: 2x * […]
Given that ABCD is a Rhombus, What is the Value of X?
In a rhombus, all four sides are of equal length, and opposite angles are equal. Additionally, the diagonals of a rhombus bisect each other at right angles. To find the value of X, we generally would need more information about the specific measurements or relationships involving the angle or length that includes X. For instance, […]
When 2x2y = 24 is solved for w, one equation is w = 8x2y + 2. Which of the following is an equivalent equation to find w?
To find an equivalent equation for w in the equation w = 8x2y + 2, we need to rearrange the original equation and isolate w. Starting with the equation: 2x2y = 24 We can first divide both sides of the equation by 2: x2y = 12 Next, we express the term x2y in relation to […]
Which of the following points does not lie on the graph of y = log3(x)?
To determine which points do not lie on the graph of the function y = log3(x), we need to analyze the properties of logarithmic functions. Logarithmic functions are defined only for positive values of x. This means that any point with an x-coordinate that is less than or equal to zero will not lie on […]
Find the slope of the line that passes through the points (3, 2) and (2, 2)
To find the slope of a line that passes through two points, we use the formula: slope (m) = (y2 – y1) / (x2 – x1) In this case, we have the points (3, 2) and (2, 2). Let’s denote: (x1, y1) = (3, 2) (x2, y2) = (2, 2) Now we can substitute these […]
How do you divide x to the 3 fourths power by x to the 1 sixth power?
To divide x to the 3 fourths power by x to the 1 sixth power, you can use the properties of exponents. When dividing two expressions that have the same base, you subtract the exponent of the denominator from the exponent of the numerator. So, you start with: x^(3/4) รท x^(1/6) Using the exponent rule: […]