Here's the transcribed and detailed explanation of the content shown in the image for an educational website:---**Title: Calculating the Direction and Magnitude of Vectors****Objective:**Understand how to determine the direction and magnitude of a given vector.**Problem Statement:**Given the vector **A** with components:\[ \vec{A} = (26 \, \text{m} \, \hat{i}) + (-8.0 \, \text{m} \, \hat{j}) \]**Part A: Finding the Direction**Calculate the direction of the vector **A** in degrees, measured counterclockwise from the positive x-axis.**Instructions:**1. Find the angle \( \theta_A \) by using the arctangent function, considering the signs of the vector components. \[ \theta_A = \tan^{-1} \left( \frac{A_y}{A_x} \right) \] Where: \[ A_x = 26 \, \text{m} \] \[ A_y = -8.0 \, \text{m} \] 2. Input your answer in degrees to the nearest whole number.**Interface Example for Answer Input:**```[θ_A = ? \degree] counterclockwise from the positive x-axis [Submit] [Request Answer]```**Part B: Finding the Magnitude**Express the magnitude of the vector **A** in meters, using two significant figures.**Instructions:**1. Calculate the magnitude \( |\vec{A}| \) using the Pythagorean theorem. \[ |\vec{A}| = \sqrt{A_x^2 + A_y^2} \]2. Enter your answer in meters, rounded to two significant figures.**Interface Example for Answer Input:**```[|\vec{A}| = ? m] [Submit] [Request Answer]```**Resource:**The problem is sourced from Pearson's educational materials, which provide extensive resources for learning vector mathematics.---**Graphical Explanation:**- There are no explicit graphical diagrams provided in the image to elaborate on.- The input interface for both angles and magnitude calculations is shown, guiding learners on where to enter their answers.By following these steps, students can accurately determine the direction and magnitude of vector quantities ### Understanding Road Grades**Definition and Example:**- A **One-Percent Grade** refers to a road that rises 1 foot for every 100 feet traveled horizontally. This type of grade is an example of a gentle incline in road engineering.- Portions of the Lewiston grade, near Lewiston, Idaho, have a more significant 6% grade, indicating a steeper incline where the road rises 6 feet for every 100 feet of horizontal travel.### Problem Statement on Calculating the Incline Angle**Part A:**- **Question:** At what angle is this road inclined above the horizontal? Express your answer using one significant figure.- **Response Box:** There is a box provided for entering the angle (θ) in degrees.- **Submission Process:** - Input an answer, and click 'Submit.' - Previous answers and requests for the correct answer can be managed through the provided buttons. - The system issues feedback on the correctness of the answer, indicating the number of attempts remaining. For instance, "Incorrect; Try Again; 7 attempts remaining" suggests the answer given was incorrect, and seven attempts are left.### Text Content:"A One-Percent GradeA road that rises 1 ft for every 100 ft traveled horizontally is said to have a 1 % grade. Portions of the Lewiston grade, near Lewiston, Idaho, have a 6 % grade."**Interface Explanation:**- There's a section to the right for answering the question, which includes: - **Input Field:** A designated space to input the angle (θ). - **Buttons:** There are functional buttons for mathematical inputs (including symbols for degrees and other operations). - **Submit Button:** Used to submit the answer for evaluation. - **Previous Answers/Request Answer:** Options to go back and view previous submissions or request the correct answer.This setup helps students understand various grades of a road and practice calculating the angles of inclines.

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Uploaded: 2024-03-05T11:56:34.000Z
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Description: Here's the transcribed and detailed explanation of the content shown in the image for an educational website:---**Title: Calculating the Direction and Magnitude of Vectors****Objective:**Understand how to determine the direction and magnitude of a g