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Find the magnitude of the vector \( <5,-3> \) \( \begin{array}{l}4 \\ 5.8 \\ 6.1 \\ 5.2\end{array} \)

Ask by Young Rodriguez. in the United States
Feb 26,2025

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The magnitude of the vector <5, -3> is approximately 5.8.

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To find the magnitude of the vector \( <5, -3> \), you can use the formula for the magnitude of a vector, which is given by: \[ \text{Magnitude} = \sqrt{x^2 + y^2} \] For the vector \( <5, -3> \): \[ \text{Magnitude} = \sqrt{5^2 + (-3)^2} = \sqrt{25 + 9} = \sqrt{34} \approx 5.83 \] So, the closest option from your list is \( 5.8 \).

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1.3.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) (2) 1.4 CASE 3: \( r=1 \) 1.4.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=1 ? \] 1.4.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) 1.5 CASE 4: \( r=-1 \) 1.5.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=-1 ? \] 1.5.2 Do the sums above approach some finite particular number as \( n \rightarrow \infty \) i.e. is the sequence divergent or convergent? 1.6 CASE 5: \( -1<r<1 \) REQUIREMENTS: - One A4 papers - Provided grid 1.6.1 Write THREE possible values of \( r \) such that \( -1<r<1 \). 1.6.2 Step 1. Cut the A4 size paper along the longest side into two equal Rectangles and define their areas to be 16 unit \( ^{2} \). 1.6.3 Step 2. Place one half of the rectangle in Step 1 on the desktop and cut the other half along the longest side in to two equal rectangles. 1.6.4 Step 3. Place one half of the rectangle in Step 2 on the desktop and cut the other half along the longest side into two equal rectangles. 1.6.5 Step 4. Continue with the procedures from Step 3 until you find it too difficult to fold and cut the piece of paper you are holding. 1.6.6 Step 5. The first piece of paper you placed on the desktop has an area of \( \frac{1}{2} \) the area of the A4. The second piece of paper has an area of \( \frac{1}{4} \) the area of the A4. Write the areas of the next three pieces of paper. (3) (I) 1.6.7 Explain why these areas form a geometric sequence.
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