find the magnitude of the resultant vector.\n(25.6, 7.7) |→r| = ?\n→v\n→w\n(11, -9.8)\nround to the nearest…

Explanation:

Step1: Find the resultant vector components

To find the resultant vector (\vec{R}), we add the corresponding components of vectors (\vec{v}) and (\vec{w}). The components of (\vec{v}) are ((25.6, 7.7)) and the components of (\vec{w}) are ((11, -9.8)). So, the (x)-component of (\vec{R}) is (25.6 + 11 = 36.6) and the (y)-component of (\vec{R}) is (7.7+(-9.8)=7.7 - 9.8=-2.1). Thus, (\vec{R}=(36.6, - 2.1)).

Step2: Calculate the magnitude of (\vec{R})

The magnitude of a vector ((x,y)) is given by the formula (|\vec{R}|=\sqrt{x^{2}+y^{2}}). Substituting (x = 36.6) and (y=-2.1) into the formula, we get (|\vec{R}|=\sqrt{(36.6)^{2}+(-2.1)^{2}}).

First, calculate ((36.6)^{2}=36.6\times36.6 = 1339.56) and ((-2.1)^{2}=(-2.1)\times(-2.1) = 4.41). Then, add these two results: (1339.56 + 4.41=1343.97). Now, take the square root of (1343.97): (\sqrt{1343.97}\approx36.65) (rounded to the nearest hundredth).

Answer:

(36.65)