Auto Loan Apr Calculator - RoadRUNNER Motorcycle Touring & Travel Magazine

🔗 Related Articles You Might Like:

📰 Solution: The matrix $\mathbf{M}$ is constructed by placing the images of the standard basis vectors as its columns. Thus, $\mathbf{M} = \begin{pmatrix} 2 & 3 \\ -1 & 4 \end{pmatrix}$. Verifying, $\mathbf{M} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$ and $\mathbf{M} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$, confirming correctness. $\boxed{\begin{pmatrix} 2 & 3 \\ -1 & 4 \end{pmatrix}}$ 📰 Question: An environmental consultant models a river's flow as the line $y = -\frac{1}{2}x + 5$. Find the point on this line closest to the pollution source at $(4, 3)$. 📰 Solution: The closest point is the projection of $(4, 3)$ onto the line. The formula for the projection of a point $(x_0, y_0)$ onto $ax + by + c = 0$ is used. Rewriting the line as $\frac{1}{2}x + y - 5 = 0$, we compute the projection. Alternatively, parametrize the line and minimize distance. Let $x = t$, then $y = -\frac{1}{2}t + 5$. The squared distance to $(4, 3)$ is $(t - 4)^2 + \left(-\frac{1}{2}t + 5 - 3\right)^2 = (t - 4)^2 + \left(-\frac{1}{2}t + 2\right)^2$. Expanding: $t^2 - 8t + 16 + \frac{1}{4}t^2 - 2t + 4 = \frac{5}{4}t^2 - 10t + 20$. Taking derivative and setting to zero: $\frac{5}{2}t - 10 = 0 \Rightarrow t = 4$. Substituting back, $y = -\frac{1}{2}(4) + 5 = 3$. Thus, the closest point is $(4, 3)$, which lies on the line. $\boxed{(4, 3)}$ 📰 Government Announces Online Games Fun And It Raises Alarms 📰 Stock Amgn Clickbait Will This Stock Skyrocket See What Investors Are Saying 8113062 📰 Crazygamres 📰 Find The Value Of Fraca3B3 Fracb3A3 1271054 📰 Payment Processing Fees 📰 Social Security Wep Gpo Boost 2576493 📰 Greatest Comic Book Characters 📰 You Wont Believe What Axbety Is Doing In The Online Casino World 1349286 📰 Usf Saint Petersburg 4545207 📰 Unlock Secret Trick That Holds Lag Bolts Like Iron 7886677 📰 Best High Interest Savings Accounts 📰 Serious Dev Grab The Sql Server 2022 Developer Editionfast Download Powerful Tools Await 5952793 📰 Low Book Sales 3697878 📰 How To Get Serial Number Of Laptop 📰 Switch Banks