$$ 1 \leftarrow $$ Find the point P on the line $$ \mathrm{y}=4 \mathrm{x} $$ that is closest to the point $$ (34,0) $$. What is the least distance between P and $$ (34,0) $$ ? Let D be the distance between the two points. What is the objective function in terms of one number, x ? $$ \mathrm{D}=\square $$ (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) The point P on the line $$ \mathrm{y}=4 \mathrm{x} $$ that is closest to the point $$ (34,0) $$ is (Type an ordered pair.) The least distance between P and $$ (34,0) $$ is approximately (Round to the nearest tenth as needed.)

Question

UpStudy AI · Accepted Answer

To find the distance $$ \mathrm{D} $$ between a point $$ P(x, 4x) $$ on the line $$ \mathrm{y} = 4\mathrm{x} $$ and the point $$ (34, 0) $$, we can use the distance formula:

$$
\mathrm{D} = \sqrt{(x - 34)^2 + (4x - 0)^2}
$$

**Objective Function in Terms of $$ x $$:**

$$
\boxed{ \mathrm{D} = \sqrt{(x - 34)^2 + (4x)^2} }
$$
The distance $$ \mathrm{D} $$ between point $$ P(x, 4x) $$ on the line $$ \mathrm{y} = 4\mathrm{x} $$ and the point $$ (34, 0) $$ is given by: $$ \mathrm{D} = \sqrt{(x - 34)^2 + (4x)^2} $$

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Calculus Questions