Question

1. **Find the distance between the line y=-2x+1 and the
point (1, 4). Sketch the line, point, and distance on a
graph.**

**2.If the discriminant is negative what type of solutions
would you have?**

Answer #1

1.) P(2, 4) lies on the graph of y=x4-2x-4
Q is the point (x, x4-2x-4)
Write an equation for the slope of the secant line through P and
Q as a function of x.
2.) Using the formula above, find the slopes fo 1.9, 1.99,
1.999, 2.001, 2.01, and 2.1 (round 4 decimal places)
3.) What is the slope of the tangent line to the curve
y=x4-2x-4 at P(2, 4)
Can you please explain in detail how to get the...

Find the shortest distance from the point P = (−1, 2, 3) to the
line of inter- section of the planes x + 2y − 3z = 4 and 2x − y +
2z = 5.

Find the shortest distance between line L1: x = 1 + 2t, y = 3
- 4t, z = 2 + t and L2: the intersection of the planes x + y + z =1
and 2x + y - 3z = 10

Find the point on the line y = 2x + 3 that is closest to the
point (1, 3)

Given dy/dx =y(y−3)(1−y)^2 dx (a) Sketch the phase line
(portrait) and classify all of the critical (equilibrium) points.
Use arrows to indicated the flow on the phase line (away or towards
a critical point). (b) Next to your phase line, sketch the graph of
solutions satisfying the initial conditions: y(0)=0, y(0)=1,
y(0)=2, y(0)=3, y(2)=4, y(0)=5.

Let T be the plane 2x+y = −4. Find the shortest distance d from
the point P0=(−1, −5, −1) to T, and the point Q in T
that is closest to P0. Use the square root symbol '√'
where needed to give an exact value for your answer.

1. Find the distance between the point and the line given by the
set of parametric equations. (Round your answer to three decimal
places.)
(8, -1, 4); x = 2t, y = t −
3, z = 2t + 2
I had put 6.87 but it shows as it being wrong.
2. Consider the following planes.
−6x + y + z
=
6
24x − 4y + 6z
=
36
Find the angle between the two planes. (Round your answer...

Find an equation of the tangent line to the graph of
2x+5/(1-2x)^3 at the point (-1,1)

find the domain, sketch and sketch the level curve ofsquare root
of 2x-y^2 +1

Suppose that f(x) = (2x)/((4-2x)^3)
Find an equation for the tangent line to the graph of f at
x=1.
Tangent line: y =

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