Are the following equations parallel, perpendicular, or neither?

Write parametric equations of the line through the points (7,1,-5) and (3,4,-2). please use the first point as your base-point w

Roman55 [17]

Given:

A line through the points (7,1,-5) and (3,4,-2).

To find:

The parametric equations of the line.

Solution:

Direction vector for the points (7,1,-5) and (3,4,-2) is

$\vec {v}=\left$

Now, the perimetric equations for initial point $(x_0,y_0,z_0)$ with direction vector $\vec{v}=\left$ , are

$x=x_0+at$

$y=y_0+bt$

$z=z_0+ct$

The initial point is (7,1,-5) and direction vector is $\vec {v}=\left$ . So the perimetric equations are

$x=(7)+(-4)t$

$x=7-4t$

Similarly,

$y=1+3t$

$z=-5+3t$

Therefore, the required perimetric equations are $x=7-4t, y=1+3t$ and $z=-5+3t$ .

5 0

3 years ago

Can someone help me please

goldenfox [79]

Answer:

$1. \quad\dfrac{1}{k^{\frac{2}{3}}}\\\\2. \quad\sqrt[7]{x^5}\\\\3. \quad\dfrac{1}{\sqrt[5]{y^2}}$

Step-by-step explanation:

The applicable rule is ...

$x^{\frac{m}{n}}=\sqrt[n]{x^m}$

It works both ways, going from radicals to frational exponents and vice versa.

The particular power or root involved can be in either the numerator or the denominator. The transformation applies to the portion of the expression that is the power or root.

7 0

4 years ago

What value of x is in the solution set of 2(4+2x)>5x+5

Serggg [28]

Answer:

x < 3

Step-by-step explanation:

2(4+2x)>5x+5

Distribute

8 +4x > 5x+5

Subtract 4x from each side

8 +4x-4x > 5x-4x+5

8 > x+5

Subtract 5 from each side

8-5 > x+5-5

3 > x

X must be less than 3

7 0

3 years ago

As you are walking down a path, you see a sign telling the path has a 2% grade (ie., a rise of 2 metres for a horizontal change

Leni [432]

Answer:

Option (A)

Step-by-step explanation:

It has been given in this question that sign telling path has a 2% grade.

2% grade means a rise of 2 meters for a horizontal change of 100 m (As given in the figure attached).

All the trigonometric ratios for the angle θ between the path and the horizontal are,

Sinθ = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Cosθ = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

tanθ = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

Since measures of the opposite side and adjacent sides are given

Therefore, tangent ratio will be applied to get the measure of the angle,

tanθ = $\frac{2}{100}$

θ = $\text{tan}^{-1}(\frac{2}{100})$

Option (A) will be the answer.

5 0

3 years ago

The sum of 2 consecutive integers is -33.If n is the first integer,which equation best models the situation?

monitta

Answer:

You can choose which equation below suits your taste but I recommend the 2n + 1 = -33.

Step-by-step explanation:

$(n) + (n + 1) = - 33 \\ 2n + 1 = - 33 \\ 2n = - 32 \\ n = - 16$

5 0

3 years ago