Solve for k: k over 6.12 = 8.7 1. k = 53.244 2. k = 1.42 3. k = 2.58

Consider the line y=-1/2x+8

OverLord2011 [107]

Given parameters:

Equation of the line is y = - $\frac{1}{2} x$ + 8

Unknown:

Slope of line parallel to this line = ?

Slope of line perpendicular = ?

Solution:

A line parallel to this line will have the same slope with it.

A line perpendicular will have the negative inverse of this slope;

Slope of line = - $\frac{1}{2}$

Slope of line parallel to this line = $-\frac{1}{2}$

Slope of line perpendicular = negative inverse = -( -( $\frac{1}{\frac{1}{2} }$ )) = 2

So, the slope of line parallel to this line is - 1/2 and that perpendicular is 2

6 0

3 years ago

What is the velocity of a car moving 20 m per second

murzikaleks [220]

20mps. Because velocity is the speed per unit. In this case it is going 20 m per second

5 0

3 years ago

4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the dia

Ad libitum [116K]

The standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

<h3>How to find the standard equation of a hyperbola</h3>

In this problem we must determine the equation of the hyperbola in its standard form from the coordinates of the foci and a general equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:

(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)

(h, k) = (2, 2)

To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the general equation of the circle into its standard form.

If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:

x² + y² - 4 · x - 4 · y + 4= 0

(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4

(x - 2)² + (y - 2)² = 2²

The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:

V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)

And the distance from the center to any of the vertices is 2 (semi-major distance, a) and the semi-minor distance is:

b = √(c² - a²)

b = √(3² - 2²)

b = √5

Therefore, the standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

To learn more on hyperbolae: brainly.com/question/27799190

#SPJ1

5 0

1 year ago

Find the answer The weight of an elephant is 10 to the 3rd power times the weight of a cat .If the the elephant weighs 14,000 po

Hitman42 [59]

Answer:

$14\ pounds$

Below is the procedure that was used to find the answer.

Step-by-step explanation:

Let be "e" the weight in pounds of the elephant and "c" the weight in pounds of the cat.

According to the information provided in the exercise, we know that The weight of an elephant is $10^3$ times the weight of a cat. Based on this we can write the following equation: