Given the points (2.1) and (-4,-5) Find the point-slope form of the line.
1 answer:
Answer: y = x - 1
<u>Step-by-step explanation:</u>
Use the Point-Slope form: y - y₁ = m(x - x₁) where
- (x₁ , y₁) is any point on the line
- m is the slope of the line
Let (x₁, y₁) = (2, 1) and (x₂, y₂) = (-4, -5)
Point-Slope form: y - 1 = 1(x - 2)
y - 1 = x - 2 <em>distributed 1 to (x - 2)</em>
y = x - 1 <em>added 1 to both sides</em>
You might be interested in
We have to use the rule of cosx° to solve this problem. Attached is a diagram of the navigator's course for the plane. It is similar to the shape of a triangle. We know the plane is 300 miles from its destination, so that will be one of the sides. On the current course, it is 325 miles from its destination, so that will be another one of the sides. The last side is 125 because that is the distance between the destination and the anticipated arrival. Cosx° is what we are looking for.
To find how many degrees off course the plane is, we must use the rules of Cosx°, which is shown in the attached image.
The plane is approximately 23° off course.
To find how many degrees off course the plane is, we must use the rules of Cosx°, which is shown in the attached image.
The plane is approximately 23° off course.
If x represents the side length of the square cut from each corner, then the dimensions of the base of the box are 26-2x by 43-2x. The volume of the box is
... V = x(26-2x)(43-2x)
where x is restricted to the domain 0 ≤ x ≤ 13.
Plotting this equation using a graphing calculator shows the maximum volume to be 2644.7 in³.
_____
The analytical solution can be found by setting the derivative of V to zero.
... V = 4x³ - 138x² +1118x
... dV/dx = 0 = 12x² -276x +1118
This has solutions given by the quadratic formula, where a=12, b=-276, c=1118:
... x = (-b±√(b²-4ac))/(2a)
The plus sign will give a solution that is not in the allowed domain of x, so the only viable solution is the one where the radical is subtracted.
... x = (276 - √(76176--53664))/24 = (23/2) - √(469/12) ≈ 5.2483 . . . inches
Then the corresponding maximum volume is found from the equation for V.
... V ≈ (5.2483)(26 - 2·5.2483)(43 - 2·5.2483) ≈ 2644.6877 in³ . . . . as above
