Complete these ordered pairs for this equation.
2 answers:
You might be interested in
Question 14, Part (i)
Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,
A+B+C+D = 360
A+90+C+90 = 360
A+C+180 = 360
A+C = 360-180
A+C = 180
Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.
==================================================
Question 14, Part (ii)
Let
x = measure of angle 1
y = measure of angle 2
z = measure of angle 3
Back in part (i) above, we showed that y + z = 180
Note that angles 1 and 2 are adjacent to form a straight line, so we can say
x+y = 180
-------
We have the two equations x+y = 180 and y+z = 180 to form this system of equations
Which is really the same as this system
The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.
Answer:
y = -x - 6
Step-by-step explanation:
If we are looking for the equation of the line tangent to the circle, we have to find the first derivative of the circle function. If that tangent line is to be parallel to the given tangent line, we need to find the slope of the the given tangent line and make sure the slope of the line we are looking for is the same. First let's find the slope of the given tangent. If the given tangent is x+y=6, then to find the slope, solve for y:
y = -x + 6. So the slope of that line, and also the slope of the tangent we are solving for, is -1. Hold that thought while we find the derivative of the function. Using implicit differentiation, we find the derivative to be:
Solving for the slope (dy/dx) gives us:
and
so
Subbing in the value of the slope we found:
so
-y = -x or, equivalently,
y = x. Now that we know that y and x are the same value, we can go back to the original circle to find out what they both are by substitution. If y = x, we make the substution:
If , then
and
and
so
y = ±3
We will choose the negative root (you'll see why in a second) and sub that in for both y and x since y and x are th same number. Going back to the fact that the slope is -1:
y - (-3) = -1(x - (-3)) simplifies a bit to:
y + 3 = -x - 3 which gives us, in slope-intercept form:
y = -x - 6
That is the equation of the tangent to the circle that is parallel to the given tangent.
If we would have chosen the principle (or positive) root of 3, our equation would have looked like this:
y - 3 = -1(x - 3) and
y = -x + 3 + 3 so
y = -x + 6. Notice that that is the EXACT SAME EQUATION as the given tangent. That's why we have to pick the negative 3 as our root.
Good luck in your calculus class! Make sure you post your questions in here! Many of us LOVE the challenge of calculus!