Answer: -1/5
Step-by-step explanation:
the equation to solve slope with two points is the y coordinate in the second point minus the y coordinate in the first point over the x coordinate in the second point minus the x coordinate in the first point so this one would be
(-2 - -1)/(12-7)
On the top you subtract a negative it becomes a positive and you get -1/5
Answer:
10
Step-by-step explanation:
20 divided by 4 = 5 and times it from there
Answer:
yp = -x/8
Step-by-step explanation:
Given the differential equation: y′′−8y′=7x+1,
The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)
First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;
y′′−8y′=0
The auxiliary equation will give us;
m²-8m = 0
m(m-8) = 0
m = 0 and m-8 = 0
m1 = 0 and m2 = 8
Since the value of the roots are real and different, the complementary solution (yc) will give us
yc = Ae^m1x + Be^m2x
yc = Ae^0+Be^8x
yc = A+Be^8x
To get yp we will differentiate yc twice and substitute the answers into the original DE
yp = Ax+B (using the method of undetermined coefficients
y'p = A
y"p = 0
Substituting the differentials into the general DE to get the constants we have;
0-8A = 7x+1
Comparing coefficients
-8A = 1
A = -1/8
B = 0
yp = -1/8x+0
yp = -x/8 (particular integral)
y = yc+yp
y = A+Be^8x-x/8
So the equation has to pass through (6,-1) and be perpendicular to y = -2x + 8.
The slope is -2, and to get the slope of a line perpendicular to another line you have to find the negative reciprocal of that slope. That means -2 is equal to
-2/1, and if you flip those numbers and find the opposite of that number making it positive, the slope of a line perpendicular to it is 1/2.
But the line also has to pass through (6,-1), so we have to find the y-intercept of the new line.
To do that, you multiply 6(the x) by the 1/2(the slope) and get 3. Then you subtract 3(previous answer) from -1(the y) and get -4. That means the y-intercept is -4!
All that's left is to build the equation with this information. The equation is:
y = -4 + 1/2x
Hope this helps!
When the incident ray passes through the focal point, a light ray striking a concave concave mirror reflect off parallel to the principal axis. The correct option among all the options given in the question is the third option or option "C". I hope the answer comes to your help.
