Y=5x - 3
Because the difference in the y values are 5, the rise is 5. That is the TOP of the slope. The difference in the x values is 1, that is the run or the BOTTOM of the slope. So m = 5/1.
Using y = mx + b
2 = 5(1) + b
-3 = b
Therefore, y = 5x -3
Answer:
Step-by-step explanation:
The slope formula is 
Here, 
is -6, 
is 4, 
is -5, and 
is 4.
So, the slope of the line passing through the points (-6,-5) and (4,4) is .
Answer:
4. dy/dx = -2
8. dy/dx = 1/2 x^(-3/2)
10/ dy/dr = 4 pi r^2
Step-by-step explanation:
4. y = -2x+7
dy/dx = -2(1)
dy/dx = -2
8. y = 4 - x^-1/2
dy/dx = - (-1/2x^ (-1/2-1)
dy/dx = 1/2 x^(-3/2)
10. y = 4/3 pi r^3
dy/dr = 4/3 pi (3r^2)
dy/dr = 4 pi r^2
Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
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