Let the ∠C be : θ
From the figure, We can see that the Side which is opposite to angle θ is measuring 7 units
Also, We can notice that Hypotenuse is 11 units
As we are dealing with opposite and hypotenuse, we can clearly use Sinθ to find out the angle θ
We know that :
![\bigstar \ \ \boxed{\sf{Sin\theta = \dfrac{Opposite \ Side}{Hypotenuse}}}](https://tex.z-dn.net/?f=%5Cbigstar%20%5C%20%5C%20%5Cboxed%7B%5Csf%7BSin%5Ctheta%20%3D%20%5Cdfrac%7BOpposite%20%5C%20Side%7D%7BHypotenuse%7D%7D%7D)
![\implies \sf{Sin\theta = \dfrac{7}{11}}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7BSin%5Ctheta%20%3D%20%5Cdfrac%7B7%7D%7B11%7D%7D)
![\implies \sf{\theta = Sin^{-1}\bigg(\dfrac{7}{11}\bigg)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B%5Ctheta%20%3D%20Sin%5E%7B-1%7D%5Cbigg%28%5Cdfrac%7B7%7D%7B11%7D%5Cbigg%29%7D)
![\implies \sf{\theta = 39.52^{\circ}}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B%5Ctheta%20%3D%2039.52%5E%7B%5Ccirc%7D%7D)
<u>Answer</u> : The measure of ∠C to the nearest degree is 38°
x*y' + y = 8x
y' + y/x = 8 .... divide everything by x
dy/dx + y/x = 8
dy/dx + (1/x)*y = 8
We have something in the form
y' + P(x)*y = Q(x)
which is a first order ODE
The integrating factor is ![u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x](https://tex.z-dn.net/?f=u%28x%29%20%3D%20e%5E%7B%5Cint%20P%28x%29dx%7D%20%3D%20e%5E%7B%5Cint%20%281%2Fx%29%20dx%7D%20%3D%20e%5E%7B%5Cln%28x%29%7D%20%3D%20x)
Multiply both sides by the integrating factor (x) and we get the following:
dy/dx + (1/x)*y = 8
x*dy/dx + x*(1/x)*y = x*8
x*dy/dx + y = 8x
y + x*dy/dx = 8x
Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).
Since (xy)' turns into y + x*dy/dx, and vice versa, this means
y + x*dy/dx = 8x turns into (xy)' = 8x
Integrating both sides with respect to x leads to
xy = 4x^2 + C
y = (4x^2 + C)/x
y = (4x^2)/x + C/x
y = 4x + Cx^(-1)
where C is a constant. In this case, C = -5 leads to a solution
y = 4x - 5x^(-1)
you can check this answer by deriving both sides with respect to x
dy/dx = 4 + 5x^(-2)
Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.
Largest angle = [5 / (4+5)] * 180 = 5 * 180 / 9 = 900/9 = 100 degrees answer
Answer:
0
Step-by-step explanation:
m= y2-y1/x2-x1
=0-0/-3-5
=0/-8
=0