Answer:
a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Step-by-step explanation:
for the equation
(1 + x⁴) dy + x*(1 + 4y²) dx = 0
(1 + x⁴) dy = - x*(1 + 4y²) dx
[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx
∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx
now to solve each integral
I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁
I₂= ∫[-x/(1 + x⁴)] dx
for u= x² → du=x*dx
I₂= ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ = - tan⁻¹ (x²) +C₂
then
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C
for y(x=1) = 0
1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C
since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for π*N , we will choose for simplicity N=0 . hen an explicit solution would be
1/2 * 0 = - π/4 + C
C= π/4
therefore
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Did you mean -1? If so your answer would be, there is no intercept with the y axis. The intercept with the x axis is at (1/2, 0)
(3,4) (9,7)
to find the slope
m = (y2-y1)/(x2-x1)
= (7-4)/(9-3)
3/6
1/2
The slope is 1/2
point slope form
y-y1 = m(x-x1)
y-4 = 1/2(x-3)
distribute
y-4 = 1/2x -3/2
add 4 to each side
y = 1/2 x -3/2 + 4
y = 1/2 x -3/2 + 8/2
y = 1/2 x + 5/2
this is in slope intercept form
I don't know if my answer is completely correct, but I think it's 100. All triangles add up to 180, and an isosceles triangle has 2 equal sides. 40 would be the 2 sides, and 180 subtracted from 80 equals 100.
Answer:
Step-by-step explanation:
Sum of angles in a triangle = 180
1. 180 = 78 + 37 + x
180 = 115 + x
Subtract 115 from both sides
180 - 115 = 115 + x - 115
180 - 115 = x
65 = x
x = 65°
2. 180 = 80 + 66 + x
180 = 146 + x
Subtract 146 from both sides
180 - 146 = 146 + x - 146
34 = x
x = 34°
