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
Answer:
for 20 the answer is B
Step-by-step explanation:
Answer:
58.208 times 8 equals 465.664 rounded down to 465.66
Step-by-step explanation:
The answer is D because 35x3 is 105 + the $5 fee is 110
M∠ rst + m∠ vst = 180°
3 x + 7° + 9 x + 17° = 180°
12 x + 24° = 180°
12 x= 180° - 24°
12 x = 156°
x = 156° : 12
x = 13°
m ∠ rst = 3 · 13° + 7° = 39° + 7° = 46°
m ∠ vst = 180° - 46° = 134°
Answer:
A ) 46° and 134°
