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:
first find the area of the big rectangle = 12×14=168
area of the small unshaded rectangle =2×5×6=60
area of the shaded region = 168-60=108
Answer:
24 mph (miles per hours)
Step-by-step explanation:
she is going 2 miles every 5 minuets. 5 can go in to 60 12 times. and 2 times 12 is 24.
Answer:
c = - 65
Step-by-step explanation:
Combine like terms on the left
2/5 c - 1/5 c + 4 = - 9
1/5 c + 4 = - 9
Subtract 4 from both sides
1/5 c = - 9 - 4
Combine like terms on the right
1/5 c = - 13
Multiply both sides by 5
5(1/5 c) = - 13 * 5
c = - 65
Answer:
Exact: $79.96 Rounded: $80.00
Step-by-step explanation:
25% x 4 = 100%
thus $19.99 x 4 = $79.96. Rounded up to $80.00
