Hello person above
How are you?
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:
6a^2
Step-by-step explanation:
Side of the room = x.
From the right triangle, where sides of the square are legs of the right triangle, and the diagonal of the square is a hypotenuse of the right triangle.
x²+x²=6²
2x²=36
x²=18
x=√18 =√(2*9)=3√2≈4.2m
Answer:
Standard deviation of the length of granola bars produced at Bernie's Bars is 0.50
Step-by-step explanation:
We are given the following information in the question:
Formula:
where,
μ is the mean and σ is the standard deviation.
Putting the values we get:
Solving the two obtained equations:
Subtracting the two obtained equation, we have:
Hence, standard deviation of the length of granola bars produced at Bernie's Bars is 0.50
