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:
-14.5
Step-by-step explanation:
To get the calculator and type 2.2+0.3-13-4
<span>f(x) = -6x +6
to find inverse
x = -6y + 6
6y = 6 - x
y = 1 - x/6
Answer
</span>f^–1(x)= 1 - x/6
Hey there!
“Which expression is equivalent to b + b – 0.56b?”
• “b” or any other letter value is considered an “unknown number” so usually we label it/them as an invisible 1
• COMBINE the LIKE TERMS
(b + b – 0.56b)
(1b + 1b – 0.56b)
1b + 1b = 2b
2b – 0.56b = 1.44b
• Therefore, b + b – 0.56b is equivalent to 2b + 0.56b
Possible answer that you could be looking for: 2b + 0.56b ☑️
Good luck on your assignment and enjoy your day!
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