It would be easier to translate this into mathematical terms first.
Let n = the unknown number
6n <span>> n + 20
Subtracting both sides by n to simplify:
6n - n </span><span>> n + 20 - n
</span>5n <span>> 20
</span><span>
Dividing both sides by 5:
5n/5 </span><span>> 20/5
</span>n <span>> 4
</span><span>
Among the choices, the correct one is the second choice.
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Answer: solutions are the same, just written differently, inequality sign is reversed when multiplying by a negative. Yes, both students are correct.Jul 8, 2018
Step-by-step explanation:
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
I hope this helps you
3 1/8=3.8+1/8=25/8
25/8-4/7
25.7/8.7-4.8/7.8
175-32/56
143/56
2 31/56
