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:
Perimeter of the ΔDEF = 10.6 cm
Step-by-step explanation:
The given question is incomplete; here is the complete question with attachment enclosed with the answer.
D, E, and F are the midpoints of the sides AB, BC, and CA respectively. If AB = 8 cm, BC = 7.2 cm and AC = 6 cm, then find the perimeter of ΔDEF.
By the midpoint theorem of the triangle,
Since D, E, F are the midpoints of the sides AB, BC and CA respectively.
Therefore, DF ║ BC and 
FD = 
= 3.6
Similarly, 
FE = 4 cm
And 
DE = 
= 3 cm
Now perimeter of ΔDEF = DE + EF + FD
= 3 + 4+ 3.6
= 10.6 cm
Perimeter of the ΔDEF is 10.6 cm.
Answer: y = 108
Step-by-step explanation:
Answer:
35 plants
Step-by-step explanation:
For this case we can make the following rule of three:
4 gallons --------------> 14 plants
x --------------------------> 35 plants
From here, we clear the value of x.
We have then:
therefore, 10 gallons are needed to irrigate 35 plants.
Answer:
it will take 10 gallons to water 35 plants
