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:
Yes
Step-by-step explanation:
Given that a teacher prepares 26 tiles with 5 vowels numbered 1 and 21 consonants numbered 2.
The probability for drawing vowel =
Prob for consonant =
If number of trials is atleast 30 we can expect reliable results.
Here the results are recorded for 120 times at random.
Since number of trials is large, we can expect a reliable and accurate results representing the actual probability.
This is because more the number of trials, the less would be the margin of error i.edeviationfrom the expected probability would be minimum
Hi there! To find the answer to that question, we can write and solve a proportion. Set it up like this: 240/x = 60/100. This is because we're looking for the whole and we already know the part, which is 240. Cross multiply the values in order to get 24,000 = 60x. Now, divide each side by 60 to isolate the variable. When you do, you get x = 400. You can check this by dividing and then multiplying that quotient by 100. 240/400 is 0.6 and 0.6 * 100 is 60. That makes 60%. There. 240 is 60% of 400.
-17 -35
-3 -3
-2 0
-31 -87
17 57
Answer:
it gives u a green marble.
Step-by-step explanation:
If I have 1 red marble replaced by a green marble then I have a green marble.
