Answer:
C IS YOUR ANSER.
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
Answer: $1846.64
Step-by-step explanation:
Given : The average summer vacation costs $2252.
If 82% of this amount is charged on credit cards, then the amount of the vacation cost is charged will be :-
![82\%\text{ of }\$2252\\\\\text{Convert percent into fraction by dividing it by 100, we get}\\\\=\$[\dfrac{82}{100}\times2252]\\\\=\$[\dfrac{184664}{100}]\\\\=\$1846.64](https://tex.z-dn.net/?f=82%5C%25%5Ctext%7B%20of%20%7D%5C%242252%5C%5C%5C%5C%5Ctext%7BConvert%20percent%20into%20fraction%20by%20dividing%20it%20by%20100%2C%20we%20get%7D%5C%5C%5C%5C%3D%5C%24%5B%5Cdfrac%7B82%7D%7B100%7D%5Ctimes2252%5D%5C%5C%5C%5C%3D%5C%24%5B%5Cdfrac%7B184664%7D%7B100%7D%5D%5C%5C%5C%5C%3D%5C%241846.64)
Therefore the amount of the vacation cost is charged= $1846.64
Answer:
-1
Step-by-step explanation:
The y-intercept is where the line crosses the y-axis.
