<u>Answer:</u>
<u>Step-by-step explanation:</u>
We are given the following equation and we are supposed to solve y in terms of x. It simpler terms, it means that we have to make y the subject of the equation while x being used in it as it is:
Taking the constant 4 to the side where x is to get:
Multiplying the denominator 3 to the other side of the equation to get:
Isolating y to make it the subject:
Answer:
c
Step-by-step explanation:
. portion of pizza eaten by Amy = portion of pizza eaten by Jack because it doesn't tell us information how much did they ate.
Answer:
B
Step-by-step explanation:
The slope is rise over run, meaning it is 3/4. The y-intercept is 2, making the equation y = (3/4)x + 2
Answer:
minimum value of z is 0
Step-by-step explanation:
if x and y both equal zero, then the value of z is zero, which is your answer.
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
