Answer:
A
Step-by-step explanation:
the last number is the y intercept so the intercept in the line is -3.5 so I just matched them up.
Answer:
(5,-4) and (-5,6)
Step-by-step explanation:
Given:
Solve it. First, express y in terms of x from the second equation:
Substitute it into the first equation:
Apply zero product property:
So,
When 
then 
When 
then 
We get two solutions: (5,-4) and (-5,6)
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
Graph 2, Option 4 would be your answer because:
If you substitute 1 into the equation (x), you would get about 212
If you substitute 2, you would get approximately 225
If you substitute 10, you would get approximately 364.
Looking at the graph, your answer would be going up and to the right, the population is getting bigger while the years are increasing as well.
If we substitute 15 into x in the equation, we would get approximately 492.
