Step-by-step explanation:
The given equation is
As a check for exactness we have
Hence the given equation is an exact differential equation and thus the solution is given by
thus the solution is given by
Similarly we have
Comparing both the solutions we infer
Hence the solution becomes
given boundary condition is that it passes through (1,1) hence
thus solution is
Answer:
75
Step-by-step explanation:
divide the interest by the amounts of years
Answer:
Correct answer: x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3
Step-by-step explanation:
Given:
3 x⁴ + 14 x² - 5 = 0 biquadratic equation
this equation is solved by a shift x² = t and get:
3 t² + 14 t - 5 = 0
t₁₂ = (-14 ± √14² - 4 · 3 · 5) / 2 · 3 = (-14 ± √196 + 60) / 6
t₁₂ = (-14 ± √256) / 6 = (-14 ± 16) / 6
t₁ = -5 or t₂ = 1 / 3
the solution t₁ = -5 is not accepted because it cannot be x² = -5
we accepted t₂ = 1 / 3
x² = 1 / 3 ⇒
x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3
God is with you!!!
Use pythagorean theorem:
sin^2 + cos^2 = 1
(-1/3)^2 + cos^2 = 1
1/9 + cos^2 = 1
cos^2 = 8/9
cos = +- sqrt(8)/sqrt(9) = +- 2sqrt(2)/3
Determine whether cos is positive or negative by looking at which quadrant the angle is in.
pi < theta < 3pi/2 ---> this is 3rd quadrant where x or cos is negative
Therefore cos(theta) = -2sqrt(2)/3
