Answer:
y(x) = c_1 e^(-1/(2 x^2))
Step-by-step explanation:
Solve the separable equation x^3 (dy(x))/(dx) - y(x) = 0:
Solve for (dy(x))/(dx):
(dy(x))/(dx) = y(x)/x^3
Divide both sides by y(x):
((dy(x))/(dx))/y(x) = 1/x^3
Integrate both sides with respect to x:
integral((dy(x))/(dx))/y(x) dx = integral1/x^3 dx
Evaluate the integrals:
log(y(x)) = -1/(2 x^2) + c_1, where c_1 is an arbitrary constant.
Solve for y(x):
y(x) = e^(-1/(2 x^2) + c_1)
Simplify the arbitrary constants:
Answer: y(x) = c_1 e^(-1/(2 x^2))
Impossible to tell. there is an infinite number of solutions to x+y=17, without knowing the difference of the numbers we cannot solve for X and Y
4.75 in simplest form is 4 3/4. 4.75 is 4 75/100 as a fraction, 75 and 100 can both be divided by 25. 75/25 = 3. 100/25 = 4. 4 and 3 have no common factors.
Answer:
10.8
Step-by-step explanation:
becaue you need to mutiply all sides
Answer:
(a)
(b) There will be 1lb left after 14 hours
Step-by-step explanation:
Solving (a): The equation
Since the substance decomposes at a proportional rate, then it follows the following equation
Where
Initial Amount
rate
time
Amount at time t
Solving (b):
We have:
First, we calculate k using:
This gives:
Substitute:
Divide both sides by 4
Take natural logarithm of both sides
This gives:
Solve for k
So, we have:
To calculate the time when 1 lb will remain, we have:
So, the equation becomes
Divide both sides by 8
Take natural logarithm of both sides
Solve for t
--- approximated