Answer:
Step-by-step explanation:
we are given
(A)
(f×g)(x)=f(x)*g(x)
now, we can plug it
we can simplify it
(B)
Domain:
Firstly, we will find domain of f(x) , g(x) and (fxg)(x)
and then we can find common domain
Domain of f(x):
we know that f(x) is undefined at x=0
so, domain will be
∪
Domain of g(x):
Since, it is polynomial
so, it is defined for all real values of x
now, we can find common domain
so, domain will be
∪..............Answer
Range:
Firstly, we will find range of f(x) , g(x) and (fxg)(x)
and then we can find common range
Range of f(x):
we know that range is all possible values of y for which x is defined
since, horizontal asymptote will be at y=0
so, range is
∪
Range of g(x):
Since, it is quadratic equation
so, its range will be
now, we can find common range
so, range will be
∪.............Answer
Answer:
y = x*sqrt(Cx - 1)
Step-by-step explanation:
Given:
dy / dx = (x^2 + 5y^2) / 2xy
Find:
Solve the given ODE by using appropriate substitution.
Solution:
- Rewrite the given ODE:
dy/dx = 0.5(x/y) + 2.5(y/x)
- use substitution y = x*v(x)
dy/dx = v + x*dv/dx
- Combine the two equations:
v + x*dv/dx = 0.5*(1/v) + 2.5*v
x*dv/dx = 0.5*(1/v) + 1.5*v
x*dv/dx = (v^2 + 1) / 2v
-Separate variables:
(2v.dv / (v^2 + 1) = dx / x
- Integrate both sides:
Ln (v^2 + 1) = Ln(x) + C
v^2 + 1 = Cx
v = sqrt(Cx - 1)
- Back substitution:
(y/x) = sqrt(Cx - 1)
y = x*sqrt(Cx - 1)
Answer:
C. Leo scored points in 3/10 of his attempts
Step-by-step explanation:
30% is 30/100
Which can simplify to
3/10
Answer:
t=7/5
Step-by-step explanation:
If you subtract 3 from each side, you end up with -5t=-7. In order to keep t isolated, you would have to divide -5 on both sides. When you do this, you will end up with t= -7/-5. You also need to simplify that. When simplified you end up with t=7/5. Hope this helps!
subtract them
593.7-573.36 = 20.34seconds
so c is the answer