Answer:
width of rectangle is 87
Step-by-step explanation:
because perimeter of rectangle = 2(l+w)
Amanda's method is linear because the number of minutes increased by an equal number every week.
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)
Hi there!
We are given a question that asks us to translate some given information into numerical format, or numbers. We can do that by first finding key words. Such words are sum and at least. Sum indicates addition, while at least indicates a greater than or equal to sign, or ≥. Now that we have found our key info, we can move on.
The question states that 3 times the sum of a number and 17. The 'sum of a number and 17' part can be represented by the expression x + 17, where x is some number. Next, three times means that we need to multiply 3 to the expression x + 17, giving us 3(x + 17). Finally, the question gives us that the whole expression 3(x + 17) is 'at least', or greater than or equal to, 22. Hence, we get the inequality 3(x + 17) ≥ 22, which is also our answer. Hope this has come of assistance to you and have a great day!
Answer:
C. Domain: −2≤x≤2; Range: −2≤y≤2
Step-by-step explanation:
