M=months
400+20m=100+40m
300=20m
m=15 months
After 15 months total savings of two options are the same.
Total savings=400+20*15=700 with either options
Answer:
+ 3x - 8 = 0
Step-by-step explanation:
ax² + bx + c = 0 (standard form)
The exact length of the curve given the following system of inequalities is ≈ 1637.
<h3>What is a system of inequalities?</h3>
A system of inequalities refers to a set of two or more inequalities with one or more variables. This kind of system is used when a problem needs a range of solutions a there is over one constraint.
<h3>What is the length of the curve with the above system of inequalities?</h3>
Step One - Let's restate the equations
We have:
x = 5 + 9t²
y = 4 + 6t³
Where
0 ≤ t ≤ 3
Step 2 - Differentiate them
The first derivative of dx/dt
= d/dt [9t² + 5)
= 9 * (d/dt) (t²) + (d/dt) (5)
= 9.2t + 0
= 18t
Also differentiate (dy/dt)
= d/dt [6t² + 4]
= 6 * (d/dt) [t³] + (d/dt) [4]
= 6.3 t² + 0
= 18t²
To find the length of the arc:
L = 
We can thus deduce that:
= 
= ![\int_{0}^{4}[18t \sqrt{1 + {18t^{2} ]](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B4%7D%5B18t%20%5Csqrt%7B1%20%2B%20%7B18t%5E%7B2%7D%20%5D)
Compute the definite integral and factor out the constraints and we have:
dt = 4912/3
≈ 1,637.3
Hence the exact length of the curve is
≈ 1637
Learn more about the system of inequalities at:
brainly.com/question/9774970
#SPJ1
Answer:
38
Step-by-step explanation:
The simplest (almost trivial) solution is to add the two inequalities:
(x +3y) +(3x +2y) ≤ (13) +(25)
4x +5y ≤ 38
The maximum value of P is 38.
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Perhaps more conventionally, you can graph the equations, or solve them to find the point of intersection of their boundary lines. That point is (x, y) = (7, 2), which is the point in the doubly-shaded solution space that gives the maximum value of P (puts the objective function line farthest from the origin).
__
In the attached graph, we have been a little sloppy, not applying the constraints that x, y ≥ 0. For the purpose of finding the requested solution, that is of no consequence.