Graph the solution set for the of linear inequalities y<1/3x+1y>=1/3x-2

Cabiolab 2020-11-02 Answered

Graph the solution set for the of linear inequalities
y<13x+1
y13x2

You can still ask an expert for help

Want to know more about Inequalities systems and graphs?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Derrick
Answered 2020-11-03 Author has 94 answers

Step 1
We make tables for the auxiliary equations.
Step 2
Then we plot the points and graph the lines. then we shade the region depending on the inequalities. (0,0) means x=0 , y=0 satisfies both inequalities. 0<1 and 02
y<13x+10<13(0)+10<1
y13x2013(0)202
For y<(13)x+1 we draw dotted line because strict inequality.
For y(13)x2 we draw solid line because equality holds.
For both shaded towards (0,0)
image

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2022-05-25
Solve a system of inequalities
{ log 2 2 ( log 2 x ) + log 2 log 2 2 x 3 4 | x 2 1 | 3 1 x 2 1
What I've tried:Make substitution t = x 2 1 and solve second inequality:
4 | t | 3 1 t <=> 4 | t | 3 1 t 0
Where I got interval for t: 1 4 t < 0
And then for x: x ( 1 ; 3 2 ] [ 3 2 ; 1 )
But I have no thoughts how to solve first inequality.
asked 2022-06-05
Consider the following system of inequalities:
{ x a b + x a c + x a d + x a b c + x a b d + x a c d + x a b c d 4 + x b c + x b d + x c d + x b c d x a b + x b c + x b d + x a b c + x a b d + x b c d + x a b c d 4 + x a c + x c d + x a d + x a c d x a c + x b c + x c d + x a b c + x a c d + x b c d + x a b c d 4 + x a b + x a d + x b d + x a b d x a d + x b d + x c d + x a b d + x a c d + x b c d + x a b c d 4 + x a b + x a c + x b c + x a b c
where each x { 0 , 1 }. Does this system of inequalities have a solution?
asked 2022-06-22
need to build the optimal controller, i.e. one that maximizes:
J = 0 t f f ( u ) d t
For the following time-dependent system:
x ˙ = g ( x , u , t )
where x ( t ) R is the state, u ( t ) R the input, t R the time and l ( t ) R the time-varying lower bound for the state. Using the Pontryagin's maximum principle, I have defined the Hamiltonian as: H = ψ g ( x , u , t ) + f ( u ) and used the necessary condition ψ ˙ = H x . As you can see I have completely ignored the time-dependent inequality, so the solution I get is correct, but of course it doesn't enforce the lower bound l on the state value.
How can I rewrite the hamiltonian so that also the inequality is considered?
asked 2022-05-21
Suppose that the polytope P = { x A x b } is totally dual integral (TDI), and that the inequality a ~ T x b ~ is satisfied at every point of P.
Does this imply that the system { A x b ,     a ~ T x b ~ } is TDI?
asked 2022-05-28
Given a system of inequalities A x b , how can I derive the upper and lower bound on x?
I have the following system of inequalities A x b, where x 1 and x 2 are unknown, and the a's and и's are constants.
[ a 11 a 12 a 21 a 22 ] [ x 1 x 2 ] [ b 1 b 2 ]
asked 2022-05-12
T { x [ n ] } = k = min ( n , n 0 ) max ( n , n 0 ) x [ k ]
for some integer constant n 0 .
Intuitively, it's unstable, and it can be easily proven by a counterexample if x [ n ] is the unit step and n 0 = 0.However, the TA tried to use a general proof by invoking the triangle inequality. Assuming x [ n ] is bounded (or | x [ n ] | M < ), he said:
| T { x [ n ] } | = | k = min ( n , n 0 ) max ( n , n 0 ) x [ k ] | k = min ( n , n 0 ) max ( n , n 0 ) | x [ k ] | ( | n n 0 | + 1 ) M
Obviously the right-hand side is unbounded, as it goes to infinity with increasing n, but to me it doesn't seem to imply that the system on the left-hand side is unbounded (because of the inequality).
My question is, can his attempt be augmented to show that the left-hand side is also unbounded? Or is a counter-example the only way to prove it?
asked 2022-06-21
System of inequalities. Points of intersection?
x 2 + y 2 <= 81
y < x