Exam 7: Systems Of Equations and Inequalities

Find the minimum value of the objective function and where it occurs, subject to the constraints: ​ Objective function: ​ Z = 4x + y ​ Constraints: ​ X ≥ 0 Y ≥ 0 3x + y ≤ 15 4x + 3y ≤ 30 ​

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. $( 0,0 ) , ( 0 , - 3 ) , ( 4,0 )$

Select the correct graph of the inequality. $y < 4 ^ { - x - 5 }$

Solve the system of linear equations and check any solution algebraically. 3x+3y=0 6x+3y-z =0 12x+3y+3z =0

Sketch the graph and label the vertices of the solution set of the system of inequalities.Shade the solution set. $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } < 16 \\x ^ { 2 } + y ^ { 2 } \geq 25\end{array} \right.$

A warehouse supervisor is told to ship at least 50 packages of gravel that weigh 55 pounds each and at least 40 bags of stone that weigh 70 pounds each.The maximum weight capacity of the truck to be used is 9,500 pounds.Find and graph a system of inequalities describing the numbers of bags of stone and gravel that can be shipped.

Solve the system by the method of substitution.Check your solution(s) graphically. $\left\{ \begin{aligned}x - y & = - 3 \\x ^ { 2 } - y & = 3\end{aligned} \right.$

Find the value of x, y and z in the figure.​ ​ where a = 6, b = 14 ​

Use a graphing utility to graph the inequalities.Shade the region representing the solution set of the system. $\left\{ \begin{array} { l } y > x ^ { 2 } - 5 x + 2 \\y < - x ^ { 2 } + x + 2\end{array} \right.$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 5 x - 4 } { x ^ { 3 } + 5 x }$

Solve the system by the method of substitution.Check your solution(s) graphically. $\left\{ \begin{array} { r } 7 x + y = 3 \\x ^ { 3 } - 3 + y = 0\end{array} \right.$

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. $\left\{ \begin{array} { l } 2 x + y = 2 \\x - y = 4\end{array} \right.$

Solve the system graphically or algebraically.Find the solution(s) accurate to three decimal places. $\left\{ \begin{array} { r } y - e ^ { - x } = 3 \\y - \ln x = 5\end{array} \right.$

Applying Kirchhoff's Laws to the electrical network in the figure, the currents I₁, I₂, and I₃ are the solution of the system $\left\{ \begin{array} { l l } I _ { 1 } - I _ { 2 } + I _ { 3 } & = 0 \\6 I _ { 1 } + 3 I _ { 2 } & = 11 \\3 I _ { 2 } + 5 I _ { 3 } & = 6\end{array} \right.$ Find the currents. =11 volts, =6 volts =6\Omega,=3\Omega,=5\Omega

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 6 x ^ { 2 } - 1 } { ( x + 8 ) ^ { 3 } }$

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. $( 0,0 ) , ( 0,12 ) , ( 6,6 )$

Find the minimum value of the objective function and where it occurs, subject to the constraints: Objective function: Z = x + 4y Constraints: X $\ge$ 0 Y $\ge$ 0 X + 4y $\le$ 20 X + y $\le$ 18 2x + 2y $\le$ 21

A merchant plans to sell two models of MP3 players at prices of $225 and $250.The $225 model yields a profit of $30 per unit and the $250 model yields a profit of $31 per unit.The merchant estimates that the total monthly demand will not exceed 280units.The merchant does not want to invest more than $55,776 in inventory for these products.What is the optimal inventory level for each model? What is the optimal profit?

A humanitarian agency can use two models of vehicles for a refugee rescue mission.Each model A vehicle costs $1000 and each model B vehicle costs $1500.Mission strategies and objectives indicate the following constraints.A total of at least 20 vehicles must be used.A model A vehicle can hold 45 boxes of supplies.A model B vehicle can hold 24 boxes of supplies.The agency must deliver at least 690 boxes of supplies to the refugee camp.A model A vehicle can hold 17 refugees.A model B vehicle can hold 35 refugees.The agency must rescue at least 520 refugees.What is the optimal number of vehicles of each model that should be used? What is the optimal cost?

Write the partial fraction decomposition of the rational expression. $\frac { 9 } { x ^ { 2 } + 16 x + 63 }$