Graph the inequality:Y>-x+3I would very much appreciate the help :)
1 answer:
Answer:
See attached picture.
Step-by-step explanation:
To graph the inequality, use the y = mx + b form for linear equations. Here y > -x + 3 has slope of -1 and y-intercept of 3. Plot a point at (0,3) and move down 1 unit and 1 unit to the right. Plot a new point at (1,2). Connect the points with a dashed line. A dashed line is used for all inequalities which are not equal to. Finally, shade one side of the line. To determine which side, test a point not on the line. Shade the side which makes the inequality true.
y > -x + 3 test (0,0)
0 > -0 + 3
0 > 3 is false
Shade the side that does not have (0,0).
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Answer:
The average rate of change is -2
Step-by-step explanation:
we know that
To find out the average rate of change, we divide the change in the output value by the change in the input value.
In a linear function the average rate of change is a constant and is equal to the slope of the function
The linear function in slope intercept form is equal to
where
m is the slope or unit rate of the linear function
b is the y-intercept or initial value of the linear function
In this problem we have
so
therefore
The average rate of change is -2
Answer:
Option D.
Step-by-step explanation:
Minimize the objective function P = 5x + 8y for the given constraints.
The related equations of above inequalities are
For ,
x y
0 5
7.5 0
Plot (0,5) and (7.5,0) and join them by straight line.
For ,
x y
0 7.5
5 0
Plot (0,7.5) and (5,0) and join them by straight line.
Check the inequalities for (0,0).
False
False
It means both lines are solid lines and shaded region for each lies opposite side of (0,0).
From the below graph it is clear that the vertices of feasible region are (0,7.5), (3,3), (7.5,0).
Point P = 5x + 8y
(0,7.5) P=5(0)+8(7.5)=60
(3,3) P=5(3)+8(3)=15+24=39
(7.5,0) P=5(7.5)+8(0)=37.5 (Minimum)
So, minimum value is 37.5.
Therefore, the correct option is D.
Answer:
Power generated = 4.315 kW
Step-by-step explanation:
Given,
- speed of wind when enters into the turbine, V = 12 m/s
- speed of wind when exits from the turbine, U = 9 m/s
- mass flow rate of the wind, m = 137 kg/s
According to the law of conservation of energy
Energy generated = change in kinetic energy
Since, the air is exiting at same elevation. So, we will consider only kinetic energy.
Energy generated in one second will be given by,
=4315.5 J
= 4.315 kJ
So, energy is generated in one second = 4.315 kJ
Power generated can be given by,
And the energy is generated is already in per second so power generated will be 4.315 kW.