Because you have an inequality, there will be three possible intervals as solution sets for the inequality. Test a value for each possible interval to determine the solution.
C
c
Because you have an inequality, there will be three possible intervals as solution sets for the inequality. Test a value for each possible interval to determine the solution.
D
d
Because you have an inequality, there will be three possible intervals as solution sets for the inequality. Test a value for each possible interval to determine the solution.
We can simplify this result into two separate roots.
r=-46.9±31.01499.../-16.2
r_1=-46.9 + 31.01499.../-16.2
r_2=-46.9 - 31.01499.../-16.2
r_1≈ 0.98
r_2≈ 4.81
The roots states that the mall does not make profit if the monthly rent is about $980 or $4810.
b
To solve the inequality, we will first solve the related quadratic equation.
-8.1r^2+46.9r-38.2>0
⇓
-8.1r^2+46.9r-38.2=0We have already found the roots of the related quadratic equation in Part A.
r_1&=0.98
r_2&=4.81
Because we have an inequality, there are three possible intervals as solution sets for the inequality. We will test a value for each possible interval to determine the solution.
Intervals
x
-8.1r^2+46.9r-38.2
P(r)? >0
r<0.98
0
-8.1( 0)^2+46.9( 0)-38.2
-38.2≯0
0.98< r < 4.81
2
-8.1( 2)^2+46.9( 2)-38.2
23.2>0
r>4.81
5
-8.1( 5)^2+46.9( 5)-38.2
-6.2≯ 0
The solution set for the inequality is 0.98< r < 4.81. This means that the profit of the mall will be greater than $0 if the monthly rent is between $980 and $4810.
c
Let's first write the related quadratic equation for the given inequality.
-8.1r^2+46.9r-38.2>10
⇓
-8.1r^2+46.9r-38.2=10
Now, we will solve it by using the Quadratic Formula.
We can simplify this result into two separate roots.
r=-46.9±25.25727.../-16.2
r_1=-46.9 + 25.25727.../-16.2
r_2=-46.9 - 25.25727.../-16.2
r_1≈ 1.33
r_2≈ 4.45
With these results, we again have three possible intervals as solution sets. Let's test a value for each interval and decide the solution set.
Intervals
x
-8.1r^2+46.9r-48.2
P(r)? >0
r<1.33
0
-8.1( 0)^2+46.9( 0)-48.2
-48.2≯0
1.33< r < 4.45
2
-8.1( 2)^2+46.9( 2)-48.2
13.2>0
r>4.45
5
-8.1( 5)^2+46.9( 5)-48.2
-16.2≯ 0
This time, the solution set states that the profit of the mall will be greater than $10 000 if the monthly rent is between $1330 and $4450.
d
As we did in the previous parts, we will begin by determining the related quadratic equation.
-8.1r^2+46.9r-38.2< 10
⇓
-8.1r^2+46.9r-38.2=10We have already found the roots of the related quadratic equation in Part C.
r_1&=1.33
r_2&=4.45
Proceeding in the same way as we did in Part C, we can determine the solution set of the inequality.
Intervals
x
-8.1r^2+46.9r-48.2
P(r)? <0
r<1.33
0
-8.1( 0)^2+46.9( 0)-48.2
-48.2<0
1.33< r < 4.45
2
-8.1( 2)^2+46.9( 2)-48.2
13.2≮0
r>4.45
5
-8.1( 5)^2+46.9( 5)-48.2
-16.2< 0
The solution set for the inequality is either r < 1.33 or r > 4.45. Therefore, the profit of the mall will be less than $10 000 if the monthly rent is less than $1330 or greater than $4450.
