
First, let's deal with the fraction in the denominator of the exponent. Multiply the top and bottom of the exponent by 6.

Now that the fraction in the denominator is taken care of, we can reduce the denominator.
. Some professors might accept this as simplest form, but others might ask you to get rid of the negative.

Answer:
Option A.
Step-by-step explanation:
step 1
we know that
The equation of the solid line is

The solution is the shaded area above the solid line
so
The equation of the first inequality is

step 2
The equation of the dashed line is

The solution is the shaded area above the dashed line
so
The equation of the second inequality is

therefore
The system of inequalities could be


<span>To do these you will be adding or subtracting 2pi (or integer multiples of .
Since the given angles are in fraction form, it will help to have 2pi in fraction form, 2pi=10/5=6pi/3=4pi/2=18pi/9 NOTE: this>(/) stands for over like 1 over 2 EX. 1/2
too, so the addition/subtraction is easier.
Hint: When deciding if you have a number between 0 and 2pi, compare it to the fraction version of 2pi that you've been adding/subtracting.
For 17pi/5...
First we can see that 17pi/5 is more than 10pi/5 (aka 2pi). So we need to start subtracting: 17pi/5 - 10pi/5 = 7pi/5
Now we have a number between 0 and 10pi/5. So 7pi/5 is the co-terminal angle between 0 and 2pi.
I'll leave the others for you to do. Just remember that you might have to add or subtract multiple times before you get a number between 0 and 2pi.
P.S don't add or subtract at all if the number starts out between 0 and 2pi.</span>
Answer:
1250 m²
Step-by-step explanation:
Let x and y denote the sides of the rectangular research plot.
Thus, area is;
A = xy
Now, we are told that end of the plot already has an erected wall. This means we are left with 3 sides to work with.
Thus, if y is the erected wall, and we are using 100m wire for the remaining sides, it means;
2x + y = 100
Thus, y = 100 - 2x
Since A = xy
We have; A = x(100 - 2x)
A = 100x - 2x²
At maximum area, dA/dx = 0.thus;
dA/dx = 100 - 4x
-4x + 100 = 0
4x = 100
x = 100/4
x = 25
Let's confirm if it is maximum from d²A/dx²
d²A/dx² = -4. This is less than 0 and thus it's maximum.
Let's plug in 25 for x in the area equation;
A_max = 25(100 - 2(25))
A_max = 1250 m²
Answer:
The hourly wage is $8.55 per hour
Step-by-step explanation:
Step 1: Determine the expression for the gross pay
Total gross pay=(Unit rate per hour×number of hours(≤40))+(Overtime rate×number of overtime hours)
where;
Total gross pay=$380.48
Unit rate per hour=x
Number of hours=40 hours
Overtime rate=x×(1 1/2)=1.5 x
Number of overtime hours=3 hours
Step 2: Replace to solve for hourly wage
380.48=(x×40)+(1.5 x)×3
40 x+4.5 x=380.48
44.5 x=380.48
x=380.48/44.5
x=8.55
The hourly wage is $8.55 per hour