Answer:
Step-by-step explanation:
Given
-- Objective function
Constraints:
Required
Minimum value of E
To do this, we apply graphical method
See attachment for plots of and
From the attached plot, the point that satisfy is:
So, we have:
This gives:
The area of a triangle is area=1/2•base•height or a= b•h / 2
Answer:
27 feet
Step-by-step explanation:
Two walls have same area
Area of first wall(square) = 18*18 = 324
Area of second wall = 12 * x = 324
324/12 = 27
27 feet
Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
Answer:
127.17 cm²
Step-by-step explanation:
- Area of a semicircle: 1/2*π*r²
- π (pi) = 3.14
- r (radius) = d (diamater) / 2 => 18/2 = 9 cm
A = 1/2*π*r²
A = 1/2*3.14*9²
A = 1/2*3.14*81
A = 3.14*40.5
A = 127.17 cm²
Therefore, the area of the semicircle is 127.17 cm²
Hope this helps!
