Answer:
x = 80
Step-by-step explanation:
We know the sum of the angles of a triangle is 180
x+y+z = 180
Since this is an isosceles triangle y=x
x +x + z = 180
We also know that x = 4z
Writing this in terms of x since we want to find angle x
z = 1/4x
x+x+1/4x = 180
Combine like terms
2x +1/4x = 180
Multiply each side by 4 to get rid of fractions
4(2x +1/4x) = 180*4
8x +x =720
9x = 720
Divide by 9
9x/9 = 720/9
x = 80
If 8 is the first term, there are 17 terms left to reach the 18th term. So you do -2 x 17 = -34 then do 8 - 34 = -26
We can create two equations here:
(1) Volume = area of square * height of box
85.75 = s^2 h
(2) Cost = 3 * area of square + 1.5 * area of side box
C = 3 s^2 + 1.5 s h
From (1), we get:
h = 85.75 / s^2
Combining this with (2):
C = 3 s^2 + 1.5 s (85.75 / s^2)
C = 3 s^2 + 128.625 s-
Taking the 1st derivative and equating dC/ds =
0:
dC/ds = 6s – 128.625 / s^2 = 0
Multiply all by s^2:
6s^3 – 128.625 = 0
6s^3 = 128.625
s = 2.78 cm
So h is:
h = 85.75 / s^2 = 85.75 / (2.78)^2
h = 11.10 cm
So the dimensions are 2.78 cm x 2.78 cm x 11.10 cm
The total cost now is:
C = 3 (2.78)^2 + 1.5 (2.78) (11.10)
C = $69.47
Answer:p=$20
Step-by-step explanation:
145-65=80
80/4=20
so each pant costs $20
p=$20
The area of a triangle can be calculated through the equation,
A = bh / 2
where A is area, b is base, and h is height.
Substituting the known values from the given above to the equation
A = (14 in)(6 in) / 2 = 42 in²
Since, there are five of these triangles, the total area is,
total area = 5(42 in²) = 210 in²
Thus, the total area of the plywood needed is 210 in².