Answer:
80 degrees
Step-by-step explanation:
Vertical angles are congruent, meaning that if a vertical angle is 80 degrees, the other vertical angle is 80 degrees; they have the same angle measure.
m < 1 = 80 degrees
Let
x------> the length side of the square base of the box
y-------> the height of the box
we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1
<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>
surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x
step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm
the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm
50?
I'm assuming 50 because the angles to a triangle always adds up to 180 and this one has 130 and 130+50=180
Answer:
The value of (x + y)³ is 1728.
Step-by-step explanation:
First, you have to find the value of x + y :
x² + 2xy + y² = 144
x² + xy + xy + y² = 144
x(x + y) + y(x + y) = 144
(x + y)(x + y) = 144
(x + y)² = 144
x + y = √144
x + y = 12
Next, the value of (x + y)³ :
(x + y) = 12³ = 1728
5u > 64 - 14
5u > 50
u > 10
