Answer:
h = 6 cm
l = (32-2(6)) = 20 cm
w = (40-2(6)) = 28 cm
Step-by-step explanation:
Given in the question a piece of cardboard having dimensions 32 by 40
Suppose we cut square of length x
When you cut square corners from a piece of cardboard, two sides are 32-2x, and other two sides are 40-2x lengths
<h3>Step 1</h3>
Formula for the volume of box
v = height * length * width
v = x (32-2x) (40-2x)
v = 4x³ - 144x² + 1280x
<h3>Step 2</h3>
Find derivative and equal it to 0
dv/dx = 4(3)x² - (2)144x + 1280
0 = 12x² - 288x + 1280
x1 = 18.110
x2 =5.88
<h3>Step 3</h3>
Select x and plug value of x to find dimension
(32-2x) > 0
2x < 32
x < 16
so domain say that x should be less than 16 which means x = 5.88 ≈ 6 cm
h = 6 cm
l = (32-2(6)) = 20 cm
w = (40-2(6)) = 28 cm
Answer:
- ∠UTC = 55°
- ∠UCD = 70°
- ∠BCT = 55°
Step-by-step explanation:
In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.
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<h3>UTC</h3>
∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair
∠UTC = 180° -125° = 55°
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<h3>UCD</h3>
∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair
∠UCD = 180° -110° = 70°
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<h3>BCT</h3>
∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles
If if y=6 and z=1 then the equation would be 1+6(2) and that ends up to be 13
I think it's already in expanded form.
