What's is slope of 2y+8x=21
2 answers:
You might be interested in
Answer:
Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w
Part 2; The zeros for the equation of the function, are w = -14, or w = 8
Part 3
The width of the box is 8 inch
The length of the box, is 14 inches
The height of the box, is given as 2 inches
Part 4
Please find attached the graph of the function
Step-by-step explanation:
Part 1
The volume of the box Thomas wants to make, V = 224 in.³
The dimensions he cuts out from the length and width = 2 in² each
The length of the box = 6 inches + The width of the box
Let <em>l</em> represent the length of the box and let <em>w</em> represent the width of the box, we have;
l = 6 + w
The height of the box, h = The length of the cut out square = 2 inches
The volume of the box, V = Length, l × Width, w × Height, h
∴ V = l × w × h
l = 6 + w, h = 2
∴ V = (6 + w) × w × 2
V = 2·w² + 12·w,
The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224
∴ 224 = 2·w² + 12·w
Part 2
The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;
V = 224 = 2·w² + 12·w
∴ 2·w² + 12·w - 224 = 0
Dividing by 2 gives;
(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0
∴ (w + 14) × (w - 8) = 0
The zeros for the equation of the function, are w = -14, or w = 8
Part 3
We reject the value, w = -14, therefore, the width of the box, w = 8 inch
The length of the box, l = 6 + w
∴ l = 6 + 8 = 14
The length of the box, l = 8 inches
The height of the box, <em>h</em>, is given as h = 2 inches
Part 4
The graph of the function created with MS Excel is attached
Here, we want to find the diagonal of the given solid
To do this, we need the appropriate triangle
Firstly, we need the diagonal of the base
To get this, we use Pythagoras' theorem for the base
The other measures are 6 mm and 8 mm
According ro Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides
Let us have the diagonal as l
Mathematically;
Now, to get the diagonal, we use the triangle with height 5 mm and the base being the hypotenuse we calculated above
Thus, we calculate this using the Pytthagoras' theorem as follows;