Classify the triangle with side lengths of 12, 16, 20
1 answer:
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Answer:
h(x) = -16x² + 192x + 208
784ft
6 sec
13 sec
Step-by-step explanation:
a)
h(x) = -16x² +vx + h
here v represent velocity
represent initial height of launch
h(x) = -16x² + 192x + 208
b)
h(x) = -16x² + 192x + 208
here a = -16
b = 192
c = 208
x = -b/2a
= -192/2(-16)
= 6
plug this value in the equation
h(x) = -16(6)² + 192(6) + 208
= 784ft
e)
Plug h(x)=0 in the equation
0 = -16x² + 192x + 208
divide equation by -16
x² - 12x - 13 = 0
Factors
1x * -13x = -13
1x - 13x = -12
Factorised form
x² - 12x - 13 = 0
x² + x - 13x - 13 = 0
x(x+1) -13(x+1) = 0
(x+1)(x-13) = 0
x = -1
x = 13
Since time can not be negative so we will reject x = -1
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
