Answer:
or
Step-by-step explanation:
Let:
Given
Solving (a): The polynomial for the volume in terms of height
Volume (V) is calculated using:
Expand
Open brackets
Rewrite as:
Solving (b): The dimensions when Volume = 180
Substitute 180 for V in:
Rewrite as:
Factorize:
Express as difference of two squares
This gives:
Since the height can not be negative, then H = 5 or H = 6
Recall that:
When H = 5
When H = 6
Hence, the dimensions of the box are:
or
Answer:
<em>m<2 = 125°, m<8 = 55° and m<14 = 100°</em>
Step-by-step explanation:
The question is incomplete.
<em>Lines e and f are parallel. The mAngle9 = 80° and mAngle5 = 55°. Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Where lines e and c intersect, the angles are: 1, 2, 4, 3. Where lines f and c intersect, the angles are 5, 6, 8, 7. Where lines e and d intersect, the angles are 9, 10, 12, 11. Where lines f and d intersect, the angles are 13, 14, 16, 15. Which angle measures are correct? Select three options. mAngle2 = 125° mAngle3 = 55° mAngle8= 55° mAngle12 = 100° mAngle14 = 100</em>
Given
m<9 = 80°
m<5 = 55°
From the diagram, m<5+m<6 = 180°
Substitute m<5 = 55° into the formula, to get m<6
55+m<6 = 180
m<6 = 180-55
m<6 = 125°
From the diagram m<6 = m<2 = 125° (corresponding angles)
<em>Also on line e</em>, m<9 = m<12 = 80° (vertically opposite angles)
On line f, m<14+m<16 = 180° and m<12 = m<16 = 80
m<14+80° = 180°
m<14 = 180-80
m<14 = 100°
<em>Also on line f</em>, m<5 = m<8 (vertically opposite angles)
Since m<5 = 55°, m<8 = 55°
Also on line e, m<10 + m<12 = 180
Since m<2 = m<10 = 125° (corresponding angle)
To get m<12,
125+m<12 = 180
m<12 = 180-125
m<12 = 55°
Also m<10 = m<14 = 125° (corresponding angle)
On line e, m<10 = m<11 = 125° (vertically opposite angle)
Also on line e, m<3 = m<11 (corresponding angle)
This shows that m<10 = m<11 = m<3 = 125°
<em>From the above calculation the angle measure that are correct are:</em>
<em> m<2 = 125°, m<8 = 55° and m<14 = 100°</em>
