A rectangle has length 127.3 cm and width 86.5 cm, both correct to 1 decimal place. Calculate the upperbound and the lowerbound
1 answer:
Answer:
Correct to 1dp
127.3 cm = 127.0 cm
86.5 cm = 87.0 cm
Upper limits:
127.0 cm = 127.05 cm
87.0 cm = 87.05 cm
Lower Limits:
127.0 cm = 126.95 cm
87.0 cm = 86.95 cm
upper limit of perimeter of rectangle:
P = 2(l+w)
= 2(127.05 + 87.05)
= 2(214.1)
= 428.2 cm
lower limit of perimeter of rectangle:
P = 2(l+w)
= 2(126.95 + 86.95)
= 2(213.9)
= 427.8 cm
therefore;
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Melanie said:
Every angle bisector in a triangle bisects the opposite side perpendicularly.
A 'counterexample' would show an angle bisector in a triangle that DOESN'T
bisect the opposite side perpendicularly.
See my attached drawing of a counterexample.
Both of the triangles that Melanie examined have equal sides on both sides
of the angle bisector. That's the only way that the angle bisector can bisect
the opposite side perpendicularly. Melanie didn't examine enough different
triangles.
Every angle bisector in a triangle bisects the opposite side perpendicularly.
A 'counterexample' would show an angle bisector in a triangle that DOESN'T
bisect the opposite side perpendicularly.
See my attached drawing of a counterexample.
Both of the triangles that Melanie examined have equal sides on both sides
of the angle bisector. That's the only way that the angle bisector can bisect
the opposite side perpendicularly. Melanie didn't examine enough different
triangles.
General Idea:
The volume of cylinder is given by , where r is the radius and h is the height of the cylinder.
Applying the concept:
Step 1: We need to find the volume of full cylinder with the given dimensions using the formula.
Volume of full cylinder
Volume of half cylinder
Step 2: Let x be the number of minutes of filling the sand.
of sand filled every 15 seconds, there are four 15 seconds in a minute.
So volume of sand filled in 1 minute.
of sand taken out of cylindrical vase every minute.
Net volume of sand filled in 1 minute = Volume of sand filled in the vase in one minute - Volume of sand taken out in 1 minute
Net volume of sand filled in 1 minute
Volume of sand filled in x minutes .
We need to set up an equation to find the number of minutes need to fill half the volume in cylindrical vase.
Conclusion:
The number of minutes required for the base be half filled with sand is 57