Which words or phrases have the same meaning as subtraction
1 answer:
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Answer:
At 8:52:30 am they will be side-by-side again
Step-by-step explanation:
Let s be the distance ran in one 1 lap.
Here Jeff runs one extra lap compared to Mandy for coming side by side again.
Mandy runs one lap in 2 minutes and 30 seconds = 150 s
Speed of Mandy,
Jeff runs one lap in 2 minutes and 15 seconds = 135 s
Speed of Jeff,
Let t be the time when Jeff run one extra lap,
That is
So after 1350 seconds Jeff comes side by side to Mandy,
They both start at 8:30 am
1350 s = 22.5 minutes = 22 minutes 30 seconds
Time = 8:52:30 am
Option A: The height of the cylinder is equal to the diameter of the sphere.
Option C: The radius of the sphere is half the height of the cylinder.
Option E: The volume of the sphere is two-thirds the volume of the cylinder.
Solution:
The sphere is inside the cylinder.
Let r be the radius of the sphere.
Option A: The height of the cylinder is equal to the diameter of the sphere.
The sphere is fully occupied the cylinder.
If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.
Option B: The height of the cylinder is two times the diameter of the sphere.
That is h = 2d. From the above option, we know that h = d.
So, it is not true.
Option C: The radius of the sphere is half the height of the cylinder.
we know that diameter = 2 × radius (d = 2r)
From option A, we have h = d.
Substitute d = 2r, we get
⇒ h = 2r
Divide by 2 on both sides, we get
Therefore, it is true.
Option D: The diameter of the sphere is equal to the radius of the cylinder.
It is not true, because diameters of both cylinder and sphere are equal.
Option E: The volume of the sphere is two-thirds the volume of the cylinder.
Radius of cylinder and sphere = r
Height of cylinder h = 2r (by option C)
Volume of cylinder = Volume of sphere
(formula)
Hence it is true.
Option A, option C and option E are true.