Marco and Drew stacked boxes on a shell. Marco lifted 9 boxes and Drew lifted 14 boxes. The boxes that Drew lifted each weighed
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We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: , where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is:
Answer:
.
(Expand to obtain an equivalent expression for the sphere: )
Step-by-step explanation:
Apply the Pythagorean Theorem to find the distance between these two endpoints:
.
Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:
.
In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between and
would be:
.
In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:
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The equation for a sphere of radius and center
would be:
.
In this case, the equation would be:
.
Simplify to obtain:
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Expand the squares and simplify to obtain:
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