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makvit [3.9K]
2 years ago
12

two sets of 3 consecutive integers have a property that the product of the larger two is one less than seven times the smallest

set up and solve an equation that can be used to find both sets of intigers
Physics
1 answer:
Alchen [17]2 years ago
7 0
Answer:
First set is 3,4 and 5
Second set is 1,2 and 3

Explanation:
Assume that the smallest number is n.
Since the three numbers are consecutive, this means that the other two numbers would be n+1 and n+2

Now, we know that the product of the larger two numbers is 1 less tan than 7 times the smallest.
This means that: 
(n+1)(n+2) = 7n - 1 .........> equation used to find the sets
n² + 2n + n + 2 = 7n - 1
n² + 3n + 2 = 7n - 1
n² + 3n + 2 - 7n + 1 = 0
n² - 4n + 3 = 0
(n-3)(n-1) = 0
This means that:
either n-3=0 ..........> n = 3
or n-1=0 ..........> n = 1

At n = 3:
The three numbers would be 3,4 and 5

At n = 1:
The three numbers would be 1,2 and 3

Hope this helps :)

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You are trying to find out how high you have to pitch a water balloon in order for it to burst when it hits the ground. You disc
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<em>Lets explain how to solve the problem</em>

You found that the best height to pitch a water balloon in order for it to

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I'll assume that the child is on Earth at sea level at the equator, so that his distance from the geocenter is 6378000 meters.

The acceleration, g, is found from

g = GM/r²

G = 6.6743e-11 m³ kg⁻¹ sec⁻²

M = 5.9724e+24 kg

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g = 9.799086 m sec⁻²

An approximate answer is found from an equation from constant acceleration kinematics:

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Now, the above method is an approximation that makes the technically incorrect assumption that the acceleration of gravity is a constant throughout the entire fall. You get away with it because the drop is very short. In another situation, it might not be. So it would be nice to develop a more accurate method that does not assume constant gravitational acceleration. For that, we begin with the Vis Viva equation:

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