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Tems11 [23]
3 years ago
15

The difference of the square of a number and 24 is equal to 5 times that number. Find the negative solution.

Mathematics
1 answer:
vampirchik [111]3 years ago
8 0

Answer:

the "negative solution" is -3

Step-by-step explanation:

Represent the number by n.

Then n^2 - 24 = 5n

We rewrite this in standard quadratic form:

n^2 - 5n - 24 = 0

This factors as follows;  (n + 3)(n - 8) = 0

The roots are n = -3 and n = 8.  Thus, the "negative solution" is -3

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Answer:

a) k = 300\,\frac{N}{m}, b) \Delta U_{k} = 13.5\,J, c) \Delta U_{k} = 6\,J, d) \Delta U_{k} = 4.5\,J

Step-by-step explanation:

a) The spring constant is calculated by using this expression:

k = \frac{F}{x}

k = \frac{30\,N}{0.1\,m}

k = 300\,\frac{N}{m}

b) The work needed to compress the spring from its initial position is:

\Delta U_{k} = \frac{1}{2}\cdot k \cdot (x_{f}^{2}-x_{o}^{2})

\Delta U_{k} = \frac{1}{2}\cdot (300\,\frac{N}{m} )\cdot [(-0.3\,m)^{2}-(0\,m)^{2}]

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c) The work needed to stretch the spring is:

\Delta U_{k} = \frac{1}{2}\cdot (300\,\frac{N}{m} )\cdot [(0.2\,m)^{2}-(0\,m)^{2}]

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d) The work need to stretch the spring is:

\Delta U_{k} = \frac{1}{2}\cdot (300\,\frac{N}{m} )\cdot [(0.2\,m)^{2}-(0.1\,m)^{2}]

\Delta U_{k} = 4.5\,J

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Answer:

2. = 24

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