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Marina86 [1]
3 years ago
8

The equation x^3-5x=59 has a solution between 4and 5 . Use trail and improvement method. Give your answer to 1 decimal place.

Mathematics
1 answer:
3241004551 [841]3 years ago
5 0

Answer:

4.3 to 1 decimal place.

Step-by-step explanation:

x^3 - 5x - 59 = 0

Try x = 4.1:

f(4.1) = (4.1)^3 - 5(4.1) - 59 = -10.579

Try: 4.2:

f(4.2) = 4.2^3 - 5(4.2) - 59 = -5.912,  Try x = 4.3:

f(4.3) = -0.993 (getting closer to 0!!)

f(4.4) = 4.184

NOTICE - there is a change of sign in the result so the root lies between 4.3 and 4.4.

Try x = 4.35:

f(4.35) = 1.563  so it looks like the root is closer to 4.3 than 4.4 because 1.563 is closer to zero than 4.184.

Just to double check let's calculate x = 4.32:

f(4.32) = 0.0216 - which is very close to zero.

So the answer is 4.3 to 1 decimal  place.

(I've checked it out on my calculator - the root is 4.31958).

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Answer:

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Step-by-step explanation:

Since it is arithmetic series, first find the difference d between the two know series.

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Looking for the n term, use the linear method.

Tn = a+( n - 1)d

Substitute all the parameters

-29.2 = 6+( n - 1 ) -2.2

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To Find the exact sum of the arithmetic series, use the sum formula below

Sm = n/2( 2a + (n - 1)d)

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Sm = 17/2(12 - 35.2)

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