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grigory [225]
4 years ago
13

The sum of three consecutive number is 54 Find the first two number.​

Mathematics
1 answer:
nirvana33 [79]4 years ago
3 0
  • <em>Answer:</em>

<em>a = 17</em>

<em>b = 18</em>

<em>c = 19</em>

  • <em>Step-by-step explanation:</em>

<em>Hi there ! </em>

<em>a + b + c = 54</em>

<em>b = a + 1</em>

<em>c = a + 2</em>

<em>replace b ; c</em>

<em>a  + (a + 1) + (a + 2) = 54</em>

<em>3a = 54 - 3</em>

<em>3a = 51</em>

<em>a = 51 : 3</em>

<em>a = 17</em>

<em>b = 18</em>

<em>c = 19</em>

<em>Good luck !</em>

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Answer:

{ \underline{ \sf{\int\limits^2_1 {x^{2}-8x+8 } \, dx}  \: =  \:  - 1}}

Step-by-step explanation:

{ \tt{\int\limits^2_1 {x^{2}-8x+8 } \, dx}} \\  \\ =  { \tt{[ \frac{ {x}^{3} }{3}  - 4 {x}^{2}  + 8x ] {}^{2} _{1}}}

Substitute x with the limits:

= { \tt{( \frac{ {2}^{3} }{3}  - 4( {2)}^{2} + 8(2)) - ( \frac{ {1}^{3} }{3}  - 4( {1)}^{2}  + 8(1)) }} \\  = { \tt{( \frac{8}{3}  -  \frac{11}{3} )}} \\  \\  = { \tt{ - 1}}

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Using integration, it is found that the area under the graph of f(x) in the desired interval is of 1 unit squared.

<h3>How is the area under a graph found?</h3>

The area under the graph of a curve f(x) between x = a and x = b is given by the following integral:

A = \int_{a}^{b} f(x) dx

In this problem, the function and the limits of integration are given by:

f(x) = \frac{1}{x\ln{x}}

a = e, b = e^e

Hence:

A = \int_{e}^{e^e} \frac{1}{x\ln{x}} dx

Using substitution:

u = \ln{x}

du = \frac{1}{x} dx

dx = x du

Hence:

\int \frac{1}{x\ln{x}} dx = \int \frac{1}{u} du = \ln{u} = \ln{\ln{x}}

Applying the Fundamental Theorem of Calculus:

A = \ln{\ln{e^e}} - \ln{\ln{e}} = \ln{e\ln{e}} = \ln{\ln{e}} = \ln{e} - \ln{1} = 1

Hence, the area under the graph of f(x) in the desired interval is of 1 unit squared.

To learn more about integration, you can take a look at brainly.com/question/20733870

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