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GalinKa [24]
3 years ago
11

A machine at a graphic design studio produces paper labels for juice bottles. This graph represents the number of labels produce

d over time.
Zoom in if you cannot see!

Don’t answer if you don’t know the answer. Whoever gets the correct answer will get Brainliest! :)

Mathematics
2 answers:
Jobisdone [24]3 years ago
6 0

Answer:

Option B, would be the correct answer: 75 labels per minute

Step-by-step explanation:

The number of labels produced per minute would be a constant value which would be the slope of this graph represented above.

Slope = \frac{rise}{run}

Slope = \frac{150}{2}

Slope = 75

Hope this helps!

Igoryamba3 years ago
5 0
I think it’s 150 since 1 minute= 150 labels
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The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find
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Answer:

<em>The particular integral of given differential equation</em>

<em>                  </em>y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))<em></em>

<em> General solution of given differential equation</em>

<em>      </em>y = y_{c} + y_{p}<em></em>

<em>  </em>Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))<em></em>

<em></em>

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Given Differential equation  y'' − 5 y' + 4 y = x

Given equation in operator form

        D²y - 5 Dy +  4 y = x

⇒     ( D² - 5 D +  4 ) y =x

⇒    f(D) y = Q

where  f(D) = D² - 5 D +  4 and Q(x) = x

<em>The auxiliary equation  f(m) =0</em>

<em>           m²-5 m + 4 =0</em>

         m² - 4 m - m + 4 =0

        m ( m -4 ) -1 ( m-4) =0

         (m - 1) =0   and ( m-4) =0

        <em> m = 1 and m =4</em>

<em>The complementary function </em>

<em></em>Y_{c} = C_{1} e^{x} + C_{2} e^{4x}<em></em>

<u><em>Step(ii)</em></u>:-

<u><em>particular integral</em></u>

<em>Particular integral</em>

<em>     </em>y_{p} = \frac{1}{f(D)} Q(x) = \frac{1}{D^{2}  - 5 D +  4} X<em></em>

<em>taking common '4' </em>

<em>                          </em>= \frac{1}{4(1 +  (\frac{D^{2}  - 5 D}{4} ))} X<em></em>

<em>                         </em>

<em>                           </em>=\frac{1}{4}  (1 + (\frac{D^{2} -5D}{4})^{-1} )} X<em></em>

<em>applying binomial expression</em>

<em>      ( 1 + x )⁻¹    = 1 - x + x² - x³ +.....       </em>

<em>                          </em>=\frac{1}{4}  (1 - (\frac{D^{2} -5D}{4}) +((\frac{D^{2} -5D}{4})^{2} -...} )X<em></em>

<em>Now simplifying and we will use notation D = </em>\frac{dy}{dx}<em></em>

<em>                        </em>=\frac{1}{4}  (x - (\frac{D^{2} -5D}{4})x +((\frac{D^{2} -5D}{4})^{2}(x) -...}<em></em>

<em>Higher degree terms are neglected</em>

<em>                     </em>=\frac{1}{4}  (x - (\frac{ -5 D}{4}) x)<em></em>

<em>The particular integral of given differential equation</em>

<em>                  </em>y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))<em></em>

<u><em>Final answer</em></u><em>:-</em>

<em>          General solution of given differential equation</em>

<em>      </em>y = y_{c} + y_{p}<em></em>

<em>  </em>Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))<em></em>

<em></em>

<em></em>

<em>         </em>

<em> </em>

     

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