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KIM [24]
3 years ago
10

Two laboratory technicians are running product quality tests. One technician takes 6 minutes less than the

Mathematics
1 answer:
kodGreya [7K]3 years ago
3 0

Answer:

The time it will take will be ;

t = (2x -6)/(x^2-6x)

Where x is the amount of time

in minutes taken by the technician who is slower

Step-by-step explanation:

We want to write the time it would take to run the tests if the technicians work together.

Let the time taken by the first technician be x minutes

The time that would. taken by the second is 6 minutes less which is (x -6) minutes

So if they work together, how long will it take?

That would be ;

t = 1/x + 1/(x-6)

t = (x + x -6)/(x(x-6))

t = (2x -6)/(x^2 -6x)

The time it will take if they both work together is ;

t = (2x -6)/(x^2-6x)

where x minutes is the amount of time taken by the technician who is slower of the two

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<h3><u>Answer:</u></h3>

\large\boxed{\pink{\sf \leadsto Value \ of \ LM \ is \ 11 \ units . }}

<h3><u>Step-by-step explanation:</u></h3>

A figure is given to us in which we can see two triangles one is ∆ MPL and other is ∆MPN .

<u>Figure</u><u> </u><u>:</u><u>-</u><u> </u>

\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\linethickness{0.25mm}\put(0,0){\line(1,2){2}} \put(0.001,0){\line(1,0){4}}\put(2,0){\vector(0,1){5}}\put(4,0){\line( - 1,2){2}}\put(0,-0.4){$\bf L $}\put(2,-0.4){$\bf P$}\put(4,-0.4){$\bf N $}\put(2.2,4){$\bf M $}\put(2.8, - .4){$\bf 5 $}\put(1, - .4){$\bf 5 $}\put(3.4, 2){$\bf 11 $}\put(2.3,0){\line(0,1){.3}}\put(2.3,.3){\line( - 1,0){.3}}\end{picture}

\underline{\blue{\sf In\: \triangle MPL \ \& \ \triangle MPN :- }}

\qquad \bullet LP = PN = 5 \:\:(given) \\\\\qquad \bullet MP = MP \:\:(Common) \\\\\qquad \bullet \angle MPN = \angle MPL = 90^{\circ} \:\: (given)

Hence by SAS congruence condition ,

\orange{\bf \triangle MPL \cong \triangle MPN }

Hence by cpct ( Corresponding parts of congruent triangles ) we can say that , LM = NM = 11 units .

<h3><u>Hence </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>LM</u><u> </u><u>is</u><u> </u><u>1</u><u>1</u><u> </u><u>units</u><u> </u><u>.</u></h3>
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