Question

plz help me in this 2 question ​

Answer 1

$\large\underline{\sf{Given \:Question - }}$

At 't' minutes past 5 pm, the time needed by the minutes hand of a clock to show 6 pm was found to be 25 minutes less than 3t^2/4 minutes. Find t.

$\large\underline{\sf{Solution-}}$

Given that,

At t' minutes past 5 pm, the time needed by the minutes hand of a clock to show 6 pm = 60 - t minutes.

Also,

Time needed by the minute hand to show 6 pm was found to be 25 minutes less than 3t^2/4 minutes.

It means,

Time needed by the minute hand to show 6 pm = 3t^2/4 - 25 minutes.

So,

$\rm :\longmapsto\:60 - t = \dfrac{3 {t}^{2} }{4} - 25$

$\rm :\longmapsto\:60 - t = \dfrac{3 {t}^{2} - 100 }{4}$

$\rm :\longmapsto\:4(60 - t) = {3t}^{2} - 100$

$\rm :\longmapsto\:240 - 4t = {3t}^{2} - 100$

$\rm :\longmapsto\:{3t}^{2} + 4t - 240 - 100 = 0$

$\rm :\longmapsto\:{3t}^{2} + 4t - 340 = 0$

$\rm :\longmapsto\:{3t}^{2} + 34t - 30t - 340 = 0$

$\rm :\longmapsto\:t(3t + 34) - 10(3t + 34) = 0$

$\rm :\longmapsto\:(3t + 34)(t - 10) = 0$

$\bf\implies \:t = 10 \: \: \: or \: \: \: t = - \: \dfrac{34}{3} \: \{ \: rejected \: \}$

So,

$\bf\implies \:\boxed{ \bf{ \: t \: = \: 10 \: }}$

Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac

Answer 2

Answer:

$t = 10$

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