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vodka [1.7K]
3 years ago
5

Show that 5(3y-2)=15y-10 for at least 5 values of y

Mathematics
1 answer:
Vsevolod [243]3 years ago
7 0
<span>Solving the equation for Y = 1. 5 * (3 * 1 - 2) = 15 * 1 - 10 5 * (3 - 2) = 15 -10 5 * 1 = 5 5 = 5 Solving the equation for Y = 2. 5 * (3 * 2 - 2) = 15 * 2 - 10 5 * (6 - 2) = 30 -10 5 * 4 = 20 20 = 20 Solving the equation for Y = 4. 5 * (3 * 4 - 2) = 15 * 4 - 10 5 * (12 - 2) = 60 -10 5 * 10 = 50 50 = 50 Solving the equation for Y = 8. 5 * (3 * 8 - 2) = 15 * 8 - 10 5 * (24 - 2) = 120 -10 5 * 22 = 110 110 = 110 Solving the equation for Y = 9. 5 * (3 * 9 - 2) = 15 * 9 - 10 5 * (27 - 2) = 135 -10 5 * 25 = 125 125 = 125 This proves that the equation holds good for at least 5 values of 'y', which are 1, 2, 4, 8 and 9. However, it can be proved that the equation holds good for any value of y. Expression 5(3y-2) can be simplified to 15y -10 which is the same expression on the right had side of the equation provided. So, equation 5(3y-2)=15y-10 is actually 15y-10=15y-10 and since this is true for all values of y, it has been proved that it is true for at least 5 values of y.</span>
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Step-by-step explanation:

The right Riemann Sum uses the right endpoints of a sub-interval:

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where

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To find the Riemann sum for \int\limits^{4}_{-6} {3x-1} \, dx with n = 5 rectangles, using right endpoints you must:

We know that a = -6, b = 4 and n = 5, so

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We need to divide the interval −6 ≤ x ≤ 4 into n = 5 sub-intervals of length \Delta{x}=2

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Now, we just evaluate the function at the right endpoints:

f\left(x_{1}\right)=f\left(-4\right)=-13=-13

f\left(x_{2}\right)=f\left(-2\right)=-7=-7

f\left(x_{3}\right)=f\left(0\right)=-1=-1

f\left(x_{4}\right)=f\left(2\right)=5=5

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Finally, just sum up the above values and multiply by 2

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