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natka813 [3]
3 years ago
14

By which least number should 12500 10be multiplied to make them perfect squares

Mathematics
1 answer:
Katarina [22]3 years ago
6 0

Answer:

5

The least number 12500 need to be multiplied by to make it a perfect square is 5.

Corrected question;

By which least number should 12500 be multiplied to make them perfect squares

Step-by-step explanation:

Perfect squares are squares of whole numbers.

Like 4,9,16 etc.

For 12500, we need to first of all reduce it to its Lowest factors.

12500 = 2×2×5×5×5×5×5

Grouping the factors into pairs of thesame factors.

12500 = (2×2) × (5×5) × (5×5) × 5

Looking at the pairs of factors, we can observe that the last factor 5 need to be paired to make the number a perfect square.

So, when the number is multiplied by 5;

12500 × 5 = (2×2) × (5×5) × (5×5) × (5×5)

62500 = (2×2) × (5×5) × (5×5) × (5×5)

62500 = (2×5×5×5)^2 = 250^2

Hence, 62500 is a perfect square.

The least number 12500 need to be multiplied by to make it a perfect square is 5.

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3 years ago
The cost, C, to produce b baseball bats per day is modeled by the function C(b) = 0.06b2 – 7.2b + 390. What number of bats shoul
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Check the picture below, that's just an example of a parabola opening upwards.

so the cost equation C(b), which is a quadratic with a positive leading term's coefficient, has the graph of a parabola like the one in the picture, so the cost goes down and down and down, reaches the vertex or namely the minimum, and then goes back up.

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\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ C(b) = \stackrel{\stackrel{a}{\downarrow }}{0.06}b^2\stackrel{\stackrel{b}{\downarrow }}{-7.2}b\stackrel{\stackrel{c}{\downarrow }}{+390} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)

\bf \left( -\cfrac{-7.2}{2(0.06)}~~,~~390-\cfrac{(-7.2)^2}{4(0.06)} \right)\implies (60~~,~~390-216) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\textit{number of bats}}{60}~~,~~\stackrel{\textit{total cost}}{174})~\hfill

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