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Volgvan
3 years ago
14

Perform the following multiplication. 4.7314 × 10 = 47.314 0.47314 473.14 4,731.4

Mathematics
1 answer:
Dima020 [189]3 years ago
6 0

Answer:

47.314

Step-by-step explanation:

We want find the results of the multiplication,

4.7314 \times 10

When we multiply by 10, we move the decimal point forward once.

When we divide by 10, we move the decimal point backwards once.

In this case, we are multiplying, so

4.7314 \times 10 = 47.314

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Step-by-step explanation:

Following order of operations:

16-2+3-4

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Find the roots of h(t) = (139kt)^2 − 69t + 80
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Answer:

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Step-by-step explanation:

Let h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80, roots are those values of t so that h(t) = 0. That is:

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Roots are determined analytically by the Quadratic Formula:

t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}

t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }

The smaller root is t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }, and the larger root is t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }.

h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80 has one real root when \frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0. Then, we solve the discriminant for k:

\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}

k \approx \pm 0.028

The positive value of k will result in exactly one real root is approximately 0.028.

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