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dedylja [7]
4 years ago
15

One terameter equals 1012 meters. One micrometer equals 10 meter.

Mathematics
1 answer:
Butoxors [25]4 years ago
3 0

Answer:

<h2>a)  10⁶metres</h2><h2>b) 10¹⁸metres</h2>

Step-by-step explanation:

Given One terameter equals 10¹² meters. One micrometer equals 10⁻⁶ meter, one nanometer equals 10⁻⁹meter;

a) The product of one terameter and one micrometer will be expressed as;

10¹²  * 10⁻⁶

Since the both have the same base, we will add their power according to one of the law in indices as shown

10¹²  * 10⁻⁶ = 10⁻⁶⁺¹²

= 10⁶metres

b) The quotient of one terameter and one micrometer can be gotten by taking their ratio as shown below;

Note that when taking the quotient, the power are subtracted

= \frac{10^{12} }{10^{-6} } \\= 10^{12-(-6)}  \\= 10^{12+6} \\= 10^{18}metres

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18. h = 14.4

19. h = 4.23

20. h = 15.28

21. h = 11.46

All answers are rounded to two decimal places.

Step-by-step explanation:

18. To find the height if you know all 3 sides. Multiply sides a & b, and divide the product by c.

x = (a * b)/c

x = (18 * 24)/30

x = 432/30

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x = 14.4

19. We know that the entire length of the hypotenuse is 27. However, 24 is needed here. That's 8/9 of 27, so 80 degrees is one of the angles. So we need to find the hypotenuse first. That can be done like this: b/sin(β)

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Now to find the first leg, which will be the height of the entire triangle.

x = √c² - b²

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20. This one requires similar work to #19, but the hypotenuse of the smaller triangle is x.

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23.0940109

√23.0940109² - 20²

√533.333339 - 400

√133.333339

11.5470056

î The answer above is leg 2 of the smaller triangle.

x = √10² + 133.333339

x = √100 + 133.333339

x = √233.33339

x = 15.2752525

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21. There is no need to figure out what the height is. The entire triangle is 45-45-90.

x = (√18² + 18²) - 15

x = (√324 + 324) - 15

x = (√648) - 15

x = 25.46 - 15

x = 11.46

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3 years ago
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