Answer:
2800
Step-by-step explanation:
round 278 to 280
then round 11 to 10
then times the 2 answers together
Multiply the coefficients and the powers of 10 with each other:
![(3.8 \times 10^{-6}) \times (2.37 \times 10^{-3}) = (3.8\times2.37) \times (10^{-6} \times10^{-3})](https://tex.z-dn.net/?f=%283.8%20%5Ctimes%2010%5E%7B-6%7D%29%20%5Ctimes%20%282.37%20%5Ctimes%2010%5E%7B-3%7D%29%20%3D%20%283.8%5Ctimes2.37%29%20%5Ctimes%20%2810%5E%7B-6%7D%20%5Ctimes10%5E%7B-3%7D%29)
The numeric part simply yields
![3.8\times2.37 = 9.006](https://tex.z-dn.net/?f=%203.8%5Ctimes2.37%20%3D%209.006%20)
As for the powers of 10, you have to add the exponents, using the rule
![a^b \times a^c = a^{b+c}](https://tex.z-dn.net/?f=%20a%5Eb%20%5Ctimes%20a%5Ec%20%3D%20a%5E%7Bb%2Bc%7D%20)
So, we have
![10^{-6} \times10^{-3} = 10^{-6-3} = 10^{-9}](https://tex.z-dn.net/?f=%2010%5E%7B-6%7D%20%5Ctimes10%5E%7B-3%7D%20%3D%2010%5E%7B-6-3%7D%20%3D%2010%5E%7B-9%7D)
So, the final answer is
![9.006\times 10^{-9}](https://tex.z-dn.net/?f=%209.006%5Ctimes%2010%5E%7B-9%7D%20)
Answer:
Step-by-step explanation:
The population in 2003= 47000
Since the population increase by 1200 every year,
in 2004 the population will be 47000+1200
in 2005 the population will be 47000+(1200+1200) which is the same as
47000+2(1200) where 2 is 2 years after 2003,
Therefore the population x years after 2003 is 47000+x(1200).
P= 47000+1200x
b) The population at 2009 which is 6 years after 2003 will be
47000+(1200)*6=47000+7200= 54200
The population at 2009 is 54200,
![\bold{\huge{\underline{ Solution}}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Chuge%7B%5Cunderline%7B%20Solution%7D%7D%7D)
<h3><u>Given </u><u>:</u><u>-</u></h3>
- A marker in the center of the fairway is 150 yards away from the centre of the green
- While standing on the marker and facing the green, the golfer turns 100° towards his ball
- Then he peces off 30 yards to his ball
<h3><u>To </u><u>Find </u><u>:</u><u>-</u></h3>
- <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>distance </u><u>between </u><u>the </u><u>golf </u><u>ball </u><u>and </u><u>the </u><u>center </u><u>of </u><u>the </u><u>green </u><u>.</u>
<h3><u>Let's </u><u> </u><u>Begin </u><u>:</u><u>-</u></h3>
Let assume that the distance between the golf ball and central of green is x
<u>Here</u><u>, </u>
- Distance between marker and centre of green is 150 yards
- <u>That </u><u>is</u><u>, </u>Height = 150 yards
- For facing the green , The golfer turns 100° towards his ball
- <u>That </u><u>is</u><u>, </u>Angle = 100°
- The golfer peces off 30 yards to his ball
- <u>That </u><u>is</u><u>, </u>Base = 30 yards
<u>According </u><u>to </u><u>the </u><u>law </u><u>of </u><u>cosine </u><u>:</u><u>-</u>
![\bold{\red{ a^{2} = b^{2} + c^{2} - 2ABcos}}{\bold{\red{\theta}}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cred%7B%20a%5E%7B2%7D%20%3D%20b%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-%202ABcos%7D%7D%7B%5Cbold%7B%5Cred%7B%5Ctheta%7D%7D%7D)
- Here, a = perpendicular height
- b = base
- c = hypotenuse
- cos theta = Angle of cosine
<u>So</u><u>, </u><u> </u><u>For </u><u>Hypotenuse </u><u>law </u><u>of </u><u>cosine </u><u>will </u><u>be </u><u>:</u><u>-</u>
![\sf{ c^{2} = a^{2} + b^{2} - 2ABcos}{\sf{\theta}}](https://tex.z-dn.net/?f=%5Csf%7B%20c%5E%7B2%7D%20%3D%20a%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20-%202ABcos%7D%7B%5Csf%7B%5Ctheta%7D%7D)
<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>
![\sf{ x^{2} = (150)^{2} + (30)^{2} - 2(150)(30)cos}{\sf{100°}}](https://tex.z-dn.net/?f=%5Csf%7B%20x%5E%7B2%7D%20%3D%20%28150%29%5E%7B2%7D%20%2B%20%2830%29%5E%7B2%7D%20-%202%28150%29%2830%29cos%7D%7B%5Csf%7B100%C2%B0%7D%7D)
![\sf{ x^{2} = 22500 + 900 - 900cos}{\sf{\times{\dfrac{5π}{9}}}}](https://tex.z-dn.net/?f=%5Csf%7B%20x%5E%7B2%7D%20%3D%2022500%20%2B%20900%20-%20900cos%7D%7B%5Csf%7B%5Ctimes%7B%5Cdfrac%7B5%CF%80%7D%7B9%7D%7D%7D%7D)
![\sf{ x^{2} = 22500 + 900 - 900( - 0.174)}](https://tex.z-dn.net/?f=%5Csf%7B%20x%5E%7B2%7D%20%3D%2022500%20%2B%20900%20-%20900%28%20-%200.174%29%7D)
![\sf{ x^{2} = 22500 + 900 + 156.6}](https://tex.z-dn.net/?f=%5Csf%7B%20x%5E%7B2%7D%20%3D%2022500%20%2B%20900%20%2B%20156.6%7D)
![\sf{ x^{2} = 23556.6}](https://tex.z-dn.net/?f=%5Csf%7B%20x%5E%7B2%7D%20%3D%2023556.6%7D)
![\bold{ x = 153.48\: yards }](https://tex.z-dn.net/?f=%5Cbold%7B%20x%20%3D%20153.48%5C%3A%20yards%20%7D)
Hence, The distance between the ball and the center of green is 153.48 or 153.5 yards