Answer:
2.72 x 10^4
Step-by-step explanation:
2.4 x 10^4
= 24000
3.2 x 10^3
= 3200
Therefore,
(2.4 x 10^4) + (3.2 x 10^3)
= 24000 + 3200
= 27200
= 2.72 x 10^4
Answer:
b. x>1
Step-by-step explanation:
2/3+x/3>1
Multiply the inequality by 3 to get rid of the fractions
3(2/3+x/3)>1*3
2 +x >3
Subtract 2 from each side
2+x-2 >3-2
x>1
Write tan in terms of sin and cos.
![\displaystyle \lim_{t\to0}\frac{\tan(6t)}{\sin(2t)} = \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Ctan%286t%29%7D%7B%5Csin%282t%29%7D%20%3D%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Csin%286t%29%7D%7B%5Csin%282t%29%5Ccos%286t%29%7D)
Recall that
![\displaystyle \lim_{x\to0}\frac{\sin(x)}x = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csin%28x%29%7Dx%20%3D%201)
Rewrite and expand the given limand as the product
![\displaystyle \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)} = \lim_{t\to0} \frac{\sin(6t)}{6t} \times \frac{2t}{\sin(2t)} \times \frac{6t}{2t\cos(6t)} \\\\ = \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Csin%286t%29%7D%7B%5Csin%282t%29%5Ccos%286t%29%7D%20%3D%20%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%20%5Ctimes%20%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%20%5Ctimes%20%5Cfrac%7B6t%7D%7B2t%5Ccos%286t%29%7D%20%5C%5C%5C%5C%20%3D%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B3%7D%7B%5Ccos%286t%29%7D%5Cright%29)
Then using the known limit above, it follows that
![\displaystyle \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right) = 1 \times 1 \times \frac3{\cos(0)} = \boxed{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B3%7D%7B%5Ccos%286t%29%7D%5Cright%29%20%3D%201%20%5Ctimes%201%20%5Ctimes%20%5Cfrac3%7B%5Ccos%280%29%7D%20%3D%20%5Cboxed%7B3%7D)
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Answer: $187 will be in the account after 6 years.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $100
r = 11% = 11/100 = 0.11
n = 1 because it was compounded once in a year.
t = 6 years
Therefore,.
A = 100(1 + 0.11/1)^1 × 6
A = 100(1 + 0.11)^6
A = 100(1.11)^6
A = $187