Answer:
The simplified form of
is ![12x^{18}](https://tex.z-dn.net/?f=12x%5E%7B18%7D)
Step-by-step explanation:
Given : ![\sqrt{144x^{36}}](https://tex.z-dn.net/?f=%5Csqrt%7B144x%5E%7B36%7D%7D)
We have to write the simplified form of ![\sqrt{144x^{36}}](https://tex.z-dn.net/?f=%5Csqrt%7B144x%5E%7B36%7D%7D)
Consider the given expression ![\sqrt{144x^{36}}](https://tex.z-dn.net/?f=%5Csqrt%7B144x%5E%7B36%7D%7D)
We know ![\sqrt{144}=12](https://tex.z-dn.net/?f=%5Csqrt%7B144%7D%3D12)
and ![\sqrt{x^{36}}=\sqrt{x^{18}\cdot x^{18}}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E%7B36%7D%7D%3D%5Csqrt%7Bx%5E%7B18%7D%5Ccdot%20x%5E%7B18%7D%7D)
Thus,
![\sqrt{144x^{36}}=\sqrt{12^2\cdot (x^{18})^2}](https://tex.z-dn.net/?f=%5Csqrt%7B144x%5E%7B36%7D%7D%3D%5Csqrt%7B12%5E2%5Ccdot%20%28x%5E%7B18%7D%29%5E2%7D)
Simplify, we have,
![=\sqrt{12^2\cdot (x^{18})^2}=12x^{18}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B12%5E2%5Ccdot%20%28x%5E%7B18%7D%29%5E2%7D%3D12x%5E%7B18%7D)
Thus, The simplified form of
is ![12x^{18}](https://tex.z-dn.net/?f=12x%5E%7B18%7D)
Answer:
C) 1/6
Step-by-step explanation:
2/9 of 3/4 is ...
![\dfrac{2}{9}\times\dfrac{3}{4}=\dfrac{2\cdot 3}{9\cdot 4}=\dfrac{6}{36}=\boxed{\dfrac{1}{6}}\qquad\text{matches C}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B9%7D%5Ctimes%5Cdfrac%7B3%7D%7B4%7D%3D%5Cdfrac%7B2%5Ccdot%203%7D%7B9%5Ccdot%204%7D%3D%5Cdfrac%7B6%7D%7B36%7D%3D%5Cboxed%7B%5Cdfrac%7B1%7D%7B6%7D%7D%5Cqquad%5Ctext%7Bmatches%20C%7D)
three forty eight squared inches
Answer:
<h2>
$3448.81</h2>
Step-by-step explanation:
Using the compound interest formula to calculate the amount compounded after 10years.
![A = P(1+r)^{nt}](https://tex.z-dn.net/?f=A%20%3D%20P%281%2Br%29%5E%7Bnt%7D)
P = principal = $2000
r = rate (in %) = 5.6%
t = time (in years) = 10years
n = 1year = time used in compounding
![A = 2000(1+0.056)^{10} \\A = 2000(1.056)^{10}\\A = 2000*1.7244046\\A = 3448.81 (to\ 2dp)](https://tex.z-dn.net/?f=A%20%3D%202000%281%2B0.056%29%5E%7B10%7D%20%5C%5CA%20%3D%202000%281.056%29%5E%7B10%7D%5C%5CA%20%3D%202000%2A1.7244046%5C%5CA%20%3D%203448.81%20%28to%5C%20%202dp%29)
Amount compounded after 10 years is $3448.81