In scientific notation the answer is: 0.00018 x 10^6
Hey, expressing 59.2475 would look like:
Word form: Fifty-nine and two thousand, four hundred seventy-five ten-thousandths.
Expanded Notation Form:
50 + 9 + 0.2 + 0.04 + 0.007 + 0.0005.
If
, then by rationalizing the denominator we can rewrite
![b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8](https://tex.z-dn.net/?f=b%20%3D%20%5Cdfrac1%7B%5Csqrt3-%5Csqrt%7B11%7D%7D%20%5Ctimes%20%5Cdfrac%7B%5Csqrt3%2B%5Csqrt%7B11%7D%7D%7B%5Csqrt3%2B%5Csqrt%7B11%7D%7D%20%3D%20%5Cdfrac%7B%5Csqrt3%2B%5Csqrt%7B11%7D%7D%7B%5Cleft%28%5Csqrt3%5Cright%29%5E2-%5Cleft%28%5Csqrt%7B11%7D%5Cright%29%5E2%7D%20%3D%20-%5Cdfrac%7B%5Csqrt3%2B%5Csqrt%7B11%7D%7D8)
Now,
![a^2 - b^2 = (a-b) (a+b)](https://tex.z-dn.net/?f=a%5E2%20-%20b%5E2%20%3D%20%28a-b%29%20%28a%2Bb%29)
and
![a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8](https://tex.z-dn.net/?f=a%20-%20b%20%3D%20%5Csqrt3%20-%20%5Csqrt%7B11%7D%20%2B%20%5Cdfrac%7B%5Csqrt3%20%2B%20%5Csqrt%7B11%7D%7D8%20%3D%20%5Cdfrac%7B9%5Csqrt3%20-%207%5Csqrt%7B11%7D%7D8)
![a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8](https://tex.z-dn.net/?f=a%20%2B%20b%20%3D%20%5Csqrt3%20-%20%5Csqrt%7B11%7D%20-%20%5Cdfrac%7B%5Csqrt3%20%2B%20%5Csqrt%7B11%7D%7D8%20%3D%20%5Cdfrac%7B7%5Csqrt3%20-%209%5Csqrt%7B11%7D%7D8)
![\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}](https://tex.z-dn.net/?f=%5Cimplies%20a%5E2%20-%20b%5E2%20%3D%20%5Cdfrac%7B%5Cleft%289%5Csqrt3%20-%207%5Csqrt%7B11%7D%5Cright%29%20%5Cleft%287%5Csqrt3%20-%209%5Csqrt%7B11%7D%5Cright%29%7D%7B64%7D%20%3D%20%5Cboxed%7B%5Cdfrac%7B441%20-%2065%5Csqrt%7B33%7D%7D%7B32%7D%7D)
Answer:
, ![y=\frac{32}{5}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B32%7D%7B5%7Dx)
, ![y=6.4x](https://tex.z-dn.net/?f=y%3D6.4x)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Find the value of the constant of proportionality k
take any ordered pair from the data
For x=25, y=160
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
substitute the values of x and y
![k=\frac{160}{25}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B160%7D%7B25%7D)
simplify
![k=\frac{32}{5}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B32%7D%7B5%7D)
The linear equation is equal to
![y=\frac{32}{5}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B32%7D%7B5%7Dx)
or
![y=6.4x](https://tex.z-dn.net/?f=y%3D6.4x)