The plane would travel 2550 miles
For this case we have the following expression:
![2(\sqrt[4]{16x})-2(\sqrt[4]{2y})+3(\sqrt[4]{81x})-4(\sqrt[4]{32y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B16x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B81x%7D%29-4%28%5Csqrt%5B4%5D%7B32y%7D%29)
Rewriting the numbers within the roots we have:
![2(\sqrt[4]{2*2*2*2x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3*3*3*3x})-4(\sqrt[4]{2*2*2*2*2y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B3%2A3%2A3%2A3x%7D%29-4%28%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2%2A2y%7D%29)
Then, by properties of powers we have:
![2(\sqrt[4]{2^4x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3^4x})-4(\sqrt[4]{2^42y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B2%5E4x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B3%5E4x%7D%29-4%28%5Csqrt%5B4%5D%7B2%5E42y%7D%29)
Then, by radical properties we have:
![2(2\sqrt[4]{x})-2(\sqrt[4]{2y})+3(3\sqrt[4]{x})-4(2\sqrt[4]{2y})](https://tex.z-dn.net/?f=2%282%5Csqrt%5B4%5D%7Bx%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%283%5Csqrt%5B4%5D%7Bx%7D%29-4%282%5Csqrt%5B4%5D%7B2y%7D%29)
Rewriting the expression we have:
![4\sqrt[4]{x}-2\sqrt[4]{2y}+9\sqrt[4]{x}-8\sqrt[4]{2y}](https://tex.z-dn.net/?f=4%5Csqrt%5B4%5D%7Bx%7D-2%5Csqrt%5B4%5D%7B2y%7D%2B9%5Csqrt%5B4%5D%7Bx%7D-8%5Csqrt%5B4%5D%7B2y%7D)
Finally, adding similar terms we have:
![(4+9)\sqrt[4]{x}-(2+8)\sqrt[4]{2y}](https://tex.z-dn.net/?f=%284%2B9%29%5Csqrt%5B4%5D%7Bx%7D-%282%2B8%29%5Csqrt%5B4%5D%7B2y%7D)
![13\sqrt[4]{x}-10\sqrt[4]{2y}](https://tex.z-dn.net/?f=13%5Csqrt%5B4%5D%7Bx%7D-10%5Csqrt%5B4%5D%7B2y%7D)
Answer:
The simplified form of the expression is:
Answer/Step-by-step explanation:
Scale factor: 1/4
<em>AC = DF and 10 ÷ 2.5 = 4</em>
<em>10 x 1/4 = 2.5</em>
<em />
DE length: 5
<em>AB = DE </em>
<em>20 x 1/4 = 5</em>
<em />
BC length: 30
<em>EF = BC</em>
<em>(Because EF is the dilation) 7.5 x 4 = 30</em>
$1142.25
Step-by-step explanation:
Gross pay per week = $1500
Social security deducted = 6.2% = $93
Medicare deducted = 1.45% = $21.75
Deductions for combined taxes = 16.2% = $243
Hence total deductions made from the gross salary
= 93+21.75+ 243
= $357.75
Hence, Net pay
= 1500 - 357.75
= $1142.25
Y = 5 sin(2x) + 4
The amplitude of the sin itself is 1 .
The amplitude of 5sin is 5 .
Every time the "argument" of the sin increases by 2π
another period starts.
The first period goes from zero until 2x = 2π .
So the length of the period is π .
The phase shift is the value of the angle when x=0.
That's zero.
The sin itself wiggles up and down, regularly and symmetrically,
above and below the x-axis (y=0). In this equation, the whole thing
is shifted up 4 units by that +4 on the end, so it's wiggling up and down
above and below the line y=4. The vertical shift is +4 .
If this function were an electrical signal, we would say that its
period is π seconds, its frequency is 1/π Hz, and it has an
AC amplitude of 5 riding on a DC component of 4 .
