Answer:
$375
Step-by-step explanation:
- Convert the 25% discount into a decimal, which is 0.25
- Multiply the original listed price ($500) by the discount as a decimal (0.25), which is $125
- Subtract the original list price ($500) by $125 (the discount as a number). This is $375, which is the answer.
Answer:
Step-by-step explanation:
Wave velocity of the sound = frequency * wavelength.
The frequency and wavelength depend on the medium through which the sound passes and they are both greater in the guitar string than in air as the string is denser than the air. So the sound travles faster through the guitar string.
Answer:
The absolute maximum and minimum is
Step-by-step explanation:
We first check the critical points on the interior of the domain using the
first derivative test.
![f_x=y-4=0](https://tex.z-dn.net/?f=f_x%3Dy-4%3D0)
![f_y=x=0](https://tex.z-dn.net/?f=f_y%3Dx%3D0)
The only solution to this system of equations is the point (0, 4), which lies in the domain.
![f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1](https://tex.z-dn.net/?f=f_%7Bxx%7D%3D0%2C%20%5C%3Bf_%7Byy%7D%3D0%5C%3B%20%5Ctext%7Band%7D%5C%3B%20f_%7Bxy%7D%3D-1)
![\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1](https://tex.z-dn.net/?f=%5CRightarrow%20f_%7Bxx%7Df_%7Byy%7D-f_%7Bxy%7D%3Do-1%3D-1%3C0)
is a saddle point.
Boundary points - ![(4,0), (-4,0), (0,16)](https://tex.z-dn.net/?f=%284%2C0%29%2C%20%20%28-4%2C0%29%2C%20%280%2C16%29)
Along boundary ![y=16-x^2](https://tex.z-dn.net/?f=y%3D16-x%5E2)
![f=x(16-x^2)-4x](https://tex.z-dn.net/?f=f%3Dx%2816-x%5E2%29-4x)
![=16x-x^3-4x](https://tex.z-dn.net/?f=%3D16x-x%5E3-4x)
![\Rightarrow f^'=16-3x^2-4=0](https://tex.z-dn.net/?f=%5CRightarrow%20f%5E%27%3D16-3x%5E2-4%3D0)
![\Rightarrow 3x^2=12](https://tex.z-dn.net/?f=%5CRightarrow%203x%5E2%3D12)
![\Rightarrow x=\pm2,\;\;y=14](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%5Cpm2%2C%5C%3B%5C%3By%3D14)
Values of f(x) at these points.
![\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7D%284%2C0%29%3D-16%5C%5C%28-4%2C0%29%3D16%5C%5C%280%2C16%29%3D0%5C%5C%282%2C14%29%3D20%5C%5C%28-2%2C14%29%3D-20%5Cend%7Barray%7D)
Therefore, the absolute maximum and minimum is