Answer: 0.02x
Step-by-step explanation:
The value of the cars the salesman makes is x in this instance.
The salesman makes a 2% commission on every sale so this can be represented by multiplying 2% by the value of the cars which in this case is x.
= 2% * x
= 0.02 * x
= 0.02x
If for instance he sells $40,000 worth of cars, his commission would be:
= 0.02 * x
= 0.02 * 40,000
= $800
Answer:
The mean is the average of all numbers. To find the mean you add all numbers and divide by how many numbers you have (i.e. 1+2+3 =6. 6/3 =2. Mean is 2.) Median is the middle of the numbers. To find the median arrange the numbers from least to greatest, and the number in the middle is the median. For example, 1, 2, 3, 4, 5. In this 3 is the median because it is in the middle. The outlier is the number that is different from others. For example, 1, 2, 3, 4, 17. In this case 17 is the outlier because it is different and farther than the other numbers.
Step-by-step explanation:
2/-3
The minus doesn't really matter where it goes, but it's conventional to place it on top
Answer:
Step-by-step explanation:
Given the equation 4x²+ 49y² = 196
a) Differentiating implicitly with respect to y, we have;
![8x + 98y\frac{dy}{dx} = 0\\98y\frac{dy}{dx} = -8x\\49y\frac{dy}{dx} = -4x\\\frac{dy}{dx} = \frac{-4x}{49y}](https://tex.z-dn.net/?f=8x%20%2B%2098y%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%200%5C%5C98y%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20-8x%5C%5C49y%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20-4x%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-4x%7D%7B49y%7D)
b) To solve the equation explicitly for y and differentiate to get dy/dx in terms of x,
First let is make y the subject of the formula from the equation;
If 4x²+ 49y² = 196
49y² = 196 - 4x²
![y^{2} = \frac{196}{49} - \frac{4x^{2} }{49} \\y = \sqrt{\frac{196}{49} - \frac{4x^{2} }{49} \\} \\](https://tex.z-dn.net/?f=y%5E%7B2%7D%20%3D%20%20%5Cfrac%7B196%7D%7B49%7D%20%20-%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B49%7D%20%5C%5Cy%20%3D%20%5Csqrt%7B%5Cfrac%7B196%7D%7B49%7D%20%20-%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B49%7D%20%5C%5C%7D%20%5C%5C)
Differentiating y with respect to x using the chain rule;
Let ![u= \frac{196}{49} - \frac{4x^{2} }{49}](https://tex.z-dn.net/?f=u%3D%20%20%5Cfrac%7B196%7D%7B49%7D%20%20-%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B49%7D)
![y = \sqrt{u} \\y =u^{1/2} \\](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7Bu%7D%20%5C%5Cy%20%3Du%5E%7B1%2F2%7D%20%5C%5C)
![\frac{dy}{dx} = \frac{dy}{du} * \frac{du}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%5Cfrac%7Bdy%7D%7Bdu%7D%20%2A%20%5Cfrac%7Bdu%7D%7Bdx%7D)
![\frac{dy}{du} = \frac{1}{2}u^{-1/2} \\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdu%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7Du%5E%7B-1%2F2%7D%20%5C%5C)
![\frac{du}{dx} = 0 - \frac{8x}{49} \\\frac{du}{dx} =\frac{-8x}{49} \\\frac{dy}{dx} = \frac{1}{2} ( \frac{196}{49} - \frac{4x^{2} }{49})^{-1/2} * \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} ( \frac{196-4x^{2} }{49})^{-1/2} * \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} ( \sqrt{ \frac{49}{196-4x^{2} })} * \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} *{ \frac{7}\sqrt {196-4x^{2} }} * \frac{-8x}{49}\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%20%3D%20%200%20-%20%5Cfrac%7B8x%7D%7B49%7D%20%5C%5C%5Cfrac%7Bdu%7D%7Bdx%7D%20%3D%5Cfrac%7B-8x%7D%7B49%7D%20%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%5Cfrac%7B196%7D%7B49%7D%20%20-%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B49%7D%29%5E%7B-1%2F2%7D%20%2A%20%20%5Cfrac%7B-8x%7D%7B49%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%20%5Cfrac%7B196-4x%5E%7B2%7D%20%7D%7B49%7D%29%5E%7B-1%2F2%7D%20%2A%20%20%5Cfrac%7B-8x%7D%7B49%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%5Csqrt%7B%20%5Cfrac%7B49%7D%7B196-4x%5E%7B2%7D%20%7D%29%7D%20%2A%20%20%5Cfrac%7B-8x%7D%7B49%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%7B%20%5Cfrac%7B7%7D%5Csqrt%20%7B196-4x%5E%7B2%7D%20%7D%7D%20%2A%20%20%5Cfrac%7B-8x%7D%7B49%7D%5C%5C)
![\frac{dy}{dx} = \frac{-4x}{7\sqrt{196-4x^{2} } }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-4x%7D%7B7%5Csqrt%7B196-4x%5E%7B2%7D%20%7D%20%7D)
c) From the solution of the implicit differentiation in (a)
![\frac{dy}{dx} = \frac{-4x}{49y}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-4x%7D%7B49y%7D)
Substituting
into the equation to confirm the answer of (b) can be shown as follows
![\frac{dy}{dx} = \frac{-4x}{49\sqrt{\frac{196-4x^{2} }{49} } }\\\frac{dy}{dx} = \frac{-4x}{49\sqrt{196-4x^{2}}/7} }\\\\\frac{dy}{dx} = \frac{-4x}{7\sqrt{196-4x^{2}}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-4x%7D%7B49%5Csqrt%7B%5Cfrac%7B196-4x%5E%7B2%7D%20%7D%7B49%7D%20%7D%20%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Cfrac%7B-4x%7D%7B49%5Csqrt%7B196-4x%5E%7B2%7D%7D%2F7%7D%20%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%5Cfrac%7B-4x%7D%7B7%5Csqrt%7B196-4x%5E%7B2%7D%7D%7D)
This shows that the answer in a and b are consistent.
G(x) = ax^2
y = ax^2
16 = a1^2
a = 16
Therefore, g(x) = 16x^2