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Margaret [11]
3 years ago
9

Find the second derivative at the point (2,2), given the function below. 2x^4=4y^3

Mathematics
1 answer:
Bogdan [553]3 years ago
7 0

The second derivative at the point (2,2) is 34/9

<u>Explanation:</u>

<u></u>

2x⁴ = 4y³

2x⁴ - 4y³ = 0

We first need to find dy/dx and then d²y/dx²

On differentiating the equation in terms of x

dy/dx = d(2x⁴ - 4y³) / dx

We get,

dy/dx = 2x³/3y²

On differentiating dy/dx we get,

d²y/dx² = 2x²/y² + 8x⁶/9y⁵

\frac{d^2y}{dx^2} = \frac{2 X 2^2}{2^2} + \frac{8 X 2^6}{9 X 2^5}\\  \\\frac{d^2y}{dx^2} = 2 + \frac{16}{9}\\  \\

d²y/dx² = 34/9

Therefore, the second derivative at the point (2,2) is 34/9

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A clothing store salesman had $5212 in total sales last month. He made $175 in commision. What is the commision as a percent of
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Divide the amount of commission made by the total sale, then multiply the decimal answer by 100 for the percent:

175 / 5212 = 0.03357


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Round the answer as needed.


3 0
3 years ago
find x if the distance between points L and M is 15 and point M is located in the first quadrant. L=(-6,2) M=(x,2)​
aivan3 [116]

Answer:

Therefore,

x = 9

Step-by-step explanation:

Given:

Let,  

point L( x₁ , y₁) ≡ ( -6 , 2)

point M( x₂ , y₂ )≡ (x , 2)

l(AB) = 15 units  (distance between points L and M)

To Find:    

x = ?

Solution:  

Distance formula between Two points is given as

l(LM)^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}

Substituting the values we get

15^{2}=(x--6)^{2}+(2-2)^{2}\\\\225=(x+6)^{2}

Square Rooting we get

(x+6)=\pm \sqrt{225}=\pm 15\\\\x+6 = 15\ or\ x+6 = -15\\\\x= 9\ or\ x = -21

As  point M is located in the first quadrant

x coordinate and y coordinate are positive

So x = -21 DISCARDED

Hence,

x = 9

Therefore,

x = 9

3 0
3 years ago
Part A: If (7^2)^x = 1, what is the value of x? Explain your answer. (10 points)
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Answers:Part A: The value of x is 0.Part B: X can be any real number.
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In Part B, you have to first evaluate 7^0, that is 1. Now, we have the equation 1^x = 1. In this case, 1 raised to any exponent is still only 1. Imagine 1^17, this would be 1 times itself 17 times or just 1.
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