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kobusy [5.1K]
2 years ago
12

Use implicit differentiation to find dy/dx. ln xy + 5x = 30. Please write out the steps.

Mathematics
1 answer:
Veseljchak [2.6K]2 years ago
8 0
For the answer to the question above, I' ll show the step by step on how to solve your problem,
First,
ln x+lny+5x = 30 
Then,
1/x + (1/y)(dy/dx) + 5 = 0 

the last step is

(1/y)(dy/dx) = -1/x - 5x 

<span>dy/dx = -y/x - 5xy 
I hope my explanation and answer helped you</span>
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3 years ago
Sara lost 12 pounds over the summer by jogging each week. By winter time she had gained 4 3/8 pounds. Represent this situation w
Vika [28.1K]

The situation with an expression involving signed numbers is w - 12 + 4 3/8 and the overall change in Sara’s weight is -7 5/8 pounds

<h3>Represent this situation with an expression involving signed numbers. </h3>

Let Sara's initial weight be w.

The given parameters are:

Lost = 12 pounds

Gain = 4 3/8 pounds

The situation with an expression involving signed numbers is represented as:

Weight = Initial - Lost + Gain

So, we have:

Weight = w - 12 + 4 3/8

<h3>What is the overall change in Sara’s weight?.</h3>

In (a), we have:

Weight = w - 12 + 4 3/8

The overall change is:

Change = - 12 + 4 3/8

Evaluate

Change = -7 5/8

Hence, the overall change in Sara’s weight is -7 5/8 pounds

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3 0
2 years ago
A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate off
GuDViN [60]

Correct question is;

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate offered to a buyer, the number of sets sold will increase by 210 per week

A) Find the demand function (price p as a function of units sold x).

p(x)=______

(B) How large a rebate should the company offer the buyer in order to maximize its revenue?

$=_____

Answer:

A) p(x) = (-1/10)x + 590

B) Rebate = $170

Step-by-step explanation:

A) We are told that p(x) is the demand function and x is the number of TV sets sold per week.

Now, since for each $21 rebate offered, the number of sets sold increases by 210 per week, it means that the slope here of this demand function is; m = -21/210 = -1/10

Now, he has been selling 1400 TV sets a week at $450 each. This means; p(1400) = $450

Thus, the demand function will be;

p(x) - 450 = (-1/10)(x - 1400)

Expanding the RHS;

p(x) - 450 = (-1/10)x + 140

Add 450 to both sides to get;

p(x) = (-1/10)x + 140 + 450

p(x) = (-1/10)x + 590

B) Formula for revenue is;

R = price × quantity sold

Our demand function is p = (-1/10)x + 590

Making x the subject, we have;

x = 5900 - 10p

x is quantity sold.

Thus,

R = p(5900 - 10p)

R = 5900p - 10p²

Maximum price will occur at dR/dP = 0

Thus;

dR/dP = 5900 - 20p

At dR/dP = 0,we have;

20p = 5900

p = 5900/20

p = $280

Thus, rebate = 450 - 280 = $170

6 0
2 years ago
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