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borishaifa [10]
3 years ago
10

Suppose x and y are related by the given equation and use implicit differentiation to determine dydx.x7y+y7x=7.

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
6 0

Looks like the equation is

x^7y+y^7x=7

Differentiate both sides with respect to x, taking y to be a function of x.

\dfrac{\mathrm d[x^7y+y^7x]}{\mathrm dx}=\dfrac{\mathrm d[7]}{\mathrm dx}

\dfrac{\mathrm d[x^7]}{\mathrm dx}y+x^7\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\mathrm d[y^7]}{\mathrm dx}x+y^7\dfrac{\mathrm dx}{\mathrm dx}=0

7x^6y+x^7\dfrac{\mathrm dy}{\mathrm dx}+7y^6x\dfrac{\mathrm dy}{\mathrm dx}+y^7=0

Solve for \frac{\mathrm dy}{\mathrm dx}:

(x^7+7y^6)\dfrac{\mathrm dy}{\mathrm dx}=-(7x^6y+y^7)

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{7x^6y+y^7}{x^7+7y^6}

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The 8th grade is selling tickets to the 8th grade formal.The cost per ticket is $15.The decorations and food cost $600,and each
MArishka [77]

Answer:

Step-by-step explanation:

Each ticket is $15.  The number of tickets is what we are trying to solve for.  The class spends a certain amount of money to prepare for the formal.  They hope that the money they make in ticket sales is MORE than what they spend.  The expression that represents the number of tickets at $15 each is 15x, where x is the number of tickets.  They hope that the sales are greater than what they spend, so what we have so far is

15x >

Greater than what, though?  What do they spend?  They spend 600 for the food, so

15x > 600...

but they also have to print a certain, unknown number of tickets at .50 each.  The expression that represents the printing of each ticket is .5x (we can drop the 0; it doesn't change the answer or make it wrong if we drop it off).  So the cost for this affair is the food + the printing.

15x > 600 + .5x

Solve this inequality for x.  Begin by subtracting .5 from both sides to get

14.5x > 600 so

x > 41.3

Because we are not selling (or printing) .3 of a ticket, it's safe to say (and also correct!) that they need to sell (and print) 41 tickets.  If they sell 41 tickets, the profit is found by

15(41) > 600 + .5(41)

615 > 600

This means that at 41 tickets, they make a profit.  At 40 tickets, the inequality looks like this:

15(40) > 600 + .5(40) and

600 > 620.  This is not true, so 40 tickets isn't enough.

8 0
3 years ago
How would you figure this out?
Anit [1.1K]

the 10 ounce drink is a better deal. it costs less per ounce.

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Answer:

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 ———————

    5                  

i hope this helps

Step-by-step explanation:

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