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mart [117]
3 years ago
13

Solve this derivative using the quotient rule

Mathematics
1 answer:
LekaFEV [45]3 years ago
7 0
\bf  y=\cfrac{(-x+5)^5}{3x-4}\implies y=\cfrac{(5-x)^5}{3x-4}
\\\\\\
\cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{5(5-x)^4(-1)(3x-4)~~-~~(5-x)^5(3)}{(3x-4)^2}}
\\\\\\
\cfrac{dy}{dx}=\cfrac{-5(5-x)^4(3x-4)-3(5-x)^5}{(3x-4)^2}
\\\\\\
\cfrac{dy}{dx}=\cfrac{\stackrel{common~factor}{-(5-x)^4}[5(3x-4)+3(5-x)]}{(3x-4)^2}
\\\\\\
\cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[15x-20+15-3x]}{(3x-4)^2}
\\\\\\
\cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[12x-5]}{(3x-4)^2}\implies \cfrac{dy}{dx}=\cfrac{(5-x)^4~~[5+12x]}{(3x-4)^2}
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Volgvan

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3 years ago
Find the 10th term of the following sequences T(2)=20 and the term-to-term rule is subtract 6​
rjkz [21]
<h3>Answer is   -28</h3>

==================================================

Work Shown:

T(2) = 20 means the second term is 20

T(1) = 26 because we go backwards from what the rule says (subtract 6) to step back one term. Going forward, 26-6 = 20.

Since a = 26 is the first term and d = -6 is the common difference, the nth term is

T(n) = a + d*(n-1)

T(n) = 26 + (-6)(n-1)

T(n) = 26 - 6n + 6

T(n) = -6n + 32

Plugging n = 1 into the equation above leads to T(1) = 26. Using n = 2 leads to T(2) = 20.

Plug in n = 10 to find the tenth term

T(n) = -6n + 32

T(10) = -6(10) + 32

T(10) = -60+32

T(10) = -28

5 0
3 years ago
Read 2 more answers
The circumference of a circle is 3π in.
11111nata11111 [884]

Answer:

  2.25π in²

Step-by-step explanation:

The area can be found from the circumference using the formula ...

  A = C²/(4π)

Putting in the given dimension, you have ...

  A = (3π)²/(4π) = (9/4)π = 2.25 π . . . . in²

6 0
3 years ago
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yaroslaw [1]

Answer:

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Step-by-step explanation:

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4 0
3 years ago
At the bank, Derek made 7 withdrawals, each in the same amount. His brother, John, made 5 withdrawls, each in the same amount. E
spayn [35]

At the bank, Derek made 7 withdrawals, each in the same amount. His brother, John, made 5 withdrawls, each in the same amount.

Let x be  the amount of one of Derek's withdrawals

Each of John's withdrawals was $5 more than each withdrawal that Derek made.

x + 5 is t the amount of one of John's withdrawals

Derek made 7 withdrawals

So amount withdraw 7 times = 7x

John made 5 withdrawals

So amount withdraw 5 times = 5(x+5)

Both Derek and John withdrew the same amount of money in the end

(A) 7x = 5(x+5)

(B) Solve for x

7x = 5x + 25

Subtract 5x from both sides

2x = 25

Divide by 2

x = 12.5

(C) check your solution

we plug in 12.5 for x in 7x= 5x + 25

7(12.5) = 5(12.5) + 25

87.5 = 62.5+ 25

87.5 = 87.5

(D) Each brother withdrawal 87.5 dollars



6 0
2 years ago
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