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3 years ago

Students class Presidential Votes

Mathematics

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nika2105 [10]3 years ago

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Lee is thinking of two Numbers,the product is 18. the quotient is 2

defon

X, y - the numbers

The product is 18.
$xy=18$

The quotient is 2.
$\frac{x}{y}=2 \ \ \ |\times y \\
x=2y$

Substitute 2y for x in the 1st equation:
$2y \times y=18 \\
2y^2=18 \ \ \ |\div 2 \\
y^2=9 \\
y=\pm \sqrt{9} \\
y=3 \ \lor \ y=-3 \\ \\
x=2y \\
x=2 \times 3 \ \lor \ x=2 \times (-3) \\
x=6 \ \lor \ x=-6 \\ \\
(x,y)=(6,3) \hbox{ or } (x,y)=(-6,-3)$

The numbers are 6 and 3 or -6 and -3.

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3 years ago

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Differentiate the function. f(x) = sin(9 ln(x))

gayaneshka [121]

Answer: $f'(x)=\dfrac{9\cos(9\ln (x))}{x}$ .

Step-by-step explanation:

The given function is

$f(x)=\sin(9\ln (x))$

Using chain rule differentiate w.r.t. x.

$f'(x)=\cos(9\ln (x))\dfrac{d}{dx}(9\ln (x))$ $\left[\because \dfrac{d}{dx}\sin x=\cos x\right]$

$f'(x)=\cos(9\ln (x))\left[9\dfrac{d}{dx}(\ln (x))\right]$

$f'(x)=\cos(9\ln (x))\left[9\times \dfrac{1}{x}\right]$ $\left[\because \dfrac{d}{dx}\ln x=\dfrac{1}{x}\right]$

$f'(x)=\dfrac{9\cos(9\ln (x))}{x}$

Therefore, $f'(x)=\dfrac{9\cos(9\ln (x))}{x}$ .

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3 years ago

THOROUGHLY EXPLAIN how this is done plz

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First and last terms of the given equation are perfect squares. They can be written as

(4p^2)^2+ 2.(4p^2).5+(5)^2
It's like identity 1: (a+b)^2=a^2+2ab+b^2
So a=4p^2 and b=5
Therefore it is equal to (4p^2+5)^2

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The sum of slopes of lines b and c are 0

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At a restaurant, hamburgers cost $6.50 and fries cost $3. If you buy (h) ( h repusents hamburger) hamburgers and an order of fri

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