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gavmur [86]
3 years ago
15

Find y' by implicit differentiation √x +√y =1

Mathematics
1 answer:
AleksandrR [38]3 years ago
5 0
Differentiate both sides with respect to x

\frac{d}{dx}(x^{\frac{1}{2}} + y^{\frac{1}{2}}) = \frac{d}{dx}(1)\\\\ \frac{1}{2x^{\frac{1}{2}}} + \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = 0\\\\\frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = -\frac{1}{2x^{\frac{1}{2}}}\\\\\frac{1}{2\sqrt{y}}\frac{dy}{dx} = -\frac{1}{2\sqrt{x}} \\\\\frac{dy}{dx} = -\frac{1}{2\sqrt{x}} \times 2\sqrt{y}\\\\\frac{dy}{dx} = -\frac{\sqrt{y}}{\sqrt{x}} \\\\\boxed{\bf{y'= -\frac{\sqrt{y}}{\sqrt{x}}}}
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½(4k + 3r) ÷ 3^1<br><br> k = 9<br> r = 6<br><br> show work
vampirchik [111]

Answer:

The solution is given below:

Step-by-step explanation:

\\ \frac{1}{2} (4k + 3r) \div  {3}^{1}

As we know the value of k and r so the equation will be

\\ \frac{1}{2} (4 \times 9 + 3 \times 6) \div  {3}^{1}

\\  =  \frac{1}{2} (36 + 18) \div 3

\\  =  \frac{1}{2} \times 54 \div 3

\\  =  \frac{1}{2}  \times 18

\\  = 9

3 0
3 years ago
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Are 9 and 1/9 reciprocals?
Harlamova29_29 [7]

Answer:

yes

Step-by-step explanation:

9 can be represented as 9/1, which is the reciprocal of 1/9.

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3 years ago
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What is the slope in the equation: y=4x+3
kompoz [17]

Answer:

The slope is −4 . The equation is in slope-intercept form, y=mx+c , where m is the

Step-by-step explanation:

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7 0
3 years ago
How do I solve this?
Sonbull [250]

The question is somewhat poorly posed because the equation doesn't involve <em>θ</em> at all. I assume the author meant to use <em>x</em>.

sec(<em>x</em>) = csc(<em>x</em>)

By definition of secant and cosecant,

1/cos(<em>x</em>) = 1/sin(<em>x</em>)

Multiply both sides by sin(<em>x</em>) :

sin(<em>x</em>)/cos(<em>x</em>) = sin(<em>x</em>)/sin(<em>x</em>)

As long as sin(<em>x</em>) ≠ 0, this reduces to

sin(<em>x</em>)/cos(<em>x</em>) = 1

By definition of tangent,

tan(<em>x</em>) = 1

Solve for <em>x</em> :

<em>x</em> = arctan(1) + <em>nπ</em>

<em>x</em> = <em>π</em>/4 + <em>nπ</em>

(where <em>n</em> is any integer)

In the interval 0 ≤ <em>x</em> ≤ 2<em>π</em>, you get 2 solutions when <em>n</em> = 0 and <em>n</em> = 1 of

<em>x</em> = <em>π</em>/4   <u>or</u>   <em>x</em> = 5<em>π</em>/4

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2 years ago
Find the area of a floor which is covered by 1050 tiles.each tiles measuring 20 square meters​
RoseWind [281]

Answer:

area of floor is

1050*20=21000

Step-by-step explanation:

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