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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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Can someone answer 7-11 for me by 12:00AM
lawyer [7]

Answer:

Step-by-step explanation:

<em>7).</em> x + y = 4 ⇒ y = 4 - x -----> xy = - 96

x(4 - x) = - 96 ⇔ x² - 4x - 96 = 0

D = ( - 4)² - 4(1)(- 96) = 400 = (20)²

x_{1} = (- ( - 4) - 20) ÷ 2(1) = - 8

x_{2} = ( - ( - 4) + 20) ÷ 2 = 12

Numbers are <em>- 8</em> and <em>12</em>

<em>8).</em> <em><u>It's your turn now. You can do it</u></em>

<em>9).</em> x² - 5x + 3 = 0

0 < x_{1} < 1

4 < x_{2} < 5

<em>10).</em> - x² + 3x + 1 = 0

-1 < x_{1} < 0

3 < x_{2} < 4

<em>11).</em> x² + 2x - 2 = 0

- 3 < x_{1} < - 2

0 < x_{2} < 1

5 0
2 years ago
According to the chart below, what percentage of Ralph’s expenses are items other than taxes? A circle graph titled Ralph's Annu
NeTakaya

according to the chart below, what percentage of ralph’s expenses are items other than taxes?

a. 65%

b. 71%

c. 75%

d. 94%

the answer is A 65%

3 0
2 years ago
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Analyzing graphs: Please fill in the following based on the graph. Seriously need help with this ASAP please!
Mariana [72]

Answer:

continous!

- infinite<x<infinte

y<=1

zeros at -4 and-2

(-infinite, -3)

(-3,infinite)

4 0
3 years ago
12 Divided by 8 gives what?
WARRIOR [948]
12 divided my 8 makes 1.5
8 0
3 years ago
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The height of an arrow shot upward can be given by the formula s = v0t - 16t2, where v0 is the initial velocity and t is time. H
Lina20 [59]

The arrow is at a height of 48 ft after approximately 0.55 seconds and after 5.45 seconds.

<em><u>Explanation</u></em>

The given formula is:   s=V_{0}t-16t^2

If the initial velocity is 96 ft/s , that means  V_{0}=96

For finding the time the arrow takes to reach a height of 48 ft, we will plug s= 48 into the above formula. So......

48=96t-16t^2\\ \\ 16t^2-96t+48=0\\ \\ 16(t^2-6t+3)=0\\ \\ t^2-6t+3=0\\ \\ t^2-6t =-3\\ \\ t^2-6t+9=-3+9\\ \\ (t-3)^2 = 6\\ \\ t-3= \pm \sqrt{6} \\ \\ t=3\pm \sqrt{6}\\ \\ t = 5.45 , 0.55

So, the arrow is at a height of 48 ft after approximately 0.55 seconds and after 5.45 seconds.

7 0
3 years ago
Read 2 more answers
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