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Bad White [126]
3 years ago
10

18931 divided by 83 =

Mathematics
2 answers:
gizmo_the_mogwai [7]3 years ago
8 0
228.0843373493976
This is the answer
sertanlavr [38]3 years ago
6 0
The answer: 18931/83=228.084337
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Use implicit differentiation to find the slope of the tangent line at the given point:
Salsk061 [2.6K]

Answer:

\frac{dy}{dx}=0

Step-by-step explanation:

So we have the equation:

(x^2+y^2)^2=4x^2y

And we want to find the slope of the tangent line at the point (1,1).

So, let's implicitly differentiate. Take the derivative of both sides:

\frac{d}{dx}[(x^2+y^2)^2]=\frac{d}{dx}[4x^2y]

Let's do each side individually.

Left:

We can use the chain rule:

(u(v(x))'=u'(v(x))\cdot v'(x)

Let's let v(x) be x²+y². So, u(x) is x². Thus, the u'(x) is 2x. Therefore:

\frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)(\frac{d}{dx}[x^2+y^2])

We can differentiate x like normal. However, for y, we must differentiate implicitly. pretend y is y(x). This gives us:

\frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)(\frac{d}{dx}[x^2]+\frac{d}{dx}[y^2(x)])

Differentiate:

\frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)(2x+2y\frac{dy}{dx})

Therefore, our left side is:

2(x^2+y^2)(2x+2y\frac{dy}{dx})

Right:

We have:

\frac{d}{dx}[4x^2y]

Let's move the 4 outside:

=4\frac{d}{dx}[x^2y]

Use the product rule:

=4(\frac{d}{dx}[x^2]y+x^2\frac{d}{dx}[y])

Differentiate:

=4(2xy+x^2\frac{dy}{dx})

Therefore, our entire equation is:

2(x^2+y^2)(2x+2y\frac{dy}{dx})=4(2xy+x^2\frac{dy}{dx})

So, to find the derivative at (1,1), substitute 1 for x and 1 for y.

2((1)^2+(1)^2)(2(1)+2(1)\frac{dy}{dx})=4(2(1)(1)+(1)^2\frac{dy}{dx})

Evaluate.

2((1)+(1))(2+2\frac{dy}{dx})=4(2+\frac{dy}{dx})

Simplify. Also, let's distribute the right:

2(2)(2+2\frac{dy}{dx})=8+4\frac{dy}{dx}

Multiply.

4(2+2\frac{dy}{dx})=8+4\frac{dy}{dx}

Distribute the left:

8+8\frac{dy}{dx}=8+4\frac{dy}{dx}

Subtract 8 from both sides:

8\frac{dy}{dx}=4\frac{dy}{dx}

Subtract 4(dy/dx) from both sides:

4\frac{dy}{dx}=0

Divide both sides by 4:

\frac{dy}{dx}=0

Therefore, the slope at the point (1,1) is 0.

And we're done!

We can verify this using the graph. The slope of the line tangent to the point (1,1) seems like it would be horizontal, giving us a slope of 0.

Edit: Typo

5 0
3 years ago
Read 2 more answers
What is the rate of change of g(x)=x^3-9x for x=1 to x=6
VladimirAG [237]

Answer:

105

Step-by-step explanation:

g(x)=x^{3}-9x

rate of change of g(x) is

g^{,}(x)=3x^{2} -9

for x=1

g^{'}(1)=3(1)^{2} -9=-6

for x=6

g^{'}(6)=3(6)^{2} -9=99

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3 years ago
Cuál es el conciente de 8)240
Alexxx [7]

Answer:

30

Step-by-step explanation:

jdjdneijdjdjdkjddiieue

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3 years ago
Find the value of x​
Kisachek [45]

Answer

X= 20 degree angle

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3 years ago
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Graph the system of linear inequalities.<br> y &gt; 3x + 2<br> y ≤ 3x − 4
Alisiya [41]

y > 3 \times 2 \\ solve \: for \: y \\ y > 6 \\ ye \: {6 +  \infty }

Sorry that's all i know

<h3>that is in my answer</h3>

<h2>#carryonlearning:-D</h2>
8 0
3 years ago
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