Which of the following shows the numbers in order from least to greatest

trans mom said he could spend no more than $12 for rides at the carnival. If the rides cost $0.75 each how many rides can you go

kati45 [8]

He can go on no more than 16 rides

3 0

3 years ago

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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

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What is the exact circumference of a circle that has a radius of 5 cm?

jasenka [17]

Answer:

C≈31.42cm

Step-by-step explanation:

Solution

C=2πr=2·π·5≈31.41593cm

6 0

3 years ago

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Jennifer is shopping with her Mother . They pay $2 per pound for tomato’s at the vegetable stand

Pavel [41]

What’s the question?

8 0

3 years ago

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what are two decimals with thousandths that would give 0.2 when rounded to the nearest tenth and 0.20 when rounded to the neares

egoroff_w [7]

Ur answer it 0.04 bc u would take the 0.2•0.20=0.04

3 0

3 years ago