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3 years ago

6

Paper plates come in packages of 15 or 20. George bought 10 packages and had a total of 170 plates. How many of each package did

he buy?

1 answer:

damaskus [11]3 years ago

8 0

The answer to your question is 17

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

4 years ago

can anyone help me and show work for this Find the length of the third side. If necessary, write in simplest radical form.

tiny-mole [99]

Answer:

Step-by-step explanation:

Use Pythagorean theorem

Hypotenuse² = base² + altitude²

= 9² + 10²

= 81 + 100

= 181

hypotenuse = √181

5 0

3 years ago

Write the number 3,2, and 8 addition sentence. Show two more way to find the sum.

Alexxx [7]

This doesn't make sense

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4 years ago

How to solve -1 9/12 minus 10/12

Inga [223]

Answer:

-2 7/12

Step-by-step explanation:

When the negative number is being subtracted, it is like adding, but you HAVE TO KEEP THE NEGATIVE SIGN. In this case, -1 9/12 plus -10/12 would be -1 19/12.

Simplified, it would be -2 7/12.

5 0

3 years ago

Read 2 more answers

Integral of of sin x/cosˆ2 x

marin [14]

Answer:

$\sec x + c$

Step-by-step explanation:

$\int \frac{ \sin \: x}{ { \cos}^{2}x } \: dx \\ \\ = \int \frac{ \sin \: x}{ { \cos}x } . \frac{ 1}{ { \cos}x } \: dx \\ \\ = \int \tan x . \sec x \: dx \\ \\ = \sec x + c$

7 0

3 years ago