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3 years ago

Find the equation of the tangent line. y=(9-x^2)^1/3 at (1,2)

Mathematics

1 answer:

Schach [20]3 years ago

7 0

Get the derivative:

y = (9 - x²)¹ʹ³

dy/dx = 1/3 (9 - x²)⁻²ʹ³ d/dx [9 - x²]

dy/dx = 1/3 (9 - x²)⁻²ʹ³ (-2x)

dy/dx = -2/3 x (9 - x²)⁻²ʹ³

Evaluate it at x = 1 :

dy/dx (1) = -2/3 • 8⁻²ʹ³

Since 8 = 2³, we have

8⁻²ʹ³ = 1 / 8²ʹ³ = 1 / (2³)²ʹ³ = 1 / 2² = 1/4

Then the tangent line has equation

y - 2 = 1/4 (x - 1) → y = 1/4 x + 7/4

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Multiply each equation by a constant that would help to eliminate the y terms.

Zinaida [17]

Answer:

Therefore the required resulting equation is

$6x-15y=-63\\-15x+15y=90$

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

Step-by-step explanation:

Given:

$2x-5y=-21$ ......................Equation ( 1 )

$3x-3y=-18$ ......................Equation ( 2 )

To Find:

Expression after multiplying to eliminate y term,

Solution:

So to eliminate 'y' term we need to multiply equation 1 by a constant 3 and equation 2 by a constant -5, such that equations becomes

$3(2x-5y)=3\times -21\\\\6x-15y=-63$ .....( 1 )

$-5(3x-3y)=-5\times -18\\\\-15x+15y=90$ .....( 2 )

so now by adding new equation one and two we can eliminate y term that means -15y and +15y will get cancel,

Therefore the required resulting equation is

$6x-15y=-63\\-15x+15y=90$

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

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3 years ago

Read 2 more answers

How to find the missing numbers in two digit division

abruzzese [7]

Answer:

Divide the first number of the dividend (or the two first numbers if the previous step took another digit) by the first digit of the divisor. Write the result of this division in the space of the quotient. Multiply the digit of the quotient by the divisor, write the result beneath the dividend and subtract it.Jun

Step-by-step explanation:

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3 years ago

Which expression is equivalent to 3^2-7?

Hunter-Best [27]

3 squared becomes 9. 9-7 equals 2, which is the final answer.

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4 years ago

-15= z/-2 answer please?

faust18 [17]

Answer:

Step-by-step explanation:

$-15=\frac{z}{-2}\\\\(-15)(-2)=z\\\\30=z$

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3 years ago

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$\bf 2)\\\\ 3+-5\implies 3+(-5)\implies 3+(-3-2)\implies ~~\begin{matrix} 3-3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-2\implies -2 \\\\\\ 9)\\\\ -5+(-6)\implies -5+(+5-11)\implies ~~\begin{matrix} -5+5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-11\implies -11 \\\\\\ 11)\\\\ 2+(-7)\implies 2+(-2-5)\implies ~~\begin{matrix} 2-2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-5\implies -5$

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4 years ago

Find the equation of the tangent line. y=(9-x^2)^1/3 at (1,2)​

Find the equation of the tangent line. y=(9-x^2)^1/3 at (1,2)