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3 years ago

If 3x^2+2xy+y^2=2 then the value of dy/dx at x=1 is

1 answer:

6 0

We have that
3x²+2xy+y²=2

find the derivative-------> (Implicit differentiation)
6x+2xdy/dx+2y+2ydy/dx=0
collect dy/dx terms along one side
dy/dx(2x+2y)= -6x-2y 
dy/dx= -2(3x+y)/2(x+y) = - (3x+y)/(x+y)

for x=1
dy/dx= -(3+y)/(1+y)= -(y+3)/(y+1)

the answer is
dy/dx=-(y+3)/(y+1)

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Find all zeros of function and write the polynomial as a product of linear factorsX^3-x^2+9x-9

mart [117]

Answer:

$\large\boxed{x=1\ \vee\ x=-3i\ \vee\ x=3i}$

Step-by-step explanation:

$\text{The zeros:}\\\\x^3-x^2+9x-9=0\\\\x^2(x-1)+9(x-1)=0\\\\(x-1)(x^2+9)=0\iff x-1=0\ \vee\ x^2+9=0\\\\x-1=0\qquad\text{add 1 to both sides}\\x-1+1=0+1\\\boxed{x=1}\\\\x^2+9=0\qquad\text{subtract 9 from both sides}\\x^2=-9$

8 0

3 years ago

Simplify the expression.Can you help me with this one. I'm stuck at 12^x4 - 15x^2

Blababa [14]

Simplify the given expression as shown below

$\begin{gathered} 3x(4x^4-5x)=3x*4x^4+3x(-5x)=12x^5+(-15x^2) \\ =12x^5-15x^2 \end{gathered}$ <h2>Therefore, the answer is 12x^5-15x^2</h2>

3 0

1 year ago

? Solve for X 9x + 8 = -1

larisa [96]

Answer:

x = -1

Step-by-step explanation:

9x + 8 = -1

Subtract 8 from each side

9x + 8-8 = -1-8

9x = -9

Divide each side by 9

9x/9 = -9/9

x = -1

5 0

3 years ago

How many solutions does the following equation have? 7(y + 3) = 5y + 8 answer:

vodomira [7]

Answer:

One Solution

Explanation:

7(y + 3) = 5y + 8

Simplify both sides of the equation

7(y + 3) = 5y + 8

(7)(y) + (7)(3) = 5y + 8 (Distribute)

7y + 21 = 5y + 8

Subtract 5y from both sides

7y + 21 − 5y = 5y + 8 − 5y

2y + 21 = 8

Subtract 21 from both sides

2y + 21 − 21 = 8 − 21

2y = −13

Divide both sides by 2

2y = −13

2y / 2 = -13 / 2

y = -13 / 2

-13 / 2 = -6.5

y = -13 / 2 or -6.5

6 0

3 years ago

What are the coordinates of point J’ after the rotation?

olchik [2.2K]

Step-by-step explanation:

(5,4) is the coordinate of the point j after rotation

6 0

2 years ago