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nata0808 [166]
4 years ago
6

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

Mathematics
1 answer:
Marina CMI [18]4 years ago
6 0
We have that
3x²+2xy+y²<span>=2
</span>
find the derivative-------> <span>(Implicit differentiation)
</span><span>6x+2xdy/dx+2y+2ydy/dx=0 
</span>collect dy/dx terms along one side 
<span>dy/dx(2x+2y)= -6x-2y </span>
<span>dy/dx= -2(3x+y)/2(x+y) = - (3x+y)/(x+y)
</span>
for x=1
<span>dy/dx= -(3+y)/(1+y)= -(y+3)/(y+1)
</span>
the answer is
dy/dx=-(y+3)/(y+1)

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consider the exponential function f(x)= 1/5(15x) what is the value of the growth factor of the function?
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Answer:

  15

Step-by-step explanation:

The general form of an exponential equation is ...

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That is, the "growth factor" is the base of the exponent. In your equation ...

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the growth factor is 15.

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Diego is solving the equation x^2-12x = 21
uysha [10]

Answer:

The solutions to the quadratic equations will be:

x=\sqrt{57}+6,\:x=-\sqrt{57}+6

Step-by-step explanation:

Given the expression

x^2-12x\:=\:21

Let us solve the equation by completing the square

x^2-12x\:=\:21

Add (-6)² to both sides

x^2-12x+\left(-6\right)^2=21+\left(-6\right)^2

simplify

x^2-12x+\left(-6\right)^2=57

Apply perfect square formula: (a-b)² = a²-2ab+b²

i.e.

x^2-12x+\left(-6\right)^2=\left(x-6\right)^2

so the expression becomes

\left(x-6\right)^2=57

\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}

solve

x-6=\sqrt{57}

add 6 to both sides

x-6+6=\sqrt{57}+6

Simplify

x=\sqrt{57}+6

also solving

x-6=-\sqrt{57}

add 6 to both sides

x-6+6=-\sqrt{57}+6

Simplify

x=-\sqrt{57}+6

Therefore, the solutions to the quadratic equation will be:

x=\sqrt{57}+6,\:x=-\sqrt{57}+6

5 0
3 years ago
If angle X is an acute angle with tan X = 8/7, what is the value of sec X?
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Step-by-step explanation:

As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.

Using the identity 1+\tan^{2} X=\sec^{2} X,

1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}

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1 year ago
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