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Gelneren [198K]
2 years ago
8

Solve the system of equations X=11+y 2x+y=19

Mathematics
2 answers:
raketka [301]2 years ago
6 0

Answer:

Step-by-step explanation:

To solve this system of equations, let's first find the value <em>y</em>. We can replace the x in the second equation with 11 + y, since we are told in the <em>first</em> equation that x is equal to 11 + y. So, let's replace x:

2(11 + y) + y = 19

22 + 2y + y = 19

22 + 3y = 19

3y = -3

y = -1

And look at that - we've found our y-value! Now, we can replace the y in the <em>first</em> equation with -1 to find the value of x.

x = 11 + (-1)

x = 10

So, the solution to this system of equations is (10, -1). Hopefully that's helpful!

Furkat [3]2 years ago
3 0

Answer:

x=26/3,y=-7/3

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Given f(x) = (lnx)^3 find the line tangent to f at x = 3
kirill [66]
Explanation

We must the tangent line at x = 3 of the function:

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The tangent line is given by:

y=m*(x-h)+k.

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,

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In this case, we have h = 3.

1) First, we compute the derivative of f(x):

f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.

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3) The value of k is:

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4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

y=(\ln3)^2*(x-3)+(\ln3)^3.

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

y=(\ln3)^2*(x-3)+(\ln3)^3

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