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svp [43]
3 years ago
6

Gustavo and yuki were asked to find an explicit formula for the sequence 19, 0, -19, -38...

Mathematics
1 answer:
KiRa [710]3 years ago
4 0

Answer:

<h2>Neither Gustavo nor Yuki</h2>

Step-by-step explanation:

It's an arithmetic sequence.

0-19=-19\\-19-0=-19\\-38-(-19)=-38+19=-19

The difference is constant.

The explicit formula of an arithmetic sequence:

a_n=a_1+(n-1)d

Substitute:

a_1=19,\ d=-19

a_n=19+(n-1)(-19)             <em>use distributive property</em>

a_n=19-19n+19\\\\a_n=(19+19)-19n\\\\a_n=38-19n

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1 step (B): raise both sides of the equation to the power of 2.

(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2,\\   (x+3)-2\sqrt{x+3}\cdot \sqrt{2x-1}+(2x-1)=4,\\ 3x+2-2\sqrt{x+3}\cdot \sqrt{2x-1}=4.

2 step (A): simplify to obtain the final radical term on one side of the equation.

-2\sqrt{x+3}\cdot \sqrt{2x-1}=4-3x-2,\\ -2\sqrt{x+3}\cdot \sqrt{2x-1}=2-3x,\\ 2\sqrt{x+3}\cdot \sqrt{2x-1}=3x-2.

3 step (F): raise both sides of the equation to the power of 2 again.

(2\sqrt{x+3}\cdot \sqrt{2x-1})^2=(3x-2)^2,\\ 4(x+3)(2x-1)=(3x-2)^2.

4 step (E): simplify to get a quadratic equation.

4(2x^2-x+6x-3)=(3x)^2-2\cdot 3x\cdot 2+2^2,\\ 8x^2+20x-12=9x^2-12x+4,\\ x^2-32x+16=0.

5 step (D): use the quadratic formula to find the values of x.

D=(-32)^2-4\cdot 16=1024-64=960, \\ \sqrt{D} =8\sqrt{5} ,\\ x_{1,2}=\dfrac{32\pm 8\sqrt{5}}{2} =16\pm 4\sqrt{5}.

6 step (C): apply the zero product rule.

x^2-32x+16=(x-16-4\sqrt{5}) (x-16+4\sqrt{5}) ,\\ (x-16-4\sqrt{5}) (x-16+4\sqrt{5}) =0,\\ x_1=16+4\sqrt{5} ,x_2=16-4\sqrt{5}.

Additional 7 step: check these solutions, substituting into the initial equation.

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3 years ago
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2 years ago
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Answer:

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Step-by-step explanation:

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Also, if a function is an odd function, then, f(-x) = -f(x)

You are given the below function

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Substitute 2 for x in the function

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Answer:

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Step-by-step explanation:

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