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nekit [7.7K]
3 years ago
10

If F(x)=2x^2+3, then which of the following represent f(x+1). A.2x^2+2. B. X^2+3. C. 2x^2+4x+1. D. 2x^2+4x+5

Mathematics
1 answer:
serg [7]3 years ago
5 0
Hi,
If it is f(x)=2x²+3 and not F(x)=2x²+3 then 
Answer D.

f(x)=2x^2+3\\

f(x+1)=2(x+1)^2+3\\
=2(x^2+2x+1)+3\\
=2x^2+4x+5\\


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Answer:

sin(2\theta)=\frac{\sqrt{35} }{18}

Step-by-step explanation:

Recall the formula for the sine of the double angle:

sin(2\theta)=2*sin(\theta)*cos(\theta)

we know that cos(\theta)=\frac{3}{18}, and that \theta is in the interval between 0 and 90 degrees, where both the functions sine and cosine are non-negative numbers. Based on such, we can find using the Pythagorean trigonometric property that relates sine and cosine of the same angle, what sin(\theta) is:

cos^2(\theta)+sin^2(\theta)=1\\sin^2(\theta)=1-cos^2(\theta)\\sin(\theta)=\sqrt{1-cos^2(\theta)} \\sin(\theta)=\sqrt{1-(\frac{3}{18} )^2}\\sin(\theta)=\sqrt{1-\frac{9}{324} }\\sin(\theta)=\sqrt{\frac{324-9}{324} }\\sin(\theta)=\sqrt{\frac{315}{324} }\\\\sin(\theta)=\frac{3}{18}\sqrt{35 }

With this information, we can now complete the value of the sine of the double angle requested:

sin(2\theta)=2*sin(\theta)*cos(\theta)\\sin(2\theta)=2*\frac{3}{18} \,\sqrt{35} \,\frac{3}{18}\\sin(2\theta)=\frac{2*3*3}{18*18}\,\sqrt{35} \\sin(2\theta)=\frac{\sqrt{35} }{18}

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