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steposvetlana [31]
3 years ago
13

Use an appropriate half-angle formula to find the exact value of the expression. cos 3π 8

Mathematics
1 answer:
cricket20 [7]3 years ago
4 0
The half-angle formula for cosine is
\cos{\left(\dfrac{\theta}{2}\right)}=\sqrt{\dfrac{1+\cos{\theta}}{2}}

To find cos(3π/8), we can use this formula with θ=3π/4. Cos(3π/4) = -(√2)/2, so we have

\cos{\left(\dfrac{3\pi}{8}\right)=\sqrt{\dfrac{1-\frac{\sqrt{2}}{2}}{2}}\\\\=\sqrt{\dfrac{2-\sqrt{2}}{4}}=\frac{1}{2}\sqrt{2-\sqrt{2}}
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Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.
dsp73

Answer:

The required sequence is a_n=20(\frac{1}{2})^{n-1}. The average rate of change from n = 1 to n = 3 is -7.5.

Step-by-step explanation:

From the given graph it is clear that the sequence is a GP because the all terms are half of their previous terms.

Here, a_2=10,a_3=5,a_4=2.5,a_5=1.25

r=\frac{a_3}{a_2}=\frac{5}{10}=\frac{1}{2}

The common ratio of GP is 1/2.

r=\frac{a_2}{a_1}

\frac{1}{2}=\frac{10}{a_1}

a_1=20

The first term of the sequence is 20.

The formula for sequence is

a_n=a(r)^{n-1}

Where a is first term and r is common difference.

The required sequence is

a_n=20(\frac{1}{2})^{n-1}

The formula for rate of change is

m=\frac{f(x_2)-f(x_1)}{x_2-x_1}

The average rate of change from n = 1 to n = 3 is

m=\frac{f(3)-f(1)}{3-1}

m=\frac{5-20}{3-1}

m=\frac{-15}{2}=-7.5

Therefore the required sequence is a_n=20(\frac{1}{2})^{n-1}. The average rate of change from n = 1 to n = 3 is -7.5.

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the input value in the x column is multiplied by 5 to get the output value in the y column
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