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2 years ago

Half angle tan 5pi/8

1 answer:

4 0

The half-angle formula for tangent is:

tan(a/2) = (sin a / (1 + cos a)) = ((1 - cos a) / sin a)

Now we can plug in values:

tan(5π/8) = (sin(5π/4) / (1 + cos(5π/4)) = ((1 - cos(5π/4)) / sin(5π/4)

tan(5π/8) = (-√2/2) / (1 + (-√2/2)) = (1 - (-√2/2)) / (-√2/2)

tan(5π/8) = ((-√2/2)) / ((2 - √2)/2) = ((2 + √2)/2) / (-√2/2)

Now we can solve the first half:

(-√2/2)(2 / (2 - √2))
(-√2/2)((4 + 2√2) / 2)
(-√2/2)(2 + √2)
(-2√2 - 2)/2
-√2 - 1

tan(5pi/8) = -√2 - 1

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2 years ago

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A plant can either have a smooth seed (p) or a rough seed (q). Rough seeds are recessive and smooth seeds are dominant. In a pop

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To calculate this, the Hardy-Weinberg principle can be used:

p² + 2pq + q² = 1 and p + q = 1

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a) Since 32 plants have rough seed (recessive genotype: q²) out of 100 plants in total, then

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b) q = √q² = √0.32 = 0.56

c) Since p + q = 1, then

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We need to calculate p (the allele frequency for smooth seeds).
We can find q because we know q²:

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2 years ago

Express 5.555... in the form of a geometric series.

Evgesh-ka [11]

5.555 = 5.1 + 0.05 + 0.005

= 5.5 + 0.05 + 0.05(.1)

= 5.5 + 0.05/(1-.1)

=5.5+0.05/.9

=5.5 + 5/90

= 5.5+1/18

=55/10 + 1/18

= 495/90 + 5/90

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2 years ago

A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 10 of th

Digiron [165]

Answer:

f(x) = -5x + 250

Step-by-step explanation:

* Lets explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

the line which represent the equation and c is the y-intercept

- The slope of the line m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

the linear equation between the cars' numbers and the weeks

numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴ $m=\frac{175-200}{15-10}=\frac{-25}{5}=-5$

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

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