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2 years ago

A line passes through the points (7,6) and (8,8) What is its equation in slope intercept form?

Mathematics

1 answer:

rjkz [21]2 years ago

8 0

Answer:

Step-by-step explanation:

The slope: $m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-6}{8-7}=\dfrac21=2$

y = mx + b ← slope intercept form

(8, 8) ⇒ x = 8, y = 8

so:

8 = 2·8 + b

b = - 8

The equation: y = 2x - 8

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Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using De Moivre's theorem:

If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number ⇒ z = 81(cos(3π/8) + i sin(3π/8))


Part (A) find the modulus for all of the fourth roots

∴ The modulus of the given complex number = l z l = 81

∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

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3 years ago

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Answer: C

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3 years ago

Craig Browning bakes cookies for the elementary school cookie sale. His chocolate chip cookies sell for $1.00 a dozen, and his o

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Answer and Step-by-step explanation:

Let

Number of chocolate chip cookies = x

Number of oatmeal brownie cookies = y

Bake chocolate chip cookies up to 20 dozen = x≤ 20

Bake oatmeal brownies up to 40 dozen= y≤40

Total cookies = x + y ≤ 50

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From the inequality:

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By putting the value of x=12.5 in equation y = 3x, we get

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3 years ago

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3 years ago

A line passes through the points (7,6) and (8,8) What is its equation in slope intercept form?​

A line passes through the points (7,6) and (8,8) What is its equation in slope intercept form?