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3 years ago

Find the missing value so that the two points have a slope 1/2 (7, 2 )and (3,y)

Mathematics

2 answers:

MrRissso [65]3 years ago

6 0

(7,2) , (3,0) 7-3=4 as denominator, and 2-0=2 as the numerator equaling 2/4 which is 1/2

balandron [24]3 years ago

5 0

Answer:

The missing y -coordinate is 0.

Step-by-step explanation:

Here we know the slope but must find the y-coefficient of one of the points.

y - 2

The slope is m = 1/2 = rise / run = ----------

3 - 7

y - 2

or 1/2 = ---------- which simplifies to -2 = y - 2, which yields y = 0.

-4

The missing y -coordinate is 0.

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Answer:

I prefer reading history

Step-by-step explanation:

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Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.

alexandr1967 [171]

For the numbers in $a+bi$ form, convert to polar form:

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By DeMoivre's theorem,

$(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i$

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$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

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$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

For the numbers already in polar form, DeMoivre's theorem can be applied directly:

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

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3 years ago

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3 years ago

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