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aniked [119]
3 years ago
13

Which of the following is a solution of x2 − 10x = −36? (6 points)

Mathematics
1 answer:
Softa [21]3 years ago
6 0

Answer:

D

Step-by-step explanation:

Given

x² - 10x = - 36

Solve using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 5)x + 25 = - 36 + 25

(x - 5)² = - 11 ( take the square root of both sides )

x - 5 = ± \sqrt{-11} ( add 5 to both sides )

x = 5 ± i\sqrt{11}

Thus

x = 5 - i\sqrt11} or x = 5 + i\sqrt{11}

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Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by
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Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1

Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:

z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\

z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]

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The box which measures 70cm X 36cm X 12cm is to be covered by a canvas. How many meters of canvas of width 80cm would be require
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Answer:

142.2 meters.  

Step-by-step explanation:

We have been given that a box measures 70 cm X 36 cm X 12 cm is to be covered by a canvas.      

Let us find total surface area of box using surface area formula of cuboid.

\text{Total surface area of cuboid}=2(lb+bh+hl), where,

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\text{Width of canvas* Length of canvass}=\text{Total surface area of 150 boxes}

80\text{ cm}\times\text{ Length of canvass}=150\times 7584\text{cm}^2

\text{ Length of canvass}=\frac{150\times 7584\text{ cm}^2}{80\text{ cm}}

\text{ Length of canvass}=\frac{1137600\text{ cm}^2}{80\text{ cm}}

\text{ Length of canvass}=14220\text{ cm}

Let us convert the length of canvas into meters by dividing 14220 by 100 as 1 meter equals to 100 cm.

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\text{ Length of canvass}=142.20\text{ m}

Therefore, 142.2 meters of canvas of width 80 cm required to cover 150 such boxes.

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