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Sergio039 [100]
2 years ago
7

Find the equation of the line that passes through (-1,-3) and is perpendicular to

Mathematics
2 answers:
miv72 [106K]2 years ago
3 0

Answer:

y = -2x - 5

Step-by-step explanation:

2y = x - 3

y = 1/2x - 3/2

gradient = 1/2

perpendicular gradient = negative reciprocal = -2

y = -2x + c

(-3) = -2(-1) + c

-3 = 2 + c

-5 = c

Alenkinab [10]2 years ago
3 0

Answer:

<u>y = -x/2 - 7/2</u>

Step-by-step explanation:

<u>Equation of the line (current) in y = mx + c</u>

  • 2y = x - 3
  • y = x/2 - 3/2

The slope of a perpendicular line has to be -ve to the current line.

⇒ m' = -1/2

To find the y-intercept, take the x-coordinate to be 0 and substitute in the equation :

y - y₁ = m (x - x₁)

y + 3 = -1/2 (0 + 1) [Also using the point (-1, -3) to make sure line crosses it]

y + 3 = -1/2

y = -7/2

Therefore, the new equation is :

  • <u>y = -x/2 - 7/2</u>
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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
WARRIOR [948]

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})]

3 0
3 years ago
What is the sum of5 + 4 +
Nadusha1986 [10]

Answer:

9

Step-by-step explanation:

5+4=9

6 0
3 years ago
Read 2 more answers
Hey can you please help me posted picture of question
Alex Ar [27]
The resolvent is:
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options: B, C, D are correct
3 0
3 years ago
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Please answer this question! 32 points and brainliest!!
stepladder [879]

Answer:

3x^2 -7x +2

Step-by-step explanation:

(15x^2 -35x+10) ÷5

(15/5x^2 -35/5x+10/5)

3x^2 -7x +2

This will factor

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5 0
3 years ago
What is the answer for this math problem 6x&gt;12
k0ka [10]

Answer:

The correct answer is:   " x  >  2 "  .

______________________________________________________

Step-by-step explanation:

______________________________________________________

Given the inequality:

    " 6x   >  12  "  ;

Solve in terms of "x" :

______________________________________________________

Divide each side of the inequality by "6" ;

   to isolate "x" on one side of the inequation; & to solve in terms of "x" ;

                 →  " 6x  / 6  >  12 / 6  "  ;

   to get:

                 →  "  x  >  2 " .

______________________________________________________

Hope this is helpful to you.

     Best wishes to you in your academic pursuits

               — and within the "Brainly" community!

______________________________________________________

4 0
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