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Daniel [21]
2 years ago
6

Prove that (vectors)

Mathematics
1 answer:
netineya [11]2 years ago
6 0

Answer:

I submitted a screenshot

Step-by-step explanation:

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Would the answer be c??
andrew-mc [135]

Answer:

<h2>PLEASE MARK BRAINLIEST!!</h2>

Yes

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Which rate is equivalent to 6 miles per gallon?
Talja [164]

Answer:

The answer is C becuase 18÷3=6

8 0
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Read 2 more answers
Urgent, It is a Calculus question and I’ll appreciate your help. Thanks
BaLLatris [955]

Answer:

  4733

Step-by-step explanation:

Please refer to the attached diagram.

Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.

Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.

We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...

  (12p)(12r) = -1

  r = -1/(144p)

The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:

  slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified

The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...

  tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))

__

Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...

  slope AB = ((slope AC) +2)/(1 -(slope AC)(2))

  6(p+r)=\dfrac{12p+2}{1-(12p)(2)}\\\\3(p+r)(1-24p)=6p+1\qquad\text{multiply by $1-24p$}\\\\3\left(p-\dfrac{1}{144p}\right)(1-24p)=6p+1\qquad\text{use the value for r}\\\\3(144p^2-1)(1-24p)=144p(6p+1)\qquad\text{multiply by 144p}\\\\ 3456 p^3+ 144 p^2+ 24 p+1 =0\qquad\text{put in standard form}\\\\144p^2(24p+1)+(24p+1)=0\qquad\text{factor by pairs}\\\\(144p^2+1)(24p+1)=0\qquad\text{finish factoring}\\\\p=-\dfrac{1}{24}\qquad\text{only real solution}\\\\r=\dfrac{-1}{144p}=\dfrac{1}{6}

So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...

  d^2 = (6r^2 -6p^2)^2 +(r -p)^2

  d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216

Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...

  Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b

Then a+b = 125 +4608 = 4733.

_____

<em>Comment on the solution</em>

The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.

6 0
3 years ago
Calculate the distance between the points N=(-5, 9) and P=(-1, 2) in the coordinate plane.
GalinKa [24]

Answer:

j

Step-by-step explanation:

5 0
3 years ago
A square and a rectangle have the same perimeter. The rectangle is 13 cm long and 7 cm wide.
lorasvet [3.4K]

<u>Solving</u>

Knowing that we have the information needed we will first find the perimeter of the rectangle.

Rectangle:
Length: 13cm

Width: 7cm  

Formula: L+L+W+W

13+13+7+7 = 40cm

Meaning the perimeter is 40cm and we can use this to find the length of a square. From general knowledge we know that all sides of a square is equal.

So if we divide the 4 sides by 40 we will get our answer.

40 ÷ 4 = 10

So B would be our answer...

<u>Statement</u>

<u />

Therefore the length of a side of the square is 10cm, meaning answer B is correct.

5 0
2 years ago
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