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Setler [38]
3 years ago
7

Find en equation of the tangent line to the curve

Mathematics
1 answer:
valkas [14]3 years ago
7 0
Y=MX+C   C=1  0=m(1)+1 m=-1 Y=-X+1 
You might be interested in
4 consecutive odd integers add up to -200. Find the integers.
Alexeev081 [22]
Let
x = first odd integer
x + 2 = second odd integer
x + 4 = third odd integer
x + 6 = fourth odd integer

x + (x + 2) + (x + 4) + (x + 6) = -200
4x = -200 - 2 - 4 - 6
4x = -212
x = -53

Therefore, the four consecutive integers are -53, -51, -49, -47.
4 0
3 years ago
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
Find the zeros of the function by first factoring the polynomial.
torisob [31]

Step-by-step explanation:

y2 + 4y - 5

( y + 4 )( y - 1 )

so you just need to break down the sum

5 0
3 years ago
The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2
romanna [79]

Answer:

Perimeter is irrational

<em></em>

Step-by-step explanation:

<em>The attachment is missing but the question is still answerable</em>

Given

Area = 24200 yd^2

Required

Determine if the Perimeter is rational or not

First, we need to determine the sides of the square;

Area = Length * Length

Substitute Area = 24200 yd^2

24200 = Length * Length

24200 = Length^2

Take Square root of both sides

\sqrt{24200} = Length

Length = 155.563492

The perimeter of a square is calculated as:

Perimeter = 4 * Length

Perimeter = 4 * 155.563492

Perimeter = 622.253968

<em>Because the value of </em><em>perimeter </em><em>can't be gotten by dividing two integers, then </em><em>perimeter is irrational</em>

4 0
3 years ago
1/6 + 1/8 + 1/12 what is the awnser
HACTEHA [7]

Answer:

3/8    (Decimal: 0.375)

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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