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tangare [24]
3 years ago
5

You have a tree in your yard 4 ft to the left of and 5 ft in front of the corner of your porch. A circular fence 3 ft in radius

has its center at the tree. If the corner of your porch is the origin and forward is the positive y direction, what equation represents the circle formed by the fence in your yard?
Mathematics
1 answer:
Natalka [10]3 years ago
8 0

Answer:

(x+4)^2+(y-5)^2=9

Step-by-step explanation:

If the corner of your porch is the origin

  • 4 ft to the left, x=-4
  • 5 ft in front, y=5

The tree's location is at (-4,5).

  • A circular fence 3 ft in radius has its center at the tree(-4,5).

We want to determine the equation of a circle with center (-4,5) and radius 3 ft.

The equation of a circle center (h,k) with a radius of r is given as:

(x-h)^2+(y-k)^2=r^2

(h,k)=(-4,5), r=3

The equation formed by the fence therefore is:

(x-(-4))^2+(y-5)^2=3^2\\\\$Simplifying we obtain:\\\\(x+4)^2+(y-5)^2=9

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The function h is given by h ( t ) = ( 1 − t ) ( 8 + 16 t ) models the height of a ball in feet, t seconds after it is thrown.
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Answer:

  • zeros: t = 1, t = -1/2
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Step-by-step explanation:

The zeros are the values of t that make the factors zero.

  1 -t = 0   ⇒   t = 1

  8 +16t = 0   ⇒   t = -8/16 = -1/2

The equation is used to model height after the ball is thrown. We don't expect it to be a good model before the ball is thrown (t < 0), so the zero in that region is extraneous.

Only the positive zero is in the function's domain, so that is the only one that is meaningful.

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When t = 0 (at the time the ball is thrown), the function value is ...

  h(0) = (1 -0)(8 +0) = 8

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3 years ago
Form a polynomial function whose real zeros are in -1, 1, 3 and whose degree is 3
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The polynomial function whose real zeros are in -1, 1, 3 and whose degree is 3 is x^3-3x^2-x+3=0

Step-by-step explanation:

We need to find a polynomial function whose real zeros are in -1, 1, 3 and whose degree is 3.

If -1, 1 and 3 are real zeros, it can be written as:

x= -1, x= 1, and x = 3

or x+1=0, x-1=0 and x-3=0

Finding polynomial by multiply these factors:

(x+1)(x-1)(x-3)=0\\(x+1)(x(x-3)-1(x-3))=0\\(x+1)(x^2-3x-x+3)=0\\(x+1)(x^2-4x+3)=0\\x(x^2-4x+3)+1(x^2-4x+3)=0\\x^3-4x^2+3x+x^2-4x+3=0\\Combining\,\,like\,\,terms:\\x^3-4x^2+x^2+3x-4x+3=0\\x^3-3x^2-x+3=0

So, The polynomial function whose real zeros are in -1, 1, 3 and whose degree is 3 is x^3-3x^2-x+3=0

Keywords: Real zeros of Polynomials

Learn more about Real zeros of Polynomials at:

  • brainly.com/question/1464739
  • brainly.com/question/2568692
  • brainly.com/question/10771256

#learnwithBrainly

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