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777dan777 [17]
3 years ago
11

Please answer this question

Mathematics
1 answer:
Vladimir [108]3 years ago
8 0

Answer:

  • a = 3/2
  • b = -1/2

Step-by-step explanation:

  \dfrac{\sqrt{5}-1}{\sqrt{5}+1}=\dfrac{(\sqrt{5}-1)(\sqrt{5}-1)}{(\sqrt{5}+1)(\sqrt{5}-1)}\\\\=\dfrac{5-2\sqrt{5}+1}{5-1}=\dfrac{6-2\sqrt{5}}{4}\\\\=\dfrac{3}{2}-\dfrac{1}{2}\sqrt{5}

Comparing this to the form a+b√5, we see that ...

  a = 3/2

  b = -1/2

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4 years ago
Find the value of r in the following diagram.
Andrews [41]

Answer:

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3 0
3 years ago
NEED ANSWER
grandymaker [24]

Answer:

\frac{x^{2}}{144}+\frac{y^{2}}{79.995}=1

Step-by-step explanation:

An ellipse centered a point (h,k) has the following formula:

\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1

The distance between foci is:

2\cdot c = \sqrt{[8-(-8)]^{2}+(0-0)^{2}}

2\cdot c = 16

c = 8

The center of the ellipse is:

C(x,y) = (-8 + 8, 0 + 0)

C(x,y) = (0,0)

The known vertex is on the horizontal axis of the ellipse. Then, the length of the semi-major axis is:

a = \sqrt{(12-0)^{2}+(0-0)^{2}}

a= 12

The length of the semi-minor axis is given by the following expression:

c =\sqrt{a^{2}-b^{2}}

b = \sqrt{a^{2}-c^{2}}

b = \sqrt{12^{2}-8^{2}}

b \approx 8.944

The equation of the ellipse is:

\frac{x^{2}}{144}+\frac{y^{2}}{79.995}=1

5 0
3 years ago
What are the factors of x2 - 144?<br> and
likoan [24]

Answer:

Step-by-step explanation:

x² - 144 = x² - 12²

            = (x +12)(x - 12)

a² - b² = (a + b)(a-b)

3 0
3 years ago
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