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Papessa [141]
2 years ago
14

1. Write the equation in standard form. Identify the important features of the graph:

Mathematics
1 answer:
NeTakaya2 years ago
6 0

Answer:

  1. (x-4.5)^2 +(y +5)^2 = 30.25
  2. x = (1/8)y^2 +(1/2)y +(1/2)
  3. y^2/36 -x^2/64 = 1
  4. x^2/16 +y^2/25 = 1

Step-by-step explanation:

1. Complete the square for both x and y by adding a constant equal to the square of half the linear term coefficient. Subtract 15, and rearrange to standard form.

  (x^2 -9x +4.5^2) +(y^2 +10y +5^2) = 4.5^2 +5^2 -15

  (x -4.5)^2 +(y +5)^2 = 30.25 . . . . . write in standard form

Important features: center = (4.5, -5); radius = 5.5.

__

2. To put this in the form x=f(y), we need to add 8x, then divide by 8.

  x = (1/8)y^2 +(1/2)y +(1/2)

Important features: vertex = (0, -2); focus = (2, -2); horizontal compression factor = 1/8.

__

3. We want y^2/a^2 -x^2/b^2 = 1 with a=36 and b=(36/(3/4)^2) = 64:

  y^2/36 -x^2/64 = 1

__

4. In the form below, "a" is the semi-axis in the x-direction. Here, that is 8/2 = 4. "b" is the semi-axis in the y-direction, which is 5 in this case. We want x^2/a^2 +y^2/b^2 = 1 with a=4 and b=5.

  x^2/16 +b^2/25 = 1

_____

The first attachment shows the circle and parabola; the second shows the hyperbola and ellipse.

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Marysya12 [62]

Answer:

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Step-by-step explanation:

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3.75 e < 25 - 9.50 = 15.50

e < 15.50 ÷ 3.75 ≈ 4.13

e =<em> 4 pairs of earrings</em>

3 0
2 years ago
Find the circumference of a pizza with a diameter of 18 inches
tatyana61 [14]
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I hope this helps!
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2 years ago
A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate
Lyrx [107]

Answer:

Therefore the rate change of height is  \frac{1}{\pi} m/s.

Step-by-step explanation:

Given that a vertical cylinder is leaking water at rate of 4 m³/s.

It means the rate change of volume is 4 m³/s.

\frac{dV}{dt}=4 \ m^3/s

The radius of the cylinder remains constant with respect to time, but the height of the water label changes with respect to time.

The height of the cylinder be h(say).

The volume of a cylinder is V=\pi r^2 h

                                                 =( \pi \times 2^2\times h)\ m^3

\therefore V= 4\pi h

Differentiating with respect to t.

\frac{dV}{dt}=4\pi \frac{dh}{dt}

Putting the value \frac{dV}{dt}

\Rightarrow 4\pi \frac{dh}{dt}=4

\Rightarrow \frac{dh}{dt}=\frac{4}{4\pi}

\Rightarrow \frac{dh}{dt}=\frac{1}{\pi}

The rate change of height does not depend on the height.

Therefore the rate change of height is  \frac{1}{\pi} m/s.

3 0
2 years ago
Expand and simpify (x+4)(x-7)
erica [24]

Answer:

x^2 - 3x - 28

Step-by-step explanation:

(x+4)(x-7)

x^2-7x+4x-28

x^{2}-3x-28

6 0
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scoundrel [369]

Answer:

Red: 3/4

Blue: 9/5, 8/3

Green: 2 8/12, 2 1/2

Step-by-step explanation:

8 0
2 years ago
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