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tatyana61 [14]
3 years ago
5

3. Find an equation of a parabola with a vertex at the origin and directrix y = -3.5

Mathematics
2 answers:
Lina20 [59]3 years ago
7 0

Answer:

y=\frac{1}{14}x^2

Step-by-step explanation:

we know that

The directrix of the parabola is perpendicular to the axis of symmetry of the parabola

In this problem  the directrix is y=-3.5

so

The axis of symmetry is parallel to the y-axis

we have a vertical parabola

Also, the vertex is at the origin

That means-----> the parabola open upward

The equation of a vertical parabola can be written as

x^2=4py

where

p is the distance between the vertex and the directrix

In this problem

the distance between the vertex and the directrix is 3.5

p=3.5 ----> the value of p is positive because the parabola open upward

substitute

x^2=4(3.5)y

x^2=14y

isolate the variable y

y=\frac{1}{14}x^2

nalin [4]3 years ago
4 0

For the Quadratic Relations and Conic Sections Unit Test Part 1:

1. C. Ellipse, Domain: {-1≤x≤1}, Range: {-2≤y≤2}

2. D. y=x^2/5

3. B. y=1/14 x^2

4. B. 5 inches

5. A. x=1/12 (y-4)^2+4

6. A. (x-3)^2+(y-4)^2=36

7. B. (x+8)^2+(y+4)^2=25

8. A. (x+3)^2+(y+6)^2=16

9. A. Center at (7,-6): radius 4

10. B. x^2/25+y^2/169=1

11. A. (0, ±6)

12. C. 10 feet

13. C. Conic section is on the x axis, should be two on the x axis, A and C, <em>NOT</em> the rounded one.

14. D. (0, ±5)

REMEMBER check your test to see if answers match up!!!

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What are the first, second, and third frequencies audible from a 20 cm long organ pipe when (A) only one end is open and when (B
kotykmax [81]
A) The answers are:
the first frequency - 428.75 Hz
the second frequency - 1286.25 Hz
the third frequency - 2143.75 Hz

The frequency (when the pipe is closed) is: f = v(2n - 1)/4L
v - the speed of sound
n - the frequency order
L - the length of the organ pipe

We know:
v = 343 m/s
L = 20 cm = 0.2 m

1. The first frequency (n = 1):
f = 343 * (2 * 1 - 1) / 4 * 0.2 = 343 * 1 / 0.8 = 428.75 Hz


2. The second frequency (n = 2):
f = 343 * (2 * 2 - 1) / 4 * 0.2 = 343 * 3 / 0.8 = 1286.25 Hz


3. The third frequency (n = 3):
f = 343 * (2 * 3 - 1) / 4 * 0.2 = 343 * 5 / 0.8 = 2143.75 Hz


B) The answers are:

the first frequency - 857.5 Hz
the second frequency - 1715 Hz
the third frequency - 2572.5 Hz

The frequency (when the pipe is open) is: f = vn/2L
v - the speed of sound
n - the frequency order
L - the length of the organ pipe

We know:
v = 343 m/s
L = 20 cm = 0.2 m

1. The first frequency (n = 1):
f = 343 * 1 / 2 * 0.2 = 343 / 0.4 = 857.5 Hz


2. The second frequency (n = 2):
f = 343 * 2 / 2 * 0.2 = 686 / 0.4 = 1715 Hz


3. The third frequency (n = 3):
f = 343 * 3 / 2 * 0.2 = 1029 / 0.4 = 2572.5 Hz
4 0
3 years ago
Graph the circle 2+ y2 - 14x + 2y + 41 = 0.
Luden [163]

Answer:

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Step-by-step explanation:

8 0
3 years ago
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Montano1993 [528]

Answer: for the box. x 5 / -2 / 2 / -1 / 0 / -3 / 3

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Step-by-step explanation:

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3 0
3 years ago
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aleksley [76]

Answer:

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Step-by-step explanation:

4 0
3 years ago
For the scientific notation, write the standard form: 5.61 x 102
Alekssandra [29.7K]

<em>I believe the exponential form above is 5.61 x </em>10^{2}

Answer:

561

Step-by-step explanation:

A<em> "scientific notation"</em> is being used in order to express large numbers in its <u>simplest form</u>. This is commonly used in careers that use Mathematics very often like<em> engineers</em> or<em> scientists </em>because it makes their computation easier.

The<em> "standard form"</em> refers to the standard or traditional way of writing the numbers.

In order to get the standard form above, you have to check the <em>"power of the number 10." </em>The exponent above is 2. This means that you have to move the decimal point of 5.61 to the<em> right twice.</em> So, the answer is 561.

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3 years ago
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