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BaLLatris [955]
2 years ago
8

6) You are shooting the puck along the path

Mathematics
1 answer:
Natali5045456 [20]2 years ago
7 0

Answer:

m = 58°

x = 64°

Step-by-step explanation:

When a puck touches one side of the air hockey table,

All the angles formed are located at a point on a straight line.

Therefore, sum of angles formed is 180°.

m° + m° + 64° = 180°

2m + 64 = 180

2m = 180 - 64

2m = 116

m = 58°

m∠y = m = 58° [Alternate interior angles]

Similarly, on the other side of the table,

58° + y° + x° = 180°

58° + 58° + x° = 180°

x + 116° = 180°

x = 180 - 116

x = 64°

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Simplify to an expression of the form (a sin(θ)).<br> 2sin(/8)2cos(/8)
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Answer:

Your expression equals 2 \sin(\frac{\pi}{4}) assuming the problem was to simplify 2\sin(\frac{\pi}{8}) 2\cos(\frac{\pi}{8}) to the form a\sin(\theta).

Step-by-step explanation:

2\sin(\frac{\pi}{8}) 2\cos(\frac{\pi}{8})

2(2)\sin(\frac{\pi}{8})\cos(\frac{\pi}{8})

Let's use the following identity: 2\sin(A)\cos(A)=\sin(2A)

2\sin(2 \cdot \frac{\pi}{8})

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3 years ago
Is 4/12 equal to 7/28?
mars1129 [50]

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Find the standard form of the equation for the circle with the following properties.
nataly862011 [7]

Answer:

(x+6)^2+(y+\frac{7}{6})^2=\frac{49}{36}

Step-by-step explanation:

So, we know that the center of the circle is at (-6, -7/6).

To find the equation of our circle that is tangent to the x-axis, we just need to find the vertical distance from our center to the x-axis.

Our center is at (-6, -7/6). The vertical distance from this to the x-axis directly above will be (-6, 0).

So, find our distance by subtracting our x-values:

d=r=0-(-7/6)

Subtract:

d=r=7/6

So, our distance, which is also our radius, will be 7/6.

Now, we can use the standard form for a circle, which is:

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

Where (h, k) is the center and r is the radius.

Substitute -6 for h, -7/6 for k, and 7/6 for r. This yields:

(x+6)^2+(y+\frac{7}{6})^2=\frac{49}{36}

We can confirm by graphing (using a calculator):

7 0
3 years ago
Question 1
Vitek1552 [10]

Answer:

M.A.D= 4.9

Step-by-step explanation:

Given

12.7, 22, 23.5, 24, 11, 22

Required

Determine the M.A.D

Start by calculating the Mean

Mean = \frac{\sum x}{n}

In this case, n = 6

So:

Mean = \frac{12.7 + 22 + 23.5 + 24 + 11 + 22}{6}

Mean = \frac{115.2}{6}

Mean = 19.2

Subtract the mean from each element

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22 - 19.2 = 2.8

23.5 - 19.2 = 4.3

24 - 19.2 = 4.8

11 - 19.2 = -8.2

22 - 19.2 = 2.8

Take absolute value of the results above

|-6.5| = 6.5

|2.8| = 2.8

|4.3| = 4.3

|4.8| = 4.8

|-8.2| = 8.2

|2.8| = 2.8

The mean of the above gives the MAD

M.A.D= \frac{\sum |x - u|}{n}

M.A.D= \frac{6.5 + 2.8 + 4.3 + 4.8 + 8.2 + 2.8}{6}

M.A.D= \frac{29.4}{6}

M.A.D= 4.9

7 0
3 years ago
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