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Alecsey [184]
3 years ago
5

A billiard ball is struck by a cue. It travels 100\,\text{cm}100cm100, start text, c, m, end text before ricocheting off a rail

and traveling another 120\, \text{cm}120cm120, start text, c, m, end text into a corner pocket. The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45^{\circ}45 ∘ 45, degrees. How far is the corner pocket from where the cue initially struck the ball?

Mathematics
2 answers:
miss Akunina [59]3 years ago
8 0

Answer:

\large \boxed{\text{86 cm}}

Step-by-step explanation:

I think what you are saying is represented by the diagram below.

The ball starts at A, rebounds from the far wall at a 45° angle and into the corner pocket at C.

You want the find the distance from A to C.

We can use the Law of Cosines to answer this question

\begin{array}{rcl}b^{2} & = & a^{2} + c^{2} - 2ac\cos \theta\\& = & 120^{2} + 100^{2} - 2 \times120\times100 \times \cos 45^{\circ}\\& = & 14400 + 10000 - 24000\times0.7071\\& = & 24400 - 16971\\& = & 7429\\ b & = & \textbf{86 cm}\\\end{array}\\\text{The corner pocket is $\large \boxed{\textbf{86 cm}}$ from where the cue originally struck the ball.}

Sergeeva-Olga [200]3 years ago
7 0

Answer:

  about 86 cm

Step-by-step explanation:

My understanding of the geometry is shown in the attached figure.

Since the angle of incidence is equal to the angle of reflection, the angle APP₂ will be 22.5°, and the vertical distance from the pocket P to the ball position B is ...

  (PA +AB')sin(22.5°) = 220sin(22.5°) ≈ 84.19 . . . . cm

The horizontal distance PB is

  (PA -AB)cos(22.5°) = 20cos(22.5°) ≈ 18.48 . . . . . cm

The distance PB is given by the distance formula ...

  PB = √(84.19² +18.48²) ≈ 86.19 . . . . cm

The ball was initially about 86 cm from the corner pocket.

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6 0
3 years ago
Can someone help with numbers 15 and 16
vichka [17]
15.

I had x before the movie.

x - 13.50 = 26.50

Add 13.50 to both sides of the equation:

x = 40

I had $40 before the movie.

16.

The original balance was x.

x - 161.15 = 423.28

Add 161.15 to both sides:

x = 584.43

The previous balance was $584.43
4 0
3 years ago
The coordinates of the endpoints of AB and CD are A(2,
Ratling [72]

Answer:

Option 1: CD is a perpendicular bisector of AB

Step-by-step explanation:

Let us find out the slopes of various line segments and the Distances and then we will draw the conclusions accordingly.

Formula to find slope

m= \frac{y_2-y_1}{x_2-x_1}

Formula to Find Distance between two points

D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

mAB ( represents , Slope of AB )

1. mAC= \frac{3-2}{2-5}=\frac{1}{-3}=-\frac{1}{3}

2. mBC=\frac{2-1}{5-8}=\frac{1}{-3}=-\frac{1}{3}

3. mCD=\frac{5-2}{6-5}=\frac{3}{1}=3

4. AC=\sqrt{(3-2)^2+(2-5)^2} =\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}

5. BC=\sqrt{(2-1)^2+(5-8)^2} =\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}

mAC = mBC  , and C is common point , hence these three are collinear points  making a straight line whole slope is -\frac{1}{3}

mAB=-\frac{1}{3}

mCD=3

mAB \times mCD = -\frac{1}{3} \times 3 = -1

Hence CD ⊥ AB

Also

From Point 4 and point 5 above , we see that

AC = CB

Hence CD bisect AB at C, also CD ⊥ AB

There fore

CD is a perpendicular bisector of AB

Therefor option 1 is true

4 0
3 years ago
Please help what is the volume of the rectangular prism
77julia77 [94]

Answer:

120

Step-by-step explanation:

to find the volume of rectangular prisms, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units. After doing that, you get 120

6 0
2 years ago
What is the length of if ?<br><br> 8 in.<br> 8.75 in.<br> 10.25 in.<br> 14 in.
Ket [755]

Answer:

A=8.75 in.

Step-by-step explanation:

Since ∆ HBA & ∆HKJ are similar,  

HB/HA = HK/HJ  

3/5.25 = 8/HJ  

3HJ/5.25 = 8  

3HJ = 42  

HJ = 14 in.

AJ = 14 - 5.25  

AJ = 8.75 in.

Therefore

A=8.75 in.

I hope this helped you.

5 0
3 years ago
Read 2 more answers
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