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Kay [80]
3 years ago
9

This year I caught 30 fish, which is 6 more than twice the number I caught last year. How many did I catch last year

Mathematics
1 answer:
Aliun [14]3 years ago
7 0
30 = 6 + 2x
x = 12 fish caught last year
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A group of rowdy teenagers near a wind turbine decide to place a pair of
Marrrta [24]

Answer:

a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is y = 9 + 7* sin(\pi * t / 15 - \pi  / 6)

b) Hence the height of the shorts at exactly t = 10 minutes, to

the nearest tenth of a meter is 5.5 meters

Step-by-step explanation:

a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :

x^2 + (y-yc)^2 = R^2 ,

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R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)

= 14 m / 2

= 7 m (radius of the circle)

Also, center of the circle will be at (0, 2 + R) i.e (0,9)

So,  is the trajectory path equation to the circle

Let x = 7* cos(w*t + \phi ) & y = 9 + 7* sin(w* t + \phi) be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t  

At t= 10s, y = 16 m so we have,

9 + 7 * sin(10* w + \phi) = 16 ---------------(1)

Also, at t= 25s, y =2 m so we have,

9 + 7* sin(25 * w +\phi) = 2--------------(2)

Solving we have, 10* w + \phi = \pi/2 & 25*w + \phi = 3*pi/2

15* w = \pi\\\\w = \pi/15 & \phi = \pi/2 - 10*\pi/15 = -\pi / 6  

Therefore y = 9 + 7* sin(\pi * t / 15 - \pi  / 6) is the instantaneous height of the pink short at time t ( in seconds)

b) At t= 10minutes = 10 * 60 s = 600s, we have,

y = 9 + 7 * sin(\pi * 600/15 - \pi / 6)\\\\= 9 + 7 * sin(40* \pi - \pi / 6)

= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)

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3 years ago
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aliya0001 [1]

Answer:

<u>They are perpendicular</u>

Step-by-step explanation:

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Parallel lines have the same slope.

Neither is when the lines do not follow either of these definitions.

The slope of your two lines are -3/2 and 2/3. These slopes are flipped and the opposite negations of each other. <u>This means the lines are perpendicular.</u>

<u />

4 0
3 years ago
Ricardo drove 15 miles in 20 minutes. What was his average rate in miles per hour?<br> (number form)
Rudiy27

Answer:3/4 miles per hour

Step-by-step explanation:

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faust18 [17]

Answer:

read step by step

Step-by-step explanation:

.10×55.86 = 5.58

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Describe a sequence of transformations that takes trapezoid A to trapezoid B
marin [14]

Answer:

How do you describe the sequence of transformations?

Image result for Describe a sequence of transformations that takes trapezoid A to trapezoid B

When two or more transformations are combined to form a new transformation, the result is called a sequence of transformations, or a composition of transformations. Remember, that in a composition, one transformation produces an image upon which the other transformation is then performed.

Step-by-step explanation:

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