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vichka [17]
3 years ago
14

Given AABC with coordinates A(-4,-2), B(-1,1) and C (-2,3)

Mathematics
1 answer:
Margarita [4]3 years ago
7 0

Answer: 15

15-15 = 0

10-10=0

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Answer:the number of gallons of water left is 3.5

Step-by-step explanation:

The initial amount of water in the container is 4 3/8 gallons. Converting 4 3/8 gallons to improper fraction, it becomes 35/8 gallons of water.

A hole in the container causes 7/8 gallon to leak out. The number of gallons of water left in the container would be

Initial amount - amount that leaked. It becomes

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The y intercept is 2.25 and x intercept is -3
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Step-by-step explanation:

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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 ,

where  

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)

5 0
2 years ago
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