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3 years ago

State whether the system is consistent and independent, consistent and dependent or inconsistent.

Mathematics

2 answers:

user100 [1]3 years ago

7 0

Answer:

The correct option is 1.

Step-by-step explanation:

Inconsistent system: If the given system has no solutions, then it is an inconsistent system.

Consistent and independent system: If the given system has only one solutions, then it is an consistent and independent system.

Consistent and dependent system: If the given system has many solutions, then it is an consistent and dependent system.

The given equations are

$x+3y=18$ .... (1)

$-x+2y=7$ ..... (2)

Add both equations.

$x+3y-x+2y=18+7$

$5y=25$

$y=5$

Substitute this value in equation (1).

$x+3(5)=18$

$x+15=18$

$x=3$

The system of equations has only one solution, i.e.,(3,5).

Therefore the given system is consistent and independent. Option 1 is correct.

Archy [21]3 years ago

4 0

Answer:

Given system is consistent and independent.

Step-by-step explanation:

We have given two equations.

x+3y = 18 eq(1)

-x+2y = 7 eq(2)

We have to find whether the system is consistent, inconsistent and dependent or independent.

Consistent system has at least one solution.

Inconsistent system has no solution.

Dependent solution has identical lines.

Independent systems has different lines.

We use method of elimination to solve this.

Adding -3y to both sides of eq(1), we have

x+3y-3y = 18-3y

x = 18-3y eq(3)

put eq(3) into eq(2), we have

-(18-3y)+2y = 7

-18+3y+2y = 7

adding 18 to both sides of above equation , we have

18-18+3y+2y = 18+7

Adding like terms , we have

5y = 25

y = 5

Putting the value of y in eq(3), we have

x = 18-3(5)

x = 18-15

x = 3

Hence , the solution set is (3,5).

So, given system is consistent .

Their graphs are not same.so , their are independent.

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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

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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)

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