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2 years ago

Solve for the value of x and y when 3x+2y=24 , x+y=9 step wise explanation plz

Mathematics

2 answers:

OLga [1]2 years ago

6 0

Answer:

{x,y} = {2,9}

Step-by-step explanation:

Solve equation [2] for the variable y

[2] 2y = -6x + 30

[2] y = -3x + 15

// Plug this in for variable y in equation [1]

[1] 3x + 2•(-3x+15) = 24

[1] -3x = -6

// Solve equation [1] for the variable x

[1] 3x = 6

[1] x = 2

// By now we know this much :

x = 2

y = -3x+15

// Use the x value to solve for y

y = -3(2)+15 = 9

grigory [225]2 years ago

4 0

This is what I got. Tell me if I got it wrong.

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3 years ago

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enyata [817]

Answer:

x=2, x=1

Step-by-step explanation:

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2 years ago

Let θ

konstantin123 [22]

Answer:

θ is decreasing at the rate of $\frac{21}{16}$ units/sec

or $\frac{d}{dt}$ (θ) = $\frac{-21}{16}$

Step-by-step explanation:

Given :

Length of side opposite to angle θ is y

Length of side adjacent to angle θ is x

θ is part of a right angle triangle

At this instant,

x = 8 , $\frac{dx}{dt}$ = 7

( $\frac{dx}{dt}$ denotes the rate of change of x with respect to time)

y = 8 , $\frac{dy}{dt}$ = -14

( The negative sign denotes the decreasing rate of change )

Here because it is a right angle triangle,

tanθ = $\frac{y}{x}$ -------------------------------------------------------------------1

At this instant,

tanθ = $\frac{8}{8}$ = 1

Therefore θ = π/4

We differentiate equation (1) with respect to time in order to obtain the rate of change of θ or $\frac{d}{dt}$ (θ)

$\frac{d}{dt}$ (tanθ) = $\frac{d}{dt}$ (y/x)

( Applying chain rule of differentiation for R.H.S as y*1/x)

$sec^{2}$ θ $\frac{d}{dt}$ (θ) = $\frac{1}{x}$ $\frac{dy}{dt}$ - $\frac{y}{x*x}$ $\frac{dx}{dt}$ -----------------------2

Substituting the values of x , y , $\frac{dx}{dt}$ , $\frac{dy}{dt}$ , θ at that instant in equation (2)

2 $\frac{d}{dt}$ (θ) = $\frac{1}{8}$ *(-14)- $\frac{8}{8*8}$ *7

$\frac{d}{dt}$ (θ) = $\frac{-21}{16}$

Therefore θ is decreasing at the rate of $\frac{21}{16}$ units/sec

or $\frac{d}{dt}$ (θ) = $\frac{-21}{16}$

3 0

3 years ago