Step-by-step explanation:
first step while implementing the elimination method is to look at the numbers which can be multiplied to which in order to have like terms as solved below
as you can see in equation number 2 that the number three can be multiplied with equation 1 in order to have like terms so you can cancel them out
so , multiply 3 with the whole of equation 1
3( 2x + y = -4 )
= 6x + 3y = -12
( keep in mind the sign of the number)
5x -3 y = 1
now ,
we have
6x + 3y = -12
5x -3y = 1
as you can see that now we have like terms and when we add both these equations the like terms cancel out each other as they have opposite signs ( + - gives you - )
so , once you add the like terms this is what you will get
6x + 5x +3y-3y -12+1
= 11x + 0 - 11
then you can simplify this further for x first
11x = 11
x = 11/11
<u>x </u><u>=</u><u> </u><u>1</u>
now we have the value of x let's simply further for y
let's take equation 2
5(1) - 3y =1
5 -3y = 1
5-1 = 3y
4 = 3y
<u>4</u><u>/</u><u>3</u><u> </u><u>=</u><u> </u><u>y </u>
to confirm your values you can put these values in one of the two equations given initially , let's use equation two to check .
5x-3y = 1
( now let's place the values of x and y into the equation and see if our answer is 1 )
5 (1) - 3 (4/3)
= 5 - 4
= 1
it is correct
6x-2 is -12
you are just timing -2 6 times
Newton's Law of Cooling
Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.
200=68+(210-68)e^(-10k)
132=142e^(-10k)
132/142=e^(-10k)
ln(132/142)=-10k
k=-ln(132/142)/10
k≈0.0073 so
T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?
180=68+142e^(-0.0073t)
112=142e^(-0.0073t)
112/142=e^(-0.0073t)
ln(112/142)=-0.0073t
t= -ln(112/142)/(0.0073)
t≈32.51 minutes
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Step-by-step explanation:
