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rodikova [14]
3 years ago
6

X/3 +2y/3= -1 and x-y/3=9 solve. by elimination method​

Mathematics
1 answer:
Galina-37 [17]3 years ago
8 0

Answer:

X=51/7, Y= -36/7

Step-by-step explanation:

X/3 + 2y/3 = -1 equ 1

X - y/3 = 9 equ 2

eliminate X/3.

X/3 + 2y/3 = -1..... x 1 ( co-efficient of X in equ2 )

X - y/3 = 9 ...... x 1/3 ( co-efficient of X in equ1 )

X/3 + 2y/3 = - 1 equ 3

-

X/3 - y/9 = 3 equ 4

0 + 7y/9 = -4

y = -36/7

( input the value of y into equ 4 )

X/3 -y/9 = 3

X/3 - (-36/7)/9 = 3

X/3 + 36/63 = 3

X/3 = 3 - 36/63

X/3 = 153/63

63X = 459

X = 459/63

X = 51/7.

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Answer:

Step-by-step explanation:

The rate of change of temperature of the coffee with respect to time is expressed by the differential equation

dT/dt=k(T−A) when k = -1 and A = 23. The equation will become:

dT/dt = -(T-23)

If the coffee cools at the rate of 1°C per minute, then dT/dt = -1 and T = 70

Substituting into the equation:

-1 = k(70-23)

-1 = 47k

k = -1/47

k = -0.0213

Substituting k = -0.0213 into the original equation, the differential equation will be:

dT/dt=k(T−A)

dT/dt = -0.0213(T-23)

dT/dt = -0.0213T+0.489

To get the value of T, we will use variable separable method

dt = dT/-0.0213T+0.489

Integrate both sides

t = -0.0213ln(-0.0213T+0.489)

At t = 1 minute

1 = -0.0213ln(-0.0213T+0.489)

1/-0.0213 = ln(-0.0213T+0.489)

-46.95 = ln(-0.0213T+0.489)

Apply exp to both sides

e^-46.95 = e^ln(-0.0213T+0.489)

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-0.0213T = 4.073×10^-21-0.489

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Answer:

The APR at which the money is borrowed, is approximately 651.79%

Step-by-step explanation:

The amount which one wishes to borrow for two weeks, P = $600

The amount of interest that one must pay back = $25 per $100 borrowed

Therefore;

The total interest on the $600 loan (borrowed) for two weeks = 25/100× $600 = $150

The number of days for which the amount was borrowed = 2 weeks = 14 days

The Annual Percentage Rate, APR is given as follows;

APR = \left (\dfrac{\left (\dfrac{Interest \ Paid \ for \ the  \ Loan \ duration}{The \ amount \ borrowed} \right )}{The \ number \ of \ days \ the \ amount \ was  \ borrowed } \right ) \times 365 \times 100

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