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3 years ago

Create an equation which contains the solution (-1,3)

Mathematics

2 answers:

uranmaximum [27]3 years ago

7 0

An equation 6x-(-2)y=0 where x = -1 and y = 3

slavikrds [6]3 years ago

3 0

Answer:

3x + y =0

Step-by-step explanation:

We need to create equation whose solution is (-1,3) . So let another point through which it passes be ( 0,0) .

Since at least two points are required for making a line .

Slope :-

=> m = -1-0/3-0

=> m = -1/3

Using point slope form :-

=> ( x - x1) = m( y - y1)

=> ( x - (-1)) = -1/3( y - 3)

=> (x + 1 )3= -y + 3

=> 3x +3 = -y + 3

=> 3x + y = 0

✔️ Checking :- 

(-1,3)

=> 3(-1) + 3 = 0

=> -3+3=0

=> 0 = 0

<h3>• Hence the equation can be 3x + y = 0 .</h3>

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3 years ago

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3 years ago

Ben consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Ben's body decr

Airida [17]

Answer:

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

$A(t) = A(0)e^{-kt}$

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, $A(10) = 0.7278A(0)$ . We use this to find k.

$A(t) = A(0)e^{-kt}$

$0.7278A(0) = A(0)e^{-10k}$

$e^{-10k} = 0.7278$

$\ln{e^{-10k}} = \ln{0.7278}$

$-10k = \ln{0.7278}$

$k = -\frac{\ln{0.7278}}{10}$

$k = 0.03177289938
$

Then

$A(t) = A(0)e^{-0.03177289938t}$

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?

We have to find find A(5), as a function of A(0). So

$A(5) = A(0)e^{-0.03177289938*5}$

$A(5) = 0.8531$

The decay factor is:

1 - 0.8531 = 0.1469

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

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3 years ago