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kondaur [170]
3 years ago
11

Find the solution set. |x| = -16 { } {-4, 4} {-16, 16} {-32, 32}

Mathematics
2 answers:
Otrada [13]3 years ago
7 0
This an { } solution  because the absolute value is always a positive number unless there is a negative sign in front of the brackets.  

hope this helps :)

Alchen [17]3 years ago
5 0
|x| = -16 is equivalent to
x = 16 and
-x = 16
so x = 16 and -16
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Answer:

The student's GPA is of 0.82.

Step-by-step explanation:

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To find the student's GPA, we find his weighed mean.

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M = \frac{7*3 + 6*1 + 20*0}{7+6+20} = 0.82

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Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =
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Answer:  The required solution is y=50e^{0.1386t}.

Step-by-step explanation:

We are given to solve the following differential equation :

\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

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From equation (i), we have

\dfrac{dy}{y}=kdt.

Integrating both sides, we get

\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]

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y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.

Thus, the required solution is y=50e^{0.1386t}.

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