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2 years ago

Help please!!!!

Mathematics

1 answer:

shusha [124]2 years ago

7 0

Dead deceased no words hahahahhahha and the first answer has me dead :’))))

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In a previous exercise we formulated a model for learning in the form of the differential equation dp dt = k(m − p) where p(t) m

DaniilM [7]

I assume you mean

$\dfrac{dP}{dt} = k(M-P)$

ANSWER
An expression for P(t) is

$P = M - Me^{-kt}$

EXPLANATION
This is a separable differential equation. Treat M and k as constants. Then we can divide both sides by M - P to get the P term with the differential dP and multiply both sides by dt to separate dt from the P terms

$\begin{aligned} \dfrac{dP}{dt} &= k(M-P) \\ \dfrac{dP}{M-P} &= k\, dt
\end{aligned}$

Integrate both sides of the equation.

$\begin{aligned}
\int \dfrac{dP}{M-P} &= \int k\, dt \\
-\ln|M-P| &= kt + C \\
\ln|M-P| &= -kt - C\end{aligned}$

Note that for the left-hand side, u-substitution gives us

$u = M - P \implies du = -1dP \implies dP = -du$

hence why $\int \frac{dP}{M-P} \ne \ln|M - P|$

Now we use the definition of the logarithm to convert into exponential form.

The definition is

$\ln(a) = b \iff \log_e(a) = b \iff e^b = a$

so applying it here, we get

$\begin{aligned} \ln|M-P| &= -kt - C \\ |M - P| &= e^{-kt - C} \\ 
M - P &= \pm e^{-kt - C} 
 \end{aligned}$

Exponent properties can be used to address the constant C. We use $x^{a} \cdot x^{b} = x^{a+b}$ here:

$\begin{aligned}
 M - P &= \pm e^{-kt - C} \\
M - P &= \pm e^{- C - kt} \\ 
M - P &= \pm e^{- C + (- kt)} \\ 
M - P &= \pm e^{- C} \cdot e^{- kt} \\ 
M - P &= Ke^{- kt} && (\text{\footnotesize Let $K = \pm e^{-kt}$ }) \\ 
M &= Ke^{- kt} + P\\
P &= M - Ke^{- kt}
\end{aligned}$

If we assume that P(0) = 0, then set t = 0 and P = 0

$\begin{aligned} 
0 &= M - Ke^{- k\cdot 0} \\
0 &= M - K \cdot 1 \\
M &= K
 \end{aligned}
$

Substituting into our original equation, we get our final answer of

$P = M - Me^{-kt}$

6 0

3 years ago

Read 2 more answers

Please help me solve this probe

allsm [11]

Since it wants total to brown you have to do the ratio in that order.
There are a total of 8 puppies of which two are brown.
T:B
8:2 reduces to 4:1

4 0

3 years ago

NOMBRE RELATIFS,NOMBRES POSITIFS ET NEGATIFS:DESSINER UN THERMOMETRE GRADUE ET PLACER LES VILLES SUR LEUR TEMPERATURE

hichkok12 [17]

Answer:

C'est une personne anglaise traduite en français, je ne peux rien dessiner, je n'ai pas d'outil de dessin, désolé mec

Step-by-step explanation:

8 0

2 years ago

Tommy has a pet monkey. Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana th

scoundrel [369]

Y = 4 + 2x

This equation shows that y, the number of fruit the monkey eats, is equal to 4 apples plus 2 times the amount of bananas Tommy eats.

Hope this helps!

8 0

3 years ago

Find the value of x.

andrey2020 [161]

Answer:

x = 4

Step-by-step explanation:

The angle next to (adjacent to) 19x + 3 is 180 degrees less (19x + 3):

180 - (19x + 3)

and the three interior angles of the triangle must sum up to 180 degrees:

11x - 2 + 180 - 19x - 3 + 9x + 1 = 180, or

11x - 2 - 19x - 3 + 9x + 1 = 0

Combining like terms, we get:

x = 4

4 0

3 years ago