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3 years ago

Help will fine brainliest!!! The

Mathematics

1 answer:

mihalych1998 [28]3 years ago

6 0

Hey there!

You can plug this into the slope equation to find the slope.

m= (y2-y1)/(x2-x1)

Plug in two points. I chose (0,4) and (1,7).

m= (7-4)/(1-0)

m= (3)/(1)

m= 3

3 is your answer.

I hope this helps!

~kaikers

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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

2) How can 4(3 + 8) be rewritten using the distributive property?

Lena [83]

1. 4(3 + 8)
= (4 * 3) + (4 * 8)
= 12 + 32
= 44
So, the answer to this question is the third option.
Glad I could help and have a fantastic day!
Also, can you please mark my answer as the brainliest answer?
Thanks.

8 0

3 years ago

In a Punkin’ Chunkin’ contest, the height (in feet)

Nikolay [14]

a. At t=0, the pumpkin is 25 feet above the ground (Plug 0 into the equation and solve)

b. If you plug the equation in a graphing calculator and find the rightmost zero, you get t = 10.15 seconds.

c. The vertex (maximum point) of the graph is (5, 425). Therefore, the pumpkin reaches its maximum height of 425 feet after 5 seconds in the air.

5 0

3 years ago

What system of equations does not have the same solution

Effectus [21]

Answer:

2x + y = 4

4x + 2y = 12

Step-by-step explanation:

Equations 2x + y = 4 & 4x + 2y = 12 haven't the same solution.

$2x + y = 4...(1) \\ 4x + 2y = 12 \\ 2(2x + y) = 12 \\ 2x + y = \frac{12}{2} \\ 2x + y = 6...(2) \\ rhs \: of \: equations \: (1) \: and \: (2) \: are \: \\ not \: sme.$

3 0

3 years ago

For this graph, mark the statements that are true.

Gelneren [198K]

Answer:

C and D

Step-by-step explanation:

Given is the graph of the function with no restrictions.

The domain and range are all real numbers.

Correct options are C and D

4 0

3 years ago

Read 2 more answers