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2 years ago

WILL MAKE BRAINLIEST

Mathematics

1 answer:

Anuta_ua [19.1K]2 years ago

5 0

Straight line because it’s 180 degrees.

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A cold drink is poured out at 52°F. After 2 minutes of sitting in a 72°F room, its temperature has risen to 55°F. Find an equati

I am Lyosha [343]

Answer:

The model for the temperature of the drink can be written as

$T=72-20e^{-0.08t}$

Step-by-step explanation:

For a cold drink in a hotter room, we can say that the rate of change of temperature of the drink is proportional to the difference of temperature between the drink and the room.

We can model that in this way

$\frac{dT}{dt}=k*(T_r-T)$

If we rearrange and integrate

$\int\frac{dT}{(T-Tr)} =-k*\int dt\\\\ln(T-T_r)=-kt+C1\\\\T-T_r=Ce^{-kt}\\\\T=T_r+Ce^{-kt}$

We know that at time 0, the temperature of the drink was 52°F. Then we have:

$T=T_r+Ce^{-kt}\\\\52=72+Ce^0=72+C\\\\C=-20$

We also know that at t=2, T=55°F

$T=T_r+Ce^{-kt}\\\\55=72-20e^{-k*2}\\\\e^{-k*2}=(72-55)/20=0.85\\\\-2k=ln(0.85)=-0.1625\\\\k=0.08$

The model for the temperature of the drink can be written as

$T=72-20e^{-0.08t}$

7 0

3 years ago

Is this correct plz help me

Lina20 [59]

Answer: Yes!

Step-by-step explanation:

You correctly answered!

4 0

3 years ago

Use Cramer's Rule to solve the following system: –2x – 6y = –26 5x + 2y = 13

andriy [413]

$\bf \begin{cases}
-2x-6y&=-26\\
\quad 5x+2y&=13
\end{cases}\stackrel{\textit{determinant of the coefficients}}{D=
\begin{bmatrix}
-2&-6\\5&2
\end{bmatrix}}\implies (-4)-(-30)
\\\\\\
D=-4+30\implies \boxed{D=26}\\\\
-------------------------------\\\\$

$\bf x=\cfrac{D_x}{D}\implies x=\cfrac{
\begin{bmatrix}
\boxed{-26}&-6\\\\ \boxed{13}&2
\end{bmatrix}}{D}\implies x=\cfrac{(-52)-(-78)}{26}
\\\\\\
x=\cfrac{-52+78}{26}\implies x=\cfrac{26}{26}\implies \boxed{x=1}\\\\
-------------------------------\\\\
y=\cfrac{D_y}{D}\implies y=\cfrac{
\begin{bmatrix}
-2&\boxed{-26}\\\\ 5&\boxed{13}
\end{bmatrix}}{D}\implies y=\cfrac{(-26)-(-130)}{26}
\\\\\\
y=\cfrac{-26+130}{26}\implies y=\cfrac{104}{26}\implies \boxed{y=4}$

4 0

3 years ago

Help I do not know how do you do this ?

aliya0001 [1]

$m\angle LKJ=360-m\angle KJM-m\angle JML-m\angle MLK\\
m\angle LKJ=360-132-48-m\angle MLK\\
m\angle LKJ=180-m\angle MLK\\\\
m\angle MLK=180-m\angle KLN\\
m\angle MLK=180-150\\
m\angle MLK=30^{\circ}\\\\
m\angle LKJ=180-30\\
\boxed{m\angle LKJ=150^{\circ}}$

6 0

3 years ago

A function has a constant halving time. What type of function does this represent?

Anna71 [15]

The function which has a constant halving time is in the following form

$A(t) = A_{0} ( \frac{1}{2} )^ \frac{t}{h}$
Where: A₀ is the initial amount
 h is the half life time or the halving time.
 t is the time
 A(t) the amount that remains at time t

The previous function represents an Exponential decay function.


so, The correct answer is option B. Exponential decay

8 0

3 years ago

Read 2 more answers