What is 4.1 in fraction form

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

4 years ago

How to do the monomials

Cerrena [4.2K]

<u>Given</u>:

The given monomial expression is $\frac{16 y^{8}}{4 y^{2}}$

We need to simplify the given monomial expression.

<u>Simplification:</u>

Let us simplify the given expression.

Dividing the numbers 16 and 4, we get;

$\frac{4 y^{8}}{y^{2}}$

Let us apply the exponent rule $\frac{x^{a}}{x^{b}}=x^{a-b}$ in the above expression.

Thus, we get;

$4 y^{8-2}$

Subtracting the numbers in the numerator of the above expression, we get;

$4 y^{6}$

Thus, the simplified expression is $4 y^{6}$

8 0

3 years ago

Some farms use a hay elevator to move bales of hay to the second story of a barn loft. The bottom of the elevator is 9 meters fr

-Dominant- [34]

Answer: The height is 6.07 meters

Step-by-step Explanation: The distance between the elevator and the bottom of the barn is given as 9 meters. Also for the hay elevator to move bales of hay to the second story of the barn lift it makes an angle of elevation of 34 degrees with the ground. With these we can derive a right angled triangle with the reference angle as 34 degrees, the side facing it which is the height or h (opposite) is yet unknown, and the side between the reference angle and the right angle (adjacent) is 9. We shall apply the trigonometric ratio as follows;

Tan 34 = opposite/adjacent

Tan 34 = h/9

0.6745 = h/9

0.6745 x 9 = h

6.0705 = h

Therefore the approximate height of the barn to the ground is 6.07 meters

3 0

3 years ago

Read 2 more answers

PLEASE I NEED HELP

klemol [59]

Answer: 0.25 feet

Step-by-step explanation:

Given: Jonathon has paper strips that are all equal in length.

Let x be the length of each paper strip.

Since John lines them up end to end, the length of the line of paper strips= 3 feet

Also total strips used= 12

Therefore, length of line of strips= $12x=3\ feet$

$\\\Rightarrow\ x=\frac{1}{4}\ feet\\\Rightarrow\ x= 0.25\ feet$

hence, if Jonathan is correct then the length of each strip will be 0.25 feet.

8 0

3 years ago

What does 4 3/10 equal

Dmitriy789 [7]

Using your talking about putting it into an improper fraction. it would be 43/10.

7 0

3 years ago