The solutions to the inequality y s 2x

A metal beam was brought from the outside cold into a machine shop where the temperature was held at 65degreesF. After 5 min, t

ivolga24 [154]

Answer:

The beam initial temperature is 5 °F.

Step-by-step explanation:

If T(t) is the temperature of the beam after t minutes, then we know, by Newton’s Law of Cooling, that

$T(t)=T_a+(T_0-T_a)e^{-kt}$

where $T_a$ is the ambient temperature, $T_0$ is the initial temperature, $t$ is the time and $k$ is a constant yet to be determined.

The goal is to determine the initial temperature of the beam, which is to say $T_0$

We know that the ambient temperature is $T_a=65$ , so

$T(t)=65+(T_0-65)e^{-kt}$

We also know that when $t=5 \:min$ the temperature is $T(5)=35$ and when $t=10 \:min$ the temperature is $T(10)=50$ which gives:

$T(5)=65+(T_0-65)e^{k5}\\35=65+(T_0-65)e^{-k5}$

$T(10)=65+(T_0-65)e^{k10}\\50=65+(T_0-65)e^{-k10}$

Rearranging,

$35=65+(T_0-65)e^{-k5}\\35-65=(T_0-65)e^{-k5}\\-30=(T_0-65)e^{-k5}$

$50=65+(T_0-65)e^{-k10}\\50-65=(T_0-65)e^{-k10}\\-15=(T_0-65)e^{-k10}$

If we divide these two equations we get

$\frac{-30}{-15}=\frac{(T_0-65)e^{-k5}}{(T_0-65)e^{-k10}}$

$\frac{-30}{-15}=\frac{e^{-k5}}{e^{-k10}}\\2=e^{5k}\\\ln \left(2\right)=\ln \left(e^{5k}\right)\\\ln \left(2\right)=5k\ln \left(e\right)\\\ln \left(2\right)=5k\\k=\frac{\ln \left(2\right)}{5}$

Now, that we know the value of $k$ we can use it to find the initial temperature of the beam,

$35=65+(T_0-65)e^{-(\frac{\ln \left(2\right)}{5})5}\\\\65+\left(T_0-65\right)e^{-\left(\frac{\ln \left(2\right)}{5}\right)\cdot \:5}=35\\\\65+\frac{T_0-65}{e^{\ln \left(2\right)}}=35\\\\\frac{T_0-65}{e^{\ln \left(2\right)}}=-30\\\\\frac{\left(T_0-65\right)e^{\ln \left(2\right)}}{e^{\ln \left(2\right)}}=\left(-30\right)e^{\ln \left(2\right)}\\\\T_0=5$

so the beam started out at 5 °F.

6 0

4 years ago

What is an equation

8_murik_8 [283]

A mathematical equation is an expression containing at least one variable and an equals sign with a mathematical expression on each side of it.

5 0

3 years ago

Read 2 more answers

pickupchik [31]

Answer:

7%

Step-by-step explanation:

31 + 371 + 21 = 423

31/423 = 7%

8 0

2 years ago

Kallie has $45.50 saved towards a new bike. If the bike costs $184.76 including tax, how much d

alexandr1967 [171]

Answer:

Please read the step by step.

Step-by-step explanation:

184.76 - 45.50 = 139.26.|

If she wants to buy it in six weeks and only needs $139.26 you would need to divide $139.26 by 6 to see how much money she would have to make per week to meet the mark.

$139.26 divided by 6 is $26.21

Therefore Kallie would need to make $26.21 per week to reach her goal.

Looking at the equations none of the provided answers would even come close to the answer above.

1. 139.26 - 6 is not saying if it is a 6.00 or a 0.06 so it could be 133.26 or 139.20 but that wouldn't make any since involving the question.

2. 6 multiplied by 139.26 would be 835.56 but no where was it asked to multiply.

3. 139.6 - 8 isn't even brought up in the question above.

4. 45.50 x 6 is 273 and that would be too much unless tax is unreasonably high but even then it didn't mention what the tax would be. (it would be 47.76% on the dot btw)

In that case your closest bet would have to be 6x45.50 but your teacher is kind of insane to think a middle schooler should have to figure out how much a ungodly sales tax would be out of all of this.

Good luck on your assignment, I am here if you need anything else.

4 0

4 years ago

Which equation could be used to find the area in square centimeters of. a radius of 26 centimeters

Masja [62]

I'm assuming you're talking about the area of a square, which is $\pi r$ ².
Plug in the radius, 26 cm, for r.
$\pi 26$ ² <<equation

If you want the answer, $\pi 26$ ² = 2,123.7 cm²

4 0

4 years ago

The solutions to the inequality y s 2x - 4 are shaded on