Find the percent of this number: 32% of 25 pages<br><br> Would it be 8% or 32%?

A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the

Vedmedyk [2.9K]

(a) Using Newton's Law of Cooling, $\dfrac{dT}{dt} = k(T - T_s)$ , we have $\dfrac{dT}{dt} = k(T - 75)$ where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get $\dfrac{dT}{T - 75} = k dt$ . Integrate both sides to get $\ln|T - 75| = kt + C$ .

Since $T(0) = 185$ , we solve for C:
$|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110$
So we get $\ln|T - 75| = kt + \ln 110$ . Use T(30) = 150 to solve for k:
$\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)$

So

$\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t} \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}$

But choose Positive because T > 75. Temp of turkey can't go under.

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)} = 136.929 \approx 137{}^{\circ}F$

(b)

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30} \\
100 = 75 + 110(15/22)^{t/30} \\
25 = 110(15/22)^{t/30} 
\frac{25}{110} = (15/22)^{t/30} \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22) \approx 116\ \mathrm{min}$

Dogs of the AMS.

4 0

3 years ago

E=I(R+r) solve for R

svetlana [45]

Divide I from both sides then subtract r from both sides, too so in the end:

R= (E-r)/I

8 0

3 years ago

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Solve by addition method <br>3x+y=8 <br>2x-y=7

Vinil7 [7]

Answer:

(3,-1)

Step-by-step explanation:

So we have the system of equations:

$3x+y=8\\2x-y=7$

As directed, add straight down. The y-variable will cancel:

$5x=15$

Now, divide both sides by 5. The left cancels:

$x=3$

So x is 3.

Now, substitute 3 for x in either of the equations:

$3x+y=8$

Substitute 3 for x:

$3(3)+y=8$

Multiply:

$9+y=8$

Subtract 9 from both sides:

$y=-1$

So, our answer is: x=3, y=-1 or (3,-1).

And we are done :)

7 0

3 years ago

Which of the following statements is true only if triangles EFI and GFH are similar?

Cerrena [4.2K]

Answer:

C.

Lines EI and HG are parallel

plz like and vote 5 star if answer is correct, if not still do it as it might help someone somehow

5 0

3 years ago

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The length of a pen is 5 more than its width.The perimeter is 26 m.Find the length and the width.

meriva

P=2l+2w

Since it is given that P=26m, length is 5 more than its width (w+5), we'll work it out in the perimeter formula.

26=2(w+5)+2w
26=2w+10+2w
26=4w+10
4w=26-10
4w=16
w=4

Thus the width is 4m. Let's find the length.

l=w+5
l=4+5
l=9

The length of a pen is 9m.

4 0

3 years ago

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Find the percent of this number: 32% of 25 pages Would it be 8% or 32%?