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2 years ago

The sum of two numbers is 37 and the difference is 9. What are the numbers

Mathematics

1 answer:

solmaris [256]2 years ago

7 0

Answer:

23 and 14

Step-by-step explanation:

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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

A shirt is on sale for 30% off the original price of $85.00.

wlad13 [49]

Answer:

59.5

Step-by-step explanation:

30% of 85 is 25.5

85-25.5=59.5

5 0

2 years ago

What is reciprocal of the fraction in the equation 3/5(2x+8)=18?

Katen [24]

Answer:

5/3

Step-by-step explanation:

The reciprocal is the fraction upside down.

3 0

2 years ago

Which fractions are greater than 1/2 Check all that apply. 1/8 10/12 15/16 3/12 13/16

marishachu [46]

Answer:

10/12

15/16

13/16

Step-by-step explanation:

each time you divide each of these they are over .5 or 50%

7 0

3 years ago

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Type the missing number to complete the porportion

Nataliya [291]

34 x 2 = 17 x 4

answer = 4

6 0

3 years ago

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