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frosja888 [35]
3 years ago
8

After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F.

Mathematics
1 answer:
laila [671]3 years ago
4 0

Answer:

  • Question 1: 0.081 min⁻¹
  • Question 2: 168ºF

Explanation:

The missing equation is:

             T=T_a+(T_0-T_a)e^{-kt}

You are given:

  • Ta = the temperature surrounding the object = 73ºF
  • T₀ = the initial temperature of the object = 204ºF
  • t = 2.5 min
  • T after 2.5 min = 180ºF

Question 1: Find the the value of k.

Substitute the data into the equation and solve for k:

          180\º=73\º+(204\º-73\º)e^{-k\cdot 2.5min}\\ \\ 107\º=131\ºe^{-k\cdot 2.5min}\\\\-k\cdot 2.5min=\ln (107/131)\\\\k=0.081min^{-1}

Question 2: Find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.

Subsititute into the formula and compute:

            T=73\ºF+(204\ºF-73\ºF)e^{-0.081min^{-1}\times 4min}\\ \\ T=73\ºF+(131\ºF)(0.72325024)\\\\T=168\ºF

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sveticcg [70]
We have that

1)<span>Circle W has center (−3, 0) and radius 8
the equation of a circle W is
(x+3)</span>²+(y)²=8²

2)<span>Circle V is a translation of circle W, 2 units down.
the center of circle V--------> (-3,0-2)---------> (-3,-2)

3)</span><span>Circle V is a dilation of circle W with a scale factor of 2.
then the radius circle V is 8*2------> 16 units
</span>the equation of a circle V is
(x+3)²+(y+2)²=16²

therefore

 case <span>A. Circle V and circle W are similar.---------> is correct
</span>because  I can transform circle V to circle W using only translations, rotations and scaling  (In the case of circles, no rotations are necessary).

case <span>B. Circle V and circle W have the same center.-------> is not correct

case </span><span>C. The radius of circle V is 16.-----------> is correct

case </span><span>D. The center of circle V is (−5, 0).----------> is not correct


the answer is
</span> case A. Circle V and circle W are similar.---------> is correct
 case C. The radius of circle V is 16.-----------> is correct
3 0
3 years ago
12.6% of<br>RI 149 390bn​
galina1969 [7]

Answer: RI 18,823.14

Step-by-step explanation:

I guess that we want to find the 12.6% of Rl 149,390

First, we assume that Rl 149,390 is the 100%

Then we can write an equation like:

Rl 149,390 = 100%

Then if the amount X is the 12.6%, we also have the equation:

X = 12.6%

Then we have the two equations:

X = 12.6%

Rl 149,390 = 100%

If we take the quotient between these two equations we get:

(X/Rl 149,390) = (12.6%/100%)

Solving this for X we get:

X =  (12.6%/100%)*(Rl 149,390) = RI 18,823.14

7 0
3 years ago
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galina1969 [7]
Your question is very vague, there is no multiple choice answers, your question lacks basically everything.

-2+(-2=4?
3 0
3 years ago
A distance AB is observed repeatedly using the same equipment and procedures, and the results, in meters, are listed below: 67.4
skad [1K]

Answer:

a) \bar X =\frac{67.401+67.400+67.402+67.396+67.406+67.401+67.396+67.401+67.405+67.404}{10}=67.401

b) The sample deviation is calculated from the following formula:

s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

And for this case after replace the values and with the sample mean already calculated we got:

s=0.0036

If we assume that the data represent a population then the standard deviation would be given by:

\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}

And then the deviation would be:

\sigma =0.00319

Step-by-step explanation:

For this case we have the following dataset:

67.401, 67.400, 67.402, 67.396, 67.406, 67.401, 67.396, 67.401, 67.405, and 67.404

Part a: Determine the most probable value.

For this case the most probably value would be the sample mean given by this formula:

\bar X =\frac{\sum_{i=1}^n X_i}{n}

And if we replace we got:

\bar X =\frac{67.401+67.400+67.402+67.396+67.406+67.401+67.396+67.401+67.405+67.404}{10}=67.401

Part b: Determine the standard deviation

The sample deviation is calculated from the following formula:

s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

And for this case after replace the values and with the sample mean already calculated we got:

s=0.0036

If we assume that the data represent a population then the standard deviation would be given by:

\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}

And then the deviation would be:

\sigma =0.00319

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valina [46]
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