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Aleonysh [2.5K]
3 years ago
14

A hot bowl of soup cools according to Newtons law of cooling. Its temperature (in degrees Fahrenheit) at time t is given by T(t)

= 68+144e^-0.04t, where t is given in minutes. Answer these questions What was the initial temperature of the soup? What was the temperature of the soup after 15 minutes? How long after serving is the soup 125 degrees Fahrenheit?
Mathematics
1 answer:
nata0808 [166]3 years ago
4 0
212°F
147°F
23.2 min

1) Initial temperature for t=0
T(0)=68+144e^(0)=68+144=212°F
2) After 15 min
T(15)=68+144e^(-0.04*15)=68+144e^(-0.6)=147°F
3) 125°F -> t=?
125=68+144e^(-0.04t)
144e^(-0.04t)=125-68=57
e^(-0.04t)=57/144=0.4 you can apply ln on both sides:
-0.04t=ln(0.4) solving you get t=23.3 min


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worty [1.4K]

Answer:

14 groups

Step-by-step explanation:

Given

Groupings = \frac{1}{2}\ day

Duration = 1\ week

Required

Determine the number of group in the week

To do this, we simply divide the duration by the number half day group.

This gives:

Group = \frac{Duration}{Groupings}

Group = \frac{1\ week}{1/2\ days}

Convert week to days

Group = \frac{7\ days}{1/2\ days}

Group = \frac{7}{1/2}

Group = 7 / \frac{1}{2}

Convert to multiplication

Group = 7 * \frac{2}{1}

Group = \frac{14}{1}

Group = 14

<em>Hence, there are 14 groups</em>

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3 years ago
What is the value of z?
VashaNatasha [74]

Answer:

z = 61

Step-by-step explanation:

The exterior angle is congruent (equal to) the sum of the 2 farthest angles from it, so you can set the equation like this:

z + z - 11 = z + 50

Add like terms, which would be the 2 "z's" on the left side:

2z - 11 = z + 50

Then subtract the z on the right side from both sides:

2z - 11 = z + 50

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Add 11 to both sides:

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When 12 is added to a number the result is 32 less than 3 times the number.
sdas [7]


Let the number = x

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4 0
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DerKrebs [107]

The value of n is 11.

<u>Step-by-step explanation</u>:

The given expression is (n-9) ÷ 10 = -2

<u>To find the value of n</u> :

  • From the expression, it is determined that (n-9) is the numerator and 10 is the denominator.
  • Cross multiply the denominator in the left side of the expression to the another side.

The expression becomes (n-9) = (10\times -2).

⇒ n-9 = -20

Keep the n term on one side and the constants on other side.

⇒ n = -20+9

⇒ n = -11

Therefore, the value of n is 11.

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