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Elis [28]
3 years ago
13

A baker records the internal temperature of a pie that has been left out on the counter. The room temperature is 14 Celsius. An

equation that models this situation is T (t) =68 (0.5)^r/10 where T is the temperature in degrees Celsius and t is the time in minutes. Determine the temperature to the nearest degree,of the pie after 15
minutes. How much time did it take for the pie to reach an internal temperature of 31°C?
Mathematics
1 answer:
maksim [4K]3 years ago
5 0
Assume r= t  not sure if you mistyped this.
t =  15 min

T(t)  = 68 (0.5)^(15/10) = 24 Celsius

31 = (0.5)^(t/10) take ln

ln31 = (t/10) ln (0.5) + ln68

t = (ln32 - ln 68/ln0.5) * 10 = 11.3 min 


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The sum of a 3 digit number and a 1 digit number is 217. The product of the numbers is 642. If one number is between 200 and 225
algol [13]
Let, the numbers be "x" and "y". Consider "x" as the triple digit number.
Now, according to the question,
x + y = 217..........................equation (1)

x * y = 642............................equation (2)

Now,
Taking equation (2),
x * y = 642
y = 642 / x..................................equation (3)

Now, Taking equation (1),
x+y=217

Substituting the value of y from equation (3), we get,

x+ \frac{642}{x} =217

\frac{x *x+642}{x} =217

x^{2} +642 =217*x

x^{2} +642 =217x

x^{2} +642-217x =0

x^{2} -217x+642 =0

x^{2} -3x-214x+642 =0

x(x-3)-214(x-3)=0

(x-3)(x-214)=0

Using zero product property,
EITHER,
           x - 3 = 0
                x = 3
OR,
          x - 214 = 0
                  x  = 214
Since, "x" is the triple digit number, x = 214.
Now,
Taking equation (2),
x * y = 642
Substituting the value of "x" in the equation, we get,
(214) * y = 642
y = 642 / 214
y = 3

So, the numbers are 214 and 3.



5 0
3 years ago
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