If you're studying differential equations, you can find the solution to the given equation using the boundary conditions given.
Some of us would rather cut to the chase. We recognize that this is an exponential decay problem in which the initial temperature difference from the 75 °F room temperature is decaying to zero.
In 10 minutes, the temperature difference has decayed from 180-75 = 105 to 100-75 = 25, so we can write the temperature function of time as
.. T(t) = 75 +105*(25/105)^(t/10)
We can solve this for
.. T(t) = 80
using logarithms, but it may be easier to do it graphically.
To the nearest minute, it will take 21 minutes for the coffee to cool to 80 °F.
There are a lot of numbers that fall into that category...
Lets call your number x, then 400 < x < 312
That means x can be any number in between 400 and 312. But, x cannot be 400 or 312
x can be a total of 87 numbers which are listed here:
<span>
<span><span>
313,
</span>
<span>
314,
</span>
<span>
315,
</span>
<span>
316,
</span>
<span>
317,
</span>
<span>
318,
</span>
<span>
319,
</span>
<span>
320,
</span>
<span>
321,
</span>
<span>
322,
</span>
<span>
323,
</span>
<span>
324,
</span>
<span>
325,
</span>
<span>
326,
</span>
<span>
327,
</span>
<span>
328,
</span>
<span>
329, </span><span>330,
</span>
<span>
331,
</span>
<span>
332,
</span>
<span>
333,
</span>
<span>
334,
</span>
<span>
335,
</span>
<span>
336,
</span>
<span>
337,
</span>
<span>
338,
</span>
<span>
339,
</span>
<span>
340,
</span>
<span>
341,
</span>
<span>
342,
</span>
<span>
343,
</span>
<span>
344,
</span>
<span>
345,
</span>
<span>
346, </span><span>347,
</span>
<span>
348,
</span>
<span>
349,
</span>
<span>
350,
</span>
<span>
351,
</span>
<span>
352,
</span>
<span>
353,
</span>
<span>
354,
</span>
<span>
355,
</span>
<span>
356,
</span>
<span>
357,
</span>
<span>
358,
</span>
<span>
359,
</span>
<span>
360,
</span>
<span>
361,
</span>
<span>
362,
</span>
<span>
363,
</span>
<span>
364,
</span>
<span>
365, </span><span>366,
</span>
<span>
367,
</span>
<span>
368,
</span>
<span>
369,
</span>
<span>
370,
</span>
<span>
371,
</span>
<span>
372,
</span>
<span>
373,
</span>
<span>
374,
</span>
<span>
375,
</span>
<span>
376,
</span>
<span>
377,
</span>
<span>
378,
</span>
<span>
379, </span><span>380, </span><span>381,
</span>
<span>
382,
</span>
<span>
383,
</span>
<span>
384,
</span>
<span>
385,
</span>
<span>
386,
</span>
<span>
387,
</span>
<span>
388,
</span>
<span>
389,
</span>
<span>
390,
</span>
<span>
391,
</span>
<span>
392,
</span>
<span>
393,
</span>
<span>
394,
</span>
<span>
395,
</span>
<span>
396,
</span>
<span>
397,
</span>
<span>
398, and
</span>
<span>
399.
</span>
</span></span>
Answer:
b). 16.
Step-by-step explanation:
x^2 = 4
We can write this as
x^2 + 0x - 4 = 0
The discriminant (b^2 - 4ac) =
0^2 - 4 * 1* -4
= 16.
Answer:
Step-by-step explanation:
first term: put n = 1
36(1/3)^n-1 = 36(1/3)^1-1 =12 - 1 = 11
2nd term: put n = 2
36(1/3)^n-1 = 36(1/3)^2-1 = 19.784
3rd term: put n = 3
36(1/3)^n-1 = 36(1/3)^3-1 = 0.3333
4th term: put n = 4
36(1/3)^n-1 = 36(1/3)^4-1 = -0.5555
5th term: put n = 5
36(1/3)^n-1 = 36(1/3)^5-1 =-0.85185