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Mashutka [201]
3 years ago
15

How to subtract common denominator

Mathematics
1 answer:
grigory [225]3 years ago
3 0
So, here are the steps.
1. Build each fraction so that both denominators are equal. ...
2. Re-write each equivalent fraction using this new denominator.
3. Now you can subtract the numerators, and keep the denominator of the equivalent fractions.
4. Re-write your answer as a simplified or reduced fraction, if needed.
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A thermometer is taken from a room where the temperature is 20◦C to the
lord [1]

Answer:

a) T(2) = 8.265: at time t = 2 minutes the temperature will be 8.265 degress

b) 6 = T(3.55): the temperature will be 6 degrees at time t = 3.55 minutes.

Step-by-step explanation:

When dealing with temperature changes, it's best to work with Newton's Law of Cooling.

T(t) = T_s + Ce^{kt}

here:

T(t) : the temperature in the room.

T_s : ambient (or outdoor) temperature (that always remains constant, in our case: T_s = 5 )

C\,\text{and}\,k: are constants

Our conditions are provided:

1) T(0) = 20

2) T(1) = 12

using the first condition

T(0) = 5 + Ce^{k(0)}\\20 = 5 + C(1)\\C = 15

using the second condition:

T(1) = 5 + Ce^{k(1)}\\12 = 5 + Ce^{k}\\e^k = \dfrac{7}{C}

we can use our calculated value of C to find k

e^k = \dfrac{7}{15}\\k = \ln{(\dfrac{7}{15})}\\k = -0.7621

Finally we can put these constants back in the main equation:

T(t) = T_s + Ce^{kt}

T(t) = 5 + 15e^{-0.7621t} or T(t) = 5 + 15e^{\ln{(\frac{7}{15})t}

a) Reading after one more minute?

so it's asking:

T(2) = ?

T(2) = 5 + 15e^{\ln{(\frac{7}{15})(2)}}\\T(2) = \dfrac{124}{15} \approx 8.267

Hence, after one more minute the temperature of the room will be 8.267 degrees

b) When will it be 6 degrees?

T(t) = 6?

6 = 5 + 15e^{-0.7621t}\\\text{and solve for $t$}\\\\\dfrac{6-5}{15}=e^{\ln{(\frac{7}{15})}t}\\\ln{\left(\dfrac{1}{15}\right)} = \ln{\left(\dfrac{7}{15}\right)t}\\\ln{\left(\dfrac{1}{15}\right)} \div \ln{\left(\dfrac{7}{15}\right)} = t \approx 3.55\\

Hence at t = 3.55 minutes the temperature of the room will be 6 degrees.

8 0
3 years ago
An electrician charges $40 for each hour he works plus a $125 service charge. The total charge for a recent job was $1,205. Whic
maks197457 [2]

Answer:

Answer is D.

Step-by-step explanation:

40h is what you start out with since it costs 40 ever hour. then you add the service charge which makes it 40h + 125, and then since the total charge is 1205, that would complete the equation.

5 0
3 years ago
Read 2 more answers
Show all work to multiply quantity 6 plus the square root of negative 64 end quantity times quantity 3 minus the square root of
Serga [27]

Answer: 50

Step-by-step explanation:

[6+√-64] × 3-√-16

(6+8i)(3-4i)

6(3-4i)+8i(3-4i)

18-24i+24i+32

18+32=50

<h3> the answer is 50</h3>
5 0
3 years ago
2x+6y=12 what's m and b?
Elena L [17]
If you're asking about slope and how to find the equation of the line, you would do it like this:

1) Arrange the equation into slope intercept form (y=mx+b)

2) 6y+2x=12 subtract  the 2x from both sides and you get 6y= -2x +12

is in slope intercept form

3) So, m= -2 and b=12
5 0
3 years ago
Read 2 more answers
Jamie spun a colored spinner 20 times. The results of her spins are
galina1969 [7]

Answer:

80 times

Step-by-step explanation:

8 0
3 years ago
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