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3 years ago

How to subtract common denominator

1 answer:

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

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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