Match the temperatures with the times.

Mathematics
Match the temperatures with the times.

ScanSolve AI Answer

Answer

2C/h2^\circ C/h

Step 1: Average rate of temperature change from 2:00 a.m. to 11:00 a.m.

Formula:
Average rate=ΔTΔt\text{Average rate} = \frac{\Delta T}{\Delta t}

T2:00 a.m.=4CT_{2:00~\rm a.m.} = -4^\circ \rm C
T11:00 a.m.=14CT_{11:00~\rm a.m.} = 14^\circ \rm C
ΔT=14C(4C)=18C\Delta T = 14^\circ \rm C - (-4^\circ \rm C) = 18^\circ \rm C

Δt=11:00 a.m.2:00 a.m.=9 h\Delta t = 11:00~\rm a.m. - 2:00~\rm a.m. = 9~\rm h

Average rate=18C9 h=2C/h\text{Average rate} = \frac{18^\circ \rm C}{9~\rm h} = 2^\circ \rm C/\rm h

2^\circ C/h

Step 2: Average rate of temperature change from 11:00 a.m. to 2:00 p.m.

Formula:
Average rate=ΔTΔt\text{Average rate} = \frac{\Delta T}{\Delta t}

T11:00 a.m.=14CT_{11:00~\rm a.m.} = 14^\circ \rm C
T2:00 p.m.=2CT_{2:00~\rm p.m.} = -2^\circ \rm C
ΔT=2C14C=16C\Delta T = -2^\circ \rm C - 14^\circ \rm C = -16^\circ \rm C

Δt=2:00 p.m.11:00 a.m.=3 h\Delta t = 2:00~\rm p.m. - 11:00~\rm a.m. = 3~\rm h

Average rate=16C3 h=163C/h5.33C/h\text{Average rate} = \frac{-16^\circ \rm C}{3~\rm h} = -\frac{16}{3}^\circ \rm C/\rm h \approx -5.33^\circ \rm C/\rm h

-\frac{16{3}^\circ C/h}

Step 3: Average rate of temperature change from 2:00 a.m. to 2:00 p.m.

Formula:
Average rate=ΔTΔt\text{Average rate} = \frac{\Delta T}{\Delta t}

$T_{2:00~\rm a.m.} = -4^\circ \rm

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Quick Answer

Average rate of temperature change from 2:00 a.m. to 11:00 a.m.

Match the temperatures with the times.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Average rate of temperature change from 2:00 a.m. to 11:00 a.m. Formula: Average rate = ( T)/( t) T_2:00~ a.m. = -4^ C T_11:00~ a.m. = 14^ C T = 14^ C - (-4^ C) = 18^ C t = 11:00~ a.m. - 2:00~ a.m. = 9~ h Average rate = (18^ C)/(9~ h) = 2^ C/ h 2^ C/h Step 2: Average rate of temperature change from 11:00 a.m. to 2:00 p.m. Formula: Average rate = ( T)/( t) T_11:00~ a.m. = 14^ C T_2:00~ p.m. = -2^ C T = -2^ C - 14^ C = -16^ C t = 2:00~ p.m. - 11:00~ a.m. = 3~ h Average rate = (-16^ C)/(3~ h) = -(16)/(3)^ C/ h ≈ -5.33^ C/ h -(16)/(3)^ C/h Step 3: Average rate of temperature change from 2:00 a.m. to 2:00 p.m. Formula: Average rate = ( T)/( t) $T_2:00~ a.m. = -4^