3 years ago

Identify and explain the error made in the following:2x + 8x = 10x^2

Mathematics

1 answer:

Step2247 [10]3 years ago

8 0

It shouldn’t have ^2

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After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F.

laila [671]

Answer:

Question 1: 0.081 min⁻¹

Question 2: 168ºF

Explanation:

The missing equation is:

$T=T_a+(T_0-T_a)e^{-kt}$

You are given:

Ta = the temperature surrounding the object = 73ºF
T₀ = the initial temperature of the object = 204ºF
t = 2.5 min
T after 2.5 min = 180ºF

Question 1: Find the the value of k.

Substitute the data into the equation and solve for k:

$180\º=73\º+(204\º-73\º)e^{-k\cdot 2.5min}\\ \\ 107\º=131\ºe^{-k\cdot 2.5min}\\\\-k\cdot 2.5min=\ln (107/131)\\\\k=0.081min^{-1}$

Question 2: Find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.

Subsititute into the formula and compute:

$T=73\ºF+(204\ºF-73\ºF)e^{-0.081min^{-1}\times 4min}\\ \\ T=73\ºF+(131\ºF)(0.72325024)\\\\T=168\ºF$

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