The prefix "deka" is used to designate which power of ten?
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1 is the power of ten.

Explanation:

is deka.

Basically 10 is deka, same result as .

The prefix "deka" is used to designate which power of ten?

a) t = 1051.6 sec = 17.5 min

b) t = 795.5 sec = 13.25 min

Explanation:

First of all we use the initial data to find out constant 'K'.

T - Ts = (T₀ - Ts) e^(-kt)

Here, we have:

T = Final Temperature = 60° C

Ts = Surrounding Temperature = 20° C

T₀ = Initial Temperature = 90° C

t = time = 10 min = 600 sec

k = constant = ?

Therefore,

60° C - 20° C = (90° C - 20° C).e^(-k600)

40° C/70° C = e^(-k600)

ln (0.57142) = -600k

k = 9.327 x 10⁻⁴ sec⁻¹

a)

Now, for this case we have:

T = Final Temperature = 35° C

Ts = Surrounding Temperature = 20° C

T₀ = Initial Temperature = 60° C

t = time = ?

k = constant = 9.327 x 10⁻⁴ sec⁻¹

Therefore,

35° C - 20° C = (60° C - 20° C).e^(-9.327 x 10⁻⁴ sec⁻¹ x t)

15° C/40° C = e^(-9.327 x 10⁻⁴ sec⁻¹ x t)

ln (15/40) = - 9.327 x 10⁻⁴ sec⁻¹ x t

t = 1051.6 sec = 17.5 min

b)

Now, for this case we have:

T = Final Temperature = 35° C

Ts = Surrounding Temperature = -15° C

T₀ = Initial Temperature = 90° C

t = time = ?

k = constant = 9.327 x 10⁻⁴ sec⁻¹

Therefore,

35° C + 15° C = (90° C + 15° C).e^(-9.327 x 10⁻⁴ sec⁻¹ x t)

50° C/105° C = e^(-9.327 x 10⁻⁴ sec⁻¹ x t)

ln (50/105) = - 9.327 x 10⁻⁴ sec⁻¹ x t

t = 795.5 sec = 13.25 min