Multiplying and dividing in scientific notation (picture provided) Please give the answer in scientific notation

Mathematics

2 answers:

solmaris [256]3 years ago

7 0

Answer:

7.8*10^7

1.0 * 10^4

Now divide 7.8/1.0 and the power goes up to be subtracted

=7.8 * 10^(7-4)

= 7.8 * 10^3

Kitty [74]3 years ago

5 0

Answer:

7.8×10^3

Step-by-step explanation:

(7.80×10^7)÷1.0×10^4

78000000÷10000

7800

78×10^2

7.8×10^3

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Simplify the expression 1-cos^2(t) / cos^2(t)

OLEGan [10]

Answer: $\tan^2 t$

Step-by-step explanation:

$\sin^{2} t+\cos^2 t=1 \implies 1-\cos^2 t=\sin^2 t\\\\\implies \frac{1-\cos^{2}t}{\cos ^2 t}=\frac{\sin ^2 t}{\cos^2 t}=\tan^2 t$

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2 years ago

A cooler has a temperature of 32 degrees Fahrenheit. A bottled drink is placed in the cooler with an initial temperature of

FinnZ [79.3K]

Answer:

$k \approx 0.44$

Step-by-step explanation:

Given function:

$f(t) = (ce)^{-kt}+32$

As per question statement:

Initial temperature of bottle is 70 $^\circ F$ .

i.e. when time = 0 minutes, f(t) = 70 $^\circ F$

$70 = ce^{-k\times 0}+32\\\Rightarrow 38 = ce^{0}\\\Rightarrow c = 38$

After t = 3, f(t) = 42 $^\circ F$

$42 = 38 \times e^{-k\times 3}+32\\\Rightarrow 42-32 = 38 \times e^{-3k} \\\Rightarrow 10 = 38 \times e^{-3k} \\\Rightarrow e^{3k} = \dfrac{38}{10}\\\Rightarrow e^{3k} = 3.8\\\\\text{Taking } log_e \text{both the sides:}\\\\\Rightarrow log_e {e^3k} = log_e {3.8}\\\Rightarrow 3k \times log_ee=log_e {3.8} (\because log_pq^r=r \times log_pq)\\\Rightarrow 3k \times 1=log_e {3.8}\\\Rightarrow 3k = 1.34\\\Rightarrow k = \dfrac{1.34}{3}\\\Rightarrow k \approx 0.44$