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Makovka662 [10]
3 years ago
12

30 POINTS!!!

Mathematics
1 answer:
Cloud [144]3 years ago
3 0

Answer:

A, C, & D

Step-by-step explanation:

A square root has the form \sqrt[2]{x}  = x^{1/2} and can be represented in exponential form. Let's convert all the expressions to \sqrt{x} this form. 4 square root 5 is 4\sqrt{25} =\sqrt{16*5}=\sqrt{80}

A. 2\sqrt{20} =\sqrt{4*20}=\sqrt{80}

B. 6^{1/2}-5^{1/2} =\sqrt{6}-\sqrt{5}

C. 3*5^{1/2}+5^{1/2} =3\sqrt{5}+\sqrt{5}=4\sqrt{5}=\sqrt{16*5}=\sqrt{80}

D. 4*5^{1/2}=4\sqrt{5}=\sqrt{16*5}=\sqrt{80}

E.2\sqrt{10} =\sqrt{4*10}=\sqrt{40}

F.  3*5^{1/2}=3\sqrt{5}=\sqrt{9*5}=\sqrt{45}

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Step-by-step explanation:

If you took the nth root of x, it is the same as raising x to the power of 1/n. Therefore:

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The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth
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Answer:

a) N_0=250\; k=0.15

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Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies t=0. And N(0)=N_0. The process is:

N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250

b) After 2 days means t=48. So, we just replace and operate:

N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}

c) N(t_1)=4000; \;t_1=?

N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\  \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h

d) t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)

N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h

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