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konstantin123 [22]
3 years ago
11

5.4 ⋅ 103 to standard form.

Mathematics
1 answer:
kirill [66]3 years ago
7 0
5.4 * 10^3=5,400 is your answer
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A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the
serious [3.7K]

Answer:

The equation is A=6000e^{-0.23t}  at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation A=A_0e^{rt}. We can find the rate at which it decays by using t=3 hours and A=3000. This means A_0=6000 in this context.

A=A_0e^{rt}\\3000=6000e^{r(3)}

0.5=e^{(24.5)r}

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r

We know lne=1 so we were able to cancel it out and divide both sides by 3.

We solve with a calculator \frac{ln0.5}{3} =r\\-0.23=r

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is A=6000e^{-0.23t}


5 0
3 years ago
How I can solve this
gavmur [86]

Answer:

\boxed{\textrm{B)}\qquad y>4}.

Step-by-step explanation:

We start by subtracting 1 from both sides of the second inequality:

2x > 5 \iff 2x - 1 > 5 - 1 \iff 2x - 1 > 4.

Therefore, we conclude that:

y > 2x - 1 > 4 \implies y > 4.

Therefore, every point that satisfies the system has a y-coordinate greater than 4.

7 0
3 years ago
Please help if possible due in 20 minutes ❤️❤️<br><br> f(x) = x2. What is g(x)?
otez555 [7]

Answer:

c. g(x)=(1/2x^2)

Step-by-step explanation:

3 0
3 years ago
The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th
Fantom [35]

Answer:

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C

Step-by-step explanation:

To find:

∫6x^5(x^6-2)\,dx

Solution:

Method of substitution:

Let x^6-2=t

Differentiate both sides with respect to t

6x^5\,dx=dt

[use (x^n)'=nx^{n-1}]

So,

∫6x^5(x^6-2)\,dx = ∫ t\,dt = \frac{t^2}{2}+C_1 where C_1 is a variable.

(Use ∫t^n\,dt=\frac{t^{n+1} }{n+1} )

Put t=x^6-2

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1

Use (a-b)^2=a^2+b^2-2ab

So,

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C

where C=2+C_1

Without using substitution:

∫6x^5(x^6-2)\,dx = ∫6x^{11}-12x^5\,dx = \frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C

So, same answer is obtained in both the cases.

7 0
2 years ago
4,400 X 400 = ( blank hundreds) X ( blank hundreds) = 176 hundreds, thousands, hundrenths, tenths, tens, ones, thousands, or tho
kiruha [24]
Hello There!

(44 hundreds) x (4 hundreds) = 176 tens thousands.

Hope This Helps You!
Good Luck :) 

- Hannah ❤
5 0
3 years ago
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