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3 years ago

In properties of logarithms, what is log2 25?

1 answer:

8 0

$log_a(b)=c$ $log_a(b)=c$ translates to

$a^c=b$ $a^c=b$
let's say it equals y

$log_2(25)=y$ $log_2(25)=y$
trsnaltes to
$2^y=25$ $2^y=25$
doesn't help us
we can also translate it to
$log_2(5^2)$ $log_2(5^2)$ or $2log_2(5)$ $log_2(5^2)$

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The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of

Alexandra [31]

Answer:

Population of mosquitoes in the area at any time t is:

$P(t) =504,943.26 -104,943.26e^{0.693t}$

Step-by-step explanation:

assume population at any time t = P(t)

population increases at a rate proportional to the current population:

⇒dP/dt ∝ P

$\implies \frac{dP}{dt} =kP$ ----(1)

where k is constant rate at which population is doubled

solving (1)

$ln|P(t)|=kt +C\\P(t)= e^{kt+C}\\P(t)=Ce^{kt}$

$t=0\\P(0) = P_{o}\\\implies C= P_{o}\\P(t) =P_{o}e^{kt}\\$ ---- (2)

initial population = 400,000

population is doubled every week

⇒P(1)=2P(0)

Using (2)

$P_{o}e^{k(1)} = 2P_{o} e^{k(0)}\\$

$e^{k} =2\\k=ln|2|\\$

In presence of predators amount is decreased by 50,000 per day

Then amount decreased per week = 350,000

In this case (1) becomes

$\frac{dP}{dt}=kP-350,000\\\frac{dP}{dt} - kP=-350,000\\$ ---(3)

solving (3) by calculating integrating factor

$I.F=e^{\int-k dt}$

Multiplying I.F with all terms of (3)

$e^{-kt}\frac{dP}{dt} - ke^{-kt}P =-350,000 e^{-kt}\\\frac{d}{dt}(e^{-kt}P) = -350,000 e^{-kt}$

Integrating w.r.to t

$e^{-kt}P(t)= \frac{350,000e^{-kt}}{k} +C$

$P(t) =\frac{350,000}{k} +Ce^{kt}\\$

$k=ln|2| =0.693$

$P(t) =504,943.26 + Ce^{0.693t}\\$

at t=0

$P(0) =504,943.26 + Ce^{0.693(0)}$

$400,000 =504,943.26 + C$

$C = -104,943.26$

So, population of mosquitoes in the area at any time t is

$P(t) =504,943.26 -104,943.26e^{0.693t}$

6 0

3 years ago

Please help and please tell me how you got the answer will mark brainliest

valentinak56 [21]

Answer:

Steve's pay is the highest and is equal to 55 dollars per hour.

The column for pay corresponding to 1 hour is $55.

Step-by-step explanation:

Geeta's pay:

The equation for Geeta's pay is given as:

$p=75+45h$

Where, 'p' is in dollars and 'h' is in hours.

The above equation is a linear equation of the form $y=mx+b$ , where 'm' is the rate of change of pay or the pay per hour.

So, the pay per hour of Geeta is 45 dollars.

Richard's pay:

The graph of Richard's pay is a straight line. The slope of the line gives the rate of change of pay or the pay per hour.

The slope of the line is given as:

Slope = Rise over run = $\frac{80-50}{1-0}=30$ dollars per hour.

So, Richard's pay per hour is 30 dollars.

Steve's pay:

The table of hours and pay is given.

The rate of change or pay per hour can be obtained by using two values of both hours and pay.

Consider $h=3\ and\ h=5$ and $p=165\ and\ p=275$

Now, pay per hour = $\frac{275-165}{5-3}=\frac{110}{2}=55$ dollars

Therefore, Steve's pay per hour is 55 dollars.

The column for pay corresponding to 1 hour is $55.

On comparing, Steve's pay is the highest and is equal to 55 dollars per hour.

6 0

4 years ago

A small college has 800 students, 10% of which are left-handed. Suppose they take an SRS of 8 students.

Margarita [4]

Answer:

(8/2)(0.10)^2(0.90)^6

Step-by-step explanation:

Khan

3 0

3 years ago

Every female chicken lays 4 eggs. What is the constant of proportionality for the ratio of eggs to female chickens? 4 3

slega [8]

The answer is 4-3 because the chicken just went to chick fil a

4 0

3 years ago

Find a diginacci sequence with no equal term to 11: quick answer please

True [87]

Answer:

uhh hope this helps

Step-by-step explanation:

A Diginacci sequence is created as follows.

• The ﬁrst two terms are any positive whole numbers.

• Each of the remaining terms is the sum of the digits of the previous

two terms.

For example, starting with 5 and 8 the Diginacci sequence is

5, 8, 13, 12, 7, 10,. . .

The calculations for this example are

5 + 8 = 13, 8 + 1 + 3 = 12, 1+ 3 +1+ 2 = 7, 1 + 2 + 7 = 10.

a) List the ﬁrst 26 terms of the Diginacci sequence above.

b) Find, with explanation, two starting terms for a Diginacci sequence

so that its 2021st term is 11.

c) Find, with explanation, a Diginacci sequence that has no term equal

to 11.

d) Find, with explanation, a sequence with two diﬀerent starting terms

which contains ﬁve consecutive terms that are even and not all identical

Both 2 and 3 is correct.

5 0

3 years ago