Identities and properties of logarithms

Mathematics

1 answer:

Natali [406]1 year ago

8 0

$(2a^7b^5\cdot 3ab^8)^2\implies \left( 2^2 a^{(7)(2)} b^{(5)(2)} \cdot 3^2 a^2 b^{(8)(2)}\right)\implies 4a^{14}b^{10}\cdot 9a^2b^{16} \\\\\\ (4)(9)a^{14}a^2b^{10} b^{16}\implies 36a^{14+2}b^{10+16}\implies 36a^{16}b^{26}$

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Population Growth Using 20th-century U.S. census data,

asambeis [7]

The population of Ohio will be 10 million in the year 1970

The population growth of Ohio is represented by the function:

$P(t)=\frac{12.79}{1+2.402e^{-}0.0309t}$

P is the population in millions

t is the number of years since 1900

To find the year that the population of Ohio will be 10 million, substitute P = 10 into the function P(t) and solve for t

$10=\frac{12.79}{1+2.402e^{-}0.0309t}\\\\10(1+2.402e^{-}0.0309t)=12.79\\\\1+2.402e^{-}0.0309t=\frac{12.79}{10} \\\\1+2.402e^{-}0.0309t=1.279\\\\2.402e^{-}0.0309t=1.279-1\\\\2.402e^{-}0.0309t = 0.279\\\\e^{-}0.0309t =\frac{0.279}{2.402} \\\\e^{-}0.0309t =0.116\\\\-0.0309t=ln0.116\\\\-0.0309t=-2.154\\\\t=\frac{-2.154}{-0.0309} \\\\t=69.7$

t = 70 years (to the nearest whole number)

70 years after 1900 will be 1970

Therefore, the population of Ohio will be 10 million in the year 1970

Learn more here: brainly.com/question/25504185

5 0

3 years ago

Tickets are available at the Paramount Theater for three levels in the performance hall. Lower level tickets cost $35, mezzanine

tekilochka [14]

Answer:

Step-by-step explanation:

35+25y+15z=37500

x - 5z = 0

25y - 60z = 0

4 0

3 years ago

Please help me, and please explain how you get to the answer.

ololo11 [35]

Answer:

Step-by-step explanation:

first you divide both sides by 2 pi, which cancels out the other 2 pi
then you square both sides, which cancels out the square root
lastly you multiply both sides by g, which leaves you with L

to simplify:

square the things in the brackets
and multiply by g over 1, which is the same as g
and as according to the pronumeral rule, you arrange the letters in alphabetical order