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Leno4ka [110]
4 years ago
5

Solve the following quadratic equations by completing the square. y^2-14y+48=0

Mathematics
1 answer:
NISA [10]4 years ago
5 0

Answer:

  y = 6 or 8

Step-by-step explanation:

1. Subtract the constant:

  y^2 -14y = -48

2. Add the square of half the y-coefficient:

  y^2 -14y +49 = -48 +49

Write as a square, if you like:

  (y -7)^2 = 1

3. Take the square root:

  y -7 = ±√1 = ±1

4. Add the opposite of the constant on the left:

  y = 7 ±1  =  6 or 8

The solution is y = 6 or y = 8.

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a band of 45 ewoks crash-landed in the forest last night. this sounds like a small problem, but the population will grow at the
kogti [31]

Given Information:

Starting population = P₀ = 45

rate of growth = 22%

Required Information:

Population every five years from this year to the year 2050 = ?

Answer:

Year \: 2020 = P(0) = 45e^{0} = 45\\\\Year \: 2025 = P(5) = 45e^{0.22*5} = 135\\\\Year \: 2030 = P(10) = 45e^{0.22*10} = 406\\\\Year \: 2035 = P(15) = 45e^{0.22*15} = 1,220\\\\Year \: 2040 = P(20) = 45e^{0.22*20} = 3,665\\\\Year \: 2045 = P(25) = 45e^{0.22*25} = 11,011\\\\Year \: 2050 = P(30) = 45e^{0.22*30} = 33,079\\\\

Step-by-step explanation:

The population growth can be modeled as an exponential function,

P(t) = P_0e^{rt}

Where P₀ is the starting population, r is the rate of growth of the population and t is the time in years.

We are given that starting population of 45 and growth rate of 22%

P(t) = 45e^{0.22t}

Assuming that the starting year is 2020,

Year \: 2020 = P(0) = 45e^{0} = 45\\\\Year \: 2025 = P(5) = 45e^{0.22*5} = 135\\\\Year \: 2030 = P(10) = 45e^{0.22*10} = 406\\\\Year \: 2035 = P(15) = 45e^{0.22*15} = 1,220\\\\Year \: 2040 = P(20) = 45e^{0.22*20} = 3,665\\\\Year \: 2045 = P(25) = 45e^{0.22*25} = 11,011\\\\Year \: 2050 = P(30) = 45e^{0.22*30} = 33,079\\\\

Therefore, the starting population of ewoks was 45 in 2020 and increased to 33,079 by 2050 in a time span of 30 years.

8 0
3 years ago
Carly bought a new house for $125,000. The value of the house appreciates approximately 3.5% each year. What will be the value o
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Answer-

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Answer:

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Multiply this by 100% to change from decimal form to percent form

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