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Leni [432]
3 years ago
8

If M(6,9) is the midpoint of the line segment AB, and if A has coordinates (3,5), find the coordinates of B.

Mathematics
1 answer:
ANEK [815]3 years ago
3 0
(9,13) .................
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In 1859, 24 rabbits were released into the wild in Australia, where they had no natural predators. Their population grew exponen
Mashcka [7]

Answer:

a) P' = P

   P(t) = 24e^{0.693t} where t is step of 6 months

b) 7.7 years

c)1064.67 rabbits/year

Step-by-step explanation:

The differential equation describing the population growth is

\frac{dP}{dt} = P

Where t is the range of 6 months, or half of a year.

P(t) would have the form of

P(t) = P_0e^{kt}

where P_0 = 24 is the initial population

After 6 month (t = 1), the population is doubled to 48

P(1) = 24e^k = 48

e^k = 2

k = ln(2) = 0.693

Therefore P(t) = 24e^{0.693t}

where t is step of 6 months

b. We can solve for t to get how long it takes to get to a population of 1,000,000:

24e^{0.693t} = 1000000

e^{0.693t} = 1000000 / 24 = 41667

0.693t = ln(41667) = 10.64

t = 10.64 / 0.693 = 15.35

So it would take 15.35 * 0.5 = 7.7 years to reach 1000000

c. P' = P_0ke^{kt}

We need to resolve for k if t is in the range of 1 year. In half of a year (t = 0.5), the population is 48

24e^{0.5k) = 48

0.5k = ln2 = 0.693

k = 1.386

Therefore, P' = 1.386*24e^{1.386t}

At the mid of the 3rd year, where t = 2.5, we can calculate P'

P' = 1.386*24e^{1.386*2.5} = 1064.67 rabbits/year

4 0
3 years ago
7 more than 5 times a number is 122
Luba_88 [7]

Answer:

The number is 23.

Step-by-step explanation:

5n + 7 = 122               Subtract 7 on both sides

     5n = 115                 Isolate the variable by dividing 5 on both sides

        n = 23

<h3><u><em>Hope this helps!!! </em></u></h3><h3><u><em>Please mark this as brainliest!!! </em></u></h3><h3><u><em>Thank You!!! </em></u></h3><h3><u><em>:)</em></u></h3>
4 0
3 years ago
The mean of five numbers is 6 the median is 7 and the mode is 2. What is the answer?
Lady_Fox [76]

Answer:

2,2,7,9,10

mark as brainliest

8 0
3 years ago
A box of blueberries is 2/5 full. Janet and her friends had each eaten 1/10 of a box of blueberries. How many people are blueber
anyanavicka [17]

In this problem, we have to find the factor which will make (1 / 10) equal to (2 / 5). Therefore we can write it as:

x (1 / 10) = 2 / 5

where x is the number of people who ate the blueberries

x = (2 / 5) / (1 / 10)

x = 4

 

<span>Therefore 4 people ate the blueberries.</span>

7 0
3 years ago
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When a rate is simplifed so that it has a denominator of 1 unit, it is called a(n) ___________ rate.
dangina [55]

Answer:

called unit rate .

Step-by-step explanation:

6 0
3 years ago
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