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3 years ago

Refer to the figure to the right.

Mathematics

1 answer:

Law Incorporation [45]3 years ago

6 0

Step-by-step explanation:

Use arc length:

s = rθ

where r is the radius and θ is the angle in radians.

a) First, convert the angle to radians (1 degree = 60 minutes).

77 ⁵⁰/₆₀° × (π radian / 180°) = 1.358 radians

s = rθ

s = (9.67 in) (1.358 rad)

s = 13.1 in

b) s = rθ

4 in = (9.67 in) θ

θ = 0.414 radians

θ = 23.7°

θ = 23° 42'

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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

Lori bought some cookies for $2 each and muffins for $3 each. She bought twice as

Lubov Fominskaja [6]

Answer:

2 cookies

Step-by-step explanation:

let c represent cookies, m represent muffins. set up a system of equations:

2c+3m=16

m=2c

(the top equation shows that cookies are $2 each, and muffins are $3, and that the total cost is $16. the bottom equation shows that Lori bought twice as many muffins as cookies).

then solve the system of equations by substitution, substituting 2c for m in the top equation:

2c+3(2c)=16

2c+6c=16

8c=16

c=2

this means that lori bought 2 cookies.

7 0

2 years ago

Read 2 more answers

The price of a gallon of gasoline increased from 2.50 a gallon to 2.75 a gallon what was the percent increase

Vera_Pavlovna [14]

The increase in price was 10%
2.5*.1=.25
2.5+.25=2.75
hope this helps

8 0

2 years ago

Determine wheather the given lines are parallel or not. Write the reasons .

kenny6666 [7]

Answer:

yes it is parallel because the alternate interior angles are equal

7 0

3 years ago

Which expression is equivalent to s+s -4s<br> A- 1-3s<br> b- -4s<br> c- s-3<br> d- -2s

a_sh-v [17]

Answer:

D. -2s

Step-by-step explanation:

s+s-4s

=1s+1s-4s

=(1+1-4)s

=-2s

3 0

3 years ago