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3 years ago

6

A balloon rising at a constant rate will rise farther in 60 seconds than in 45 seconds. Which inequality shows this in function

notation?

1 answer:

Citrus2011 [14]3 years ago

8 0

Call f(t) the function that gives the rise of the balloon; then the statment translate to:

f(60) > f(45)

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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

What is the equation of the line that has a slope of 0 and passes through the point (6,-8)

Fofino [41]

$\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=0(x-6)\implies y+8=0\implies y=-8$

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3 years ago

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Which of the following have at least two congruent parallel bases?

koban [17]

Answer: B and C
Hope this help :)

3 0

3 years ago

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Use expressions for odd integers to confirm the conjecture that the product for two odd integers is an odd integer.

Mandarinka [93]

k, n - integers

2k+1 - an odd integer

2n+1 - another odd integer

The product of them:

(2k + 1)(2n + 1) =

= 4kn + 2k + 2n + 1 =

= 2(2kn + k + n) + 1

The product of integers (2kn) is integer

and the sum of them (2kn+k+n) also is integer

So (2k + 1)(2n + 1) = 2(2kn + k + n) + 1 is an odd integer

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3 years ago

If y = 45 when x = 180, what is the y when x= 90

bearhunter [10]

Answer:

24.5

Step-by-step explanation:

Since 180 is double 90 divide 45 by 2 and you'll get 24.5

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3 years ago