The penguin exhibit at a zoo has a raised circular island that is surrounded by water. The diameter of the island is 20 \text{ meters}20 meters20, start text, space, m, e, t, e, r, s, end text. One penguin swims half way around the island before hopping out.
How far did the penguin swim?
Give your answer in terms of pi.

Answer:

The doomsday is 146 days

Step-by-step explanation:

Given

[tex]\frac{dy}{dt} = ky^{1 +c}[/tex]

First, we calculate the solution that satisfies the initial solution

Multiply both sides by

[tex]\frac{dt}{y^{1+c}}[/tex]

[tex]\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}[/tex]

[tex]\frac{dy}{y^{1+c}} = k\ dt[/tex]

Take integral of both sides

[tex]\int \frac{dy}{y^{1+c}} = \int k\ dt[/tex]

[tex]\int y^{-1-c}\ dy = \int k\ dt[/tex]

[tex]\int y^{-1-c}\ dy = k\int\ dt[/tex]

Integrate

[tex]\frac{y^{-1-c+1}}{-1-c+1} = kt+C[/tex]

[tex]-\frac{y^{-c}}{c} = kt+C[/tex]

To find c; let t= 0

[tex]-\frac{y_0^{-c}}{c} = k*0+C[/tex]

[tex]-\frac{y_0^{-c}}{c} = C[/tex]

[tex]C =-\frac{y_0^{-c}}{c}[/tex]

Substitute [tex]C =-\frac{y_0^{-c}}{c}[/tex] in [tex]-\frac{y^{-c}}{c} = kt+C[/tex]

[tex]-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}[/tex]

Multiply through by -c

[tex]y^{-c} = -ckt+y_0^{-c}[/tex]

Take exponents of [tex]-c^{-1[/tex]

[tex]y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]

[tex]y = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]

[tex]y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]

i.e.

[tex]y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]

Next:

[tex]t= 3[/tex] i.e. 3 months

[tex]y_0 = 2[/tex] --- initial number of breeds

So, we have:

[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]

-----------------------------------------------------------------------------

We have the growth term to be: [tex]ky^{1.01}[/tex]

This implies that:

[tex]ky^{1.01} = ky^{1+c}[/tex]

By comparison:

[tex]1.01 = 1 + c[/tex]

[tex]c = 1.01 - 1 = 0.01[/tex]

[tex]y(3) = 16[/tex] --- 16 rabbits after 3 months:

-----------------------------------------------------------------------------

[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]

[tex]16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}[/tex]

[tex]16 = [-0.03 * k + 2^{-0.01}]^{-100}[/tex]

[tex]16 = [-0.03 k + 0.9931]^{-100}[/tex]

Take -1/100th root of both sides

[tex]16^{-1/100} = -0.03k + 0.9931[/tex]

[tex]0.9727 = -0.03k + 0.9931[/tex]

[tex]0.03k= - 0.9727 + 0.9931[/tex]

[tex]0.03k= 0.0204[/tex]

[tex]k= \frac{0.0204}{0.03}[/tex]

[tex]k= 0.68[/tex]

Recall that:

[tex]-\frac{y^{-c}}{c} = kt+C[/tex]

This implies that:

[tex]\frac{y_0^{-c}}{c} = kT[/tex]

Make T the subject

[tex]T = \frac{y_0^{-c}}{kc}[/tex]

Substitute: [tex]k= 0.68[/tex], [tex]c = 0.01[/tex] and [tex]y_0 = 2[/tex]

[tex]T = \frac{2^{-0.01}}{0.68 * 0.01}[/tex]

[tex]T = \frac{2^{-0.01}}{0.0068}[/tex]

[tex]T = \frac{0.9931}{0.0068}[/tex]

[tex]T = 146.04[/tex]

The doomsday is 146 days

Answer:

x=37

Step-by-step explanation:

As you can see in the image, both angles are congruent to each other. 74 degrees and 2x degrees. You have to divide 74 by 2 to find what x equals.

74/2=37

x=37

Answer:

D

Step-by-step explanation:

Because it's 340 meters per second

Answer:

6

Step-by-step explanation:

2/3 times 9 = 6

(Also: The Caps really attracted me)

Answer:

woahhhhhh too much

Step-by-step explanation:

Answer:

7.1.14-T Question Help 이 Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4528 patients treated with the drug, 102 developed the adverse reaction of nausea. Construct a 95% confidence interval for the proportion of adverse reactions. a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.)

Step-by-step explanation:

Area = l × b

= 9ft × 8ft

= 72ft²

Answer:

72 feet

Step-by-step explanation:

8 (length) • 9 (width) = 72 sq ft

Answer:

3 comic books and 4 cups of coffee

Step-by-step explanation:

8 × 3 = 24

4 × 4 = 16

16 + 24 = 40

Answer:

1/sec x- tan x

Step-by-step explanation:

sec x+ tan x

= sec x+ tan x) (sec x - tan x)/(sec x , tan x)

=sec^2x-tan^2x)(sec x- tan x)

(sec^2x-tan^2x=1)

=1/sec x- tan x

Answer:

a) At $3,300 for 600 seats, the average price per seat is 3300/600 = $5.50. The mix of tickets that results in that average can be found using an X diagram as shown below. The numbers on the right are the differences along the diagonals. When they are multiplied by 2, they add to 600. This shows that the required sales for revenue of $3,300 are

 200 adult tickets

 400 student tickets

b) When 3 student tickets are sold for each adult ticket, the average seat price is

 (3*$4.50 +7.50)/4 = $5.25

Then the shortfall in revenue is ...

 $3,300 -480*$5.25 = $780

Answer:

Yes

Step-by-step explanation:

[tex]\frac{2.5}{8} = \frac{7.5}{24} = \frac{5}{16}[/tex]

Answer:

yes it is equivalent

because when we multiple 3

to both 2.5 and 8

then it will. 7.5:24

so, answer is yes

hope it helps

Answer:

1 boy 4 girls, 2 boys 8 girls, 3 boys 12 girls, 4 boys 16 girls

Answer:

27% chance that the transistor is defective

5:17

Step-by-step explanation:

The probability that the picked up transistor is defective is 5/17

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -  

P(A) = n(A)/n(S)

where -

n(A) = Number of outcomes favorable to event A.

n(S) = Total number of outcomes

Given is that a box contains 17 ​transistors, 5 of which are defective.

Probability that the picked up transistor is defective is -

P(D) = 5/17

Therefore, the probability that the picked up transistor is defective is 5/17

To solve more questions on Probability, visit the link below -

brainly.com/question/24028840

#SPJ2

You mean Sigma notation not stigma ^^

Answer:

Look the attachment

Answer:

C 62.4square centimetres

Answer:

1000

Step-by-step explanation:

2×500=1000

hope it helps

Answer:

x=11

Step-by-step explanation:

4x+11=5x (angle adb and edf are the same)

11=5x-4x

11=x

x=11

if you want you can check by doing...

(14*11-29)+(5*11)=180

Answer:

A) WZ

Step-by-step explanation:

B,C, and D, come before RU

Answer: 500 children play soccer

Step-by-step explanation:

Take the numbers you are given

240 boys

260 girls

now add them together

240 + 260 = 500

Answer:

500

Step-by-step explanation:

There is 240 boys and 260 girls

they all play the same sport

so add does numbers you get 500.

Answer:

6

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

There are no solutions because the two lines have the same gradient (they are parallel)

Have a great day <3 and pls love me

Answer:

c i think

Step-by-step explanation:

Answer:

There is no table? try taking a screenshot

Step-by-step explanation:

Answer:

P is price per lawn, 20 is the money made per lawn, L is the number of lawns mowed, 100 is his initial cost.

Step-by-step explanation:

Answer:

Use photo math it will help you.

Answer:

9y+8

Step-by-step explanation:

I hope this helps! You add 3y+6y which is 9 and then you add 8, so the answer is 9y+8

Answer:

Step-by-step explanation:

The triangles are similar.

x/(x+4) = 7.2/12

x/(x+4) = 0.6

x = 0.6(x+4)

0.4x + 2.4

x = 6

Step-by-step explanation:

It means "a divided by 3". You need to divide a by 3. You can also write it as "1/3a".

Answer:

the answer is above me or below me

Answer:

TR is tangent

SV and ST are the chords

OT is perpendicular to tangent line T