What is 107,609 decided by 72

The government of the Republic of Lemon Island plans to transform their lemon-based economy into a tourism-based economy. They d

NNADVOKAT [17]

Step-by-step explanation:

dy/dt = (A − Be^(-t/5)) y

(a) First, find the general solution by separating the variables and integrating.

dy / y = (A − Be^(-t/5)) dt

dy / y = [A + 5B (-⅕ e^(-t/5))] dt

ln |y| = At + 5B e^(-t/5) + C

y = e^(At + 5B e^(-t/5) + C)

y = Ce^(At + 5B e^(-t/5))

Given that A = 0.06, B = 0.04, and y(0) = 50×10⁶ − 10×10⁶ = 40×10⁶:

40×10⁶ = Ce^(0.06(0) + 5(0.04) e^(-0/5))

40×10⁶ = Ce^(0.2)

C = 40×10⁶ e^(-0.2)

y = 40×10⁶ e^(-0.2) e^(0.06t + 0.2 e^(-t/5))

y = 40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5))

(b) If A = 0.02 and B = 0, and there is no transformation (y(0) = 50×10⁶), then:

50×10⁶ = Ce^(0.02(0) + 0)

50×10⁶ = C

y = 50×10⁶ e^(0.02t)

Comparing to the answer from part (a):

40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5)) = 50×10⁶ e^(0.02t)

e^(-0.2 + 0.04t + 0.2 e^(-t/5)) = 5/4

-0.2 + 0.04t + 0.2 e^(-t/5) = ln(5/4)

-5 + t + 5e^(-t/5) = 25 ln(5/4)

t + 5e^(-t/5) = 5 + 25 ln(5/4)

Solve with a calculator:

t = 9.886

The transformed economy surpasses the untransformed economy in the 10th year.

(c) In year t=5, the size of the transformed economy is:

y = 40×10⁶ e^(-0.2 + 0.06(5) + 0.2 e^(-5/5))

y = 47.6×10⁶

The percent growth is:

(47.6×10⁶ − 40×10⁶) / 40×10⁶ × 100% = 19%

The growth rate is greater than 4%, so the current government can expect to be reelected.

3 0

3 years ago

The amount of tomatoes doubles every day.Use an equation model the situation There are three tomatoes on Monday.How many will th

expeople1 [14]

There will be 12 tomatoes on Thursday. 3x4

4 0

3 years ago

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BC = 36; D = 15. What is the value of BD - AC.<br> B<br> A<br> BD - AC =

Snezhnost [94]

Answer:

BD - AC = 0

Step-by-step explanation:

Given that:

BC = 36 , CD = 15 and BD = x

As these are forming right angled triangle,

Using Pythagorean theorem,

$(BD)^2+(CD)^2=x^2\\(36)^2+(15)^2 = x^2\\1296 + 225 = x^2\\1521 = x^2\\$

Taking square root on both sides

$\sqrt{x^2}=\sqrt{1521}\\x=39$

As the given shape is rectangular, the sides parallel to each other will have same values.

AB = 15 , AD = 36 and AC = x

$(15)^2+(36)^2 = x^2 \\225 + 1296 = x^2 \\1521 = x^2 \\x = 39$

Now,

BD - AC = 39 - 39 = 0

Hence,

BD - AC = 0

5 0

3 years ago

Each of 16 students measured the circumference of a tennis ball by four different methods, which were: A: Estimate the circumfer

almond37 [142]

Answer:

Following are the solution to the given equation:

Step-by-step explanation:

Please find the complete question in the attachment file.

In point a:

$\to \mu=\frac{\sum xi}{n}$

$=22.8$

$\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}$

$=\sqrt{\frac{119.18}{16-1}}\\\\ =\sqrt{\frac{119.18}{15}}\\\\ = \sqrt{7.94533333}\\\\=2.8187$

In point b:

$\to \mu=\frac{\sum xi}{n}$

$=20.6875$

$\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}$

$=\sqrt{\frac{26.3375}{16-1}}\\\\=\sqrt{\frac{26.3375}{15}}\\\\ =\sqrt{1.75583333}\\\\ =1.3251$

In point c:

$\to \mu=\frac{\sum xi}{n}$

$=21$

$\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}$

$=\sqrt{\frac{2.62}{16-1}}\\\\ =\sqrt{\frac{2.62}{15}} \\\\= \sqrt{0.174666667}\\\\=0.4179$

In point d:

$\to \mu=\frac{\sum xi}{n}$

$=20.8375$

$\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}$

$=\sqrt{\frac{8.2975}{16-1}}\\\\ =\sqrt{\frac{8.2975}{15}} \\\\ =\sqrt{0.553166667} \\\\ =0.7438$

6 0

3 years ago

What is 0.25 as a percentage

Varvara68 [4.7K]

Answer:

25%

Step-by-step explanation:

7 0

2 years ago

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