The expression 18a-12 factored is

At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are fi

Otrada [13]

What are the options?

3 0

3 years ago

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

José’s mother is trying to decide whether or not she should buy a 12-ounce package of coffee on sale for $7.50. She knows that s

Leya [2.2K]

She should chose the $9 because it is cheaper ;)

8 0

3 years ago

Find lim x->2 for f(x)=

TiliK225 [7]

LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)

<h3>What is the limit of a function ?</h3>

The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.

It is given that

lim x->2 for f(x)

$\lim_{x \rightarrow 2^-}f(x) = \lim_{x\rightarrow 2^+}f(x)$

f(x) = 2x+1 x ≤2

f(x)= x² , x >2

When both the function tends to 2

Left Hand Limit

f(x) = 2 *2 +1

f(x) = 5

Right Hand Limit

f(x) = x² ,

f(x) = 4

LHL in not equal to RHL , Therefore the limit does not exists.

To know more about Limit of a Function

brainly.com/question/7446469

#SPJ1

8 0

2 years ago

Please help me with this i will give you a brainliest

marshall27 [118]

Answer:

2.)-7, -5, -1, 0

3.) -12, 0, 13, 14, 16, 17

5.) 5

Step-by-step explanation:

8 0

3 years ago