What is the slope of the linear equation below?

A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

$y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48$

The rumor reaches 80% at 8.48 days.

8 0

3 years ago

Jake packed 12 jars of paint in a wooden tool box. Each jar and its contents weigh 10 ounces. The empty box weighs 1 pound 14 ou

emmasim [6.3K]

The total weight of the packed box is 9 lb 6 oz

According to question:

The weight of 12 jars is 12 times the weight of one jar

The weight of jars and box together is the sum of those weights.

... 12 × (10 oz) + 1 lb + 14 oz = 1 lb + 134 oz

... = 1 lb + 8 × (16 oz) + 6 oz . . . . . . 1 lb = 16 oz

... = 9 lb 6 oz

<h3>How to convert Ounces to Pounds?</h3>

1 ounce (oz) is equal to 0.0625 pounds (lb).

1 oz = (1/16) lb = 0.0625 lb

The mass m in pounds (lb) is equal to the mass m in ounces (oz) divided by 16:

m(lb) = m(oz) / 16

Learn more about Jars:

brainly.com/question/4313883

#SPJ4

5 0

2 years ago

Write g-12 in words

larisa [96]

I'm guessing you are looking for an algebraic sentence. In that case, 12 less than g would make sense, or 12 subtracted from g

8 0

4 years ago

Y= 4.6, 13.9, 21.6, ????

denis-greek [22]

Option B: 13.9 is the value of y

Explanation:

Given triangle is a right angled triangle.

The legs of the triangle are 8 and y.

The hypotenuse of the triangle is x.

And the angle opposite to y is 60°

We need to determine the value of y.

Let us find the value of y using the tangent formula.

The formula for tan is given by

$tan \ \theta=\frac{opp}{adj}$

Since, we know that $\theta = 60^{\circ$ , $opp=y$ and $adj=8$

Substituting these values in the formula, we get,

$tan \ 60^{\circ}=\frac{y}{8}$

Multiplying both sides by 8, we have,

$8\times tan \ 60^{\circ}=y$

Substituting the value of $\tan 60^{\circ}$ , we get,

$8\times 1.732=y$

Simplifying, we have,

$13.856=y$

Rounding off, we get,

$13.9=y$

Thus, the value of y is 13.9

Hence, Option B is the correct answer.

4 0

3 years ago

Select all expressions that are<br> equivalent to<br> 64 2/3

ikadub [295]

Answer: Here is every possibility

194/3 = 388/6 = 582/9

= 776/12 = 970/15 = 1164/18

= 1358/21 = 1552/24 = 1746/27

= 1940/30 = 2134/33 = 2328/36

= 2522/39 = 2716/42 = 2910/45

= 3104/48 = 3298/51 = 3492/54

= 3686/57 = 3880/60 = 4074/63

= 4268/66 = 4462/69 = 4656/72

= 4850/75 = 5044/78 = 5238/81

= 5432/84 = 5626/87 = 5820/90

= 6014/93 = 6208/96 = 6402/99

= 6596/102 = 6790/105 = 6984/108

= 7178/111 = 7372/114 = 7566/117

= 7760/120 = 7954/123 = 8148/126

= 8342/129 = 8536/132 = 8730/135

= 8924/138 = 9118/141 = 9312/144

= 9506/147 = 9700/150 = 9894/153

= 10088/156 = 10282/159 = 10476/162

= 10670/165 = 10864/168 = 11058/171

= 11252/174 = 11446/177 = 11640/180

= 11834/183 = 12028/186 = 12222/189

= 12416/192 = 12610/195 = 12804/198

= 12998/201 = 13192/204 = 13386/207

= 13580/210 = 13774/213 = 13968/216

= 14162/219 = 14356/222 = 14550/225

= 14744/228 = 14938/231 = 15132/234

= 15326/237 = 15520/240 = 15714/243

= 15908/246 = 16102/249 = 16296/252

= 16490/255 = 16684/258 = 16878/261

= 17072/264 = 17266/267 = 17460/270

= 17654/273 = 17848/276 = 18042/279

= 18236/282 = 18430/285 = 18624/288

= 18818/291 = 19012/294 = 19206/297

Step-by-step explanation:

4 0

3 years ago