What is the value of x?

Mathematics

1 answer:

Amanda [17]2 years ago

7 0

There is a formula for Sum of interior angles of a polygon:
$Sum = 180(n-2)$
This figure has 7 sides, n = 7
$Sum = 180(7-2) = 900$
Add up all the given angles,
Subtract from 900,
This will give you value of x.

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Translate the sentence and solve: "4 is 2 less than double a number".

Elanso [62]

Answer: x = 3

Step-by-step explanation:

you would double each number meamong multiply by 2 until you get the opposite of 4 being 2 less of a number so 6.

3 x 2 = 6

and 2 less than 6 is 4 so theres your answer :)

4 0

3 years ago

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:

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