Identify the constant term in the function. y=-x^2+3x-4

The measurement of 2 and justification

Minchanka [31]

M<2=105. They must add up to 180.

8 0

3 years ago

How many positive integers under 50 are multiples of neither 4 nor 6

lyudmila [28]

Candidates range from 1 to 50.
50/4=12 positive integers are multiples of 4
50/6=8 positive integers are multiples of 6
50/12=4 positive integers are multiples of 12 (LCM of 4 and 6)
By the inclusion/exclusion principle, the number of multiples of either 4 or 6 is equal to 12+8-4=16.

Therefore, the complement is the number of positive integers that are multiples of neither 4 nor 6 = 50-16=34.

6 0

3 years ago

If you know the circumference of a circle, which step(s) can you follow to find

GarryVolchara [31]

Answer:

C. Divide by pie(mathematical term)

Step-by-step explanation:

C=2r(pie) or C=d(pie)

6 0

3 years ago

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One model for the spread of a virusis that the rate of spread is proportional to the product of the fraction of the population P

Darya [45]

Answer:

The differential equation for the model is

$\frac{dP}{dt}=kP(1-P)$

The model for P is

$P(t)=\frac{1}{1-0.99e^{t/447}}$

At half day of the 4th day (t=4.488), the population infected reaches 90,000.

Step-by-step explanation:

We can write the rate of spread of the virus as:

$\frac{dP}{dt}=kP(1-P)$

We know that P(0)=100 and P(3)=100+200=300.

We have to calculate t so that P(t)=0.9*100,000=90,000.

Solving the diferential equation

$\frac{dP}{dt}=kP(1-P)\\\\ \int \frac{dP}{P-P^2} =k\int dt\\\\-ln(1-\frac{1}{P})+C_1=kt\\\\1-\frac{1}{P}=Ce^{-kt}\\\\\frac{1}{P}=1-Ce^{-kt}\\\\P=\frac{1}{1-Ce^{-kt}}$

$P(0)= \frac{1}{1-Ce^{-kt}}=\frac{1}{1-C}=100\\\\1-C=0.01\\\\C=0.99\\\\\\P(3)= \frac{1}{1-0.99e^{-3k}}=300\\\\1-0.99e^{-3k}=\frac{1}{300}=0.99e^{-3k}=1-1/300=0.997\\\\e^{-3k}=0.997/0.99=1.007\\\\-3k=ln(1.007)=0.007\\\\k=-0.007/3=-0.00224=-1/447$

Then the model for the population infected at time t is:

$P(t)=\frac{1}{1-0.99e^{t/447}}$

Now, we can calculate t for P(t)=90,000

$P(t)=\frac{1}{1-0.99e^{t/447}}=90,000\\\\1-0.99e^{t/447}=1/90,000 \\\\0.99e^{t/447}=1-1/90,000=0.999988889\\\\e^{t/447}=1.010089787\\\\ t/447=ln(1.010089787)\\\\t=447ln(1.010089787)=447*0.010039225=4.487533$

At half day of the 4th day (t=4.488), the population infected reaches 90,000.

8 0

3 years ago

Which function has an inverse that is also a function?

Yakvenalex [24]

The inverse of a function will also be a function if it is a One-to-One function. This means, if each y value is paired with exactly one x value then the inverse of a function will also be a function.

Option C gives us such a function, all x values are different and all y values are different. So inverse of function given in option C will result in a relation which will also be a function.

In all other options, y values are being repeated, which means they are not one to one functions.

So, the answer to this question is option C

3 0

3 years ago

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