Find the area of the shaded sector in terms of pi 45° & 4

Mathematics

1 answer:

stellarik [79]2 years ago

5 0

Answer:2pi

Step-by-step explanation:

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Equation of the graph

natka813 [3]

Answer:

A and C

Step-by-step explanation:

It can not be D, since that will mean that the line is perfectly horizontal, with 0 as its slope.

It can be C, since the equation's slope is positive and has a negative y-intercept, like the graph.

Changing around A gives us y = 2x - 3. That has a positive slope and a negative y-intercept, like the graph. So, A is a possibility.

Changing around B gives us y = ²/₃x + 3. This has a positive slope, but also a positive y-intercept, so B can not be the answer.

4 0

3 years ago

A model for tumor growth is given by the Gompertz equation dV dt = a (In b-, In V) V where a >0 and b >0 are constants and

Xelga [282]

Answer:

$V(t) = b^{(1-e^{-at})}$

Step-by-step explanation:

We are given the following information in the question:

$\displaystyle\frac{dV}{dt} = a (In b - In V) V$

where a > 0 and b > 0.

$\displaystyle\frac{dV}{dt} = a (In b-In V) V\\\\\displaystyle\frac{dV}{dt} = -aV(ln\frac{V}{b})\\\\\frac{dV}{V(ln\frac{V}{b})} = (-a)dt\\\\\text{Put } ln\frac{V}{b} = z\\\\\text{Integrating both sides}\\\\\int \frac{dV}{V(ln\frac{V}{b})} = \int (-a)dt\\\\\text{We get}\\\\\int \frac{dz}{z} = \int (-a)dt\\\\\\\text{where C is the constant of integration}$