Write the recursive and explicit formula for 10, 30, 90, 270...

Mathematics

2 answers:

zysi [14]3 years ago

7 0

you multiply the previous term by 3 each time

nadezda [96]3 years ago

6 0

Answer:

Multiply by 3 each time

After 270 youll get 810 because i multiplied 270 by 3

The formula is 3 . 10 right? Correct me if im wrong.

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The angle of sector of cicle of diameter 8cm is 135 . find the area of the sector<br>

Naddik [55]

Answer:

18.85 cm²

Step-by-step explanation:

The formula to find the area of a sector = θ/360 × πr²

We are given:

θ = Angle of the sector = 135°

Radius = Diameter/2

Diameter = 8cm , Hence Radius = 8cm/2 = 4cm

Hence,

Area of a sector = 135/360 × π ×(4cm)²

= 18.849555922 cm²

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Therefore, the area of the sector is 18.85 cm²

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Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and t

WINSTONCH [101]

Answer:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

$\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}$

Seperate the differential equation and solve for the constant C.

$\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}$