It equals 96. hope that helped
Answer:
The volume of the cone is;
100 π inches^3
Step-by-step explanation:
To calculate the volume, we need the height
We can get the height from the slant height and the radius
Mathematically, we use Pythagoras’ theorem for this as the slant height, the radius and the height forms a right-angled triangle
The right-angled triangle has the slant height as its hypotenuse
By the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
Let the height be h
Thus;
12^2 = 5^2 + h^2
169= 25 + h^2
h^2 = 169-25
h^2 = 144
h = √1144 inches = 12 inches
The volume of the cone is;
1/3 * π * r^2 * h
= 1/3 * π * 5^2 * 12
= 100 π inches^3
Answer: The required solution is 
Step-by-step explanation:
We are given to solve the following differential equation :

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.
From equation (i), we have

Integrating both sides, we get
![\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]](https://tex.z-dn.net/?f=%5Cint%5Cdfrac%7Bdy%7D%7By%7D%3D%5Cint%20kdt%5C%5C%5C%5C%5CRightarrow%20%5Clog%20y%3Dkt%2Bc~~~~~~%5B%5Ctextup%7Bc%20is%20a%20constant%20of%20integration%7D%5D%5C%5C%5C%5C%5CRightarrow%20y%3De%5E%7Bkt%2Bc%7D%5C%5C%5C%5C%5CRightarrow%20y%3Dae%5E%7Bkt%7D~~~~%5B%5Ctextup%7Bwhere%20%7Da%3De%5Ec%5Ctextup%7B%20is%20another%20constant%7D%5D)
Also, the conditions are

and

Thus, the required solution is 
Answer:
2,973
Step-by-step explanation:
The black bear population B(t), in the park is modeled by the following function:

Where t is the time(in years) elapsed since the beginning of the study.
We want to determine the black bear population in 25 years time, t=25.

There will be 2,973 black bears in 25 years time.