The number of people who took ride in the big ferris wheel at a fair can be calculated by proper dimensional analysis. This can be done through the equation below,
n = (number of minutes)(rate at which the chair passes the exit platform)(number of persons per chair)
Substituting the known values to the equation,
n = (30 minutes)(1 chair / minute)(2 persons / chair)
n = 60 persons
Answer: 60 persons
Exponential:
It is called the exponential function of base a, to that whose generic form is f (x) = a ^ x, being a positive number other than 1.
Every exponential function of the form f (x) = a^x, complies with the followingProperties:
1. The function applied to the zero value is always equal to 1: f (0) = a ^ 0 = 1
2. The exponential function of 1 is always equal to the base: f (1) = a ^ 1 = a.
3. The exponential function of a sum of values is equal to the product of the application of said function on each value separately.
f (m + n) = a ^ (m + n) = a ^ m · a ^ n
= f (m) · f (n).
4. The exponential function of a subtraction is equal to the quotient of its application to the minuend divided by the application to the subtrahend:
f (p - q) = a ^ (p - q) = a ^ p / a ^ q
Logarithm:
In the loga (b), a is called the base of the logarithm and b is called an argument, with a and b positive.
Therefore, the definition of logarithm is:
loga b = n ---> a ^ n = b (a> 0, b> 0)
Take the width to be 1.7 feet and the length to be (2.2 + 0.9) feet.
Then the area is (1.7 ft)(3.1 ft) = 5.27 ft^2 (answer)
Answer:
Step-by-step explanation:
<u>Rates of Change as Derivatives</u>
If some variable V is a function of another variable r, we can compute the rate of change of one with respect to the other as the first derivative of V, or
The volume of a sphere of radius r is
The volume of the balloon is growing at a rate of 
. This can be written as
We need to compute the rate of change of the radius. Note that both the volume and the radius are functions of time, so we need to use the chain rule. Differentiating the volume with respect to t, we get
solving for 
We need to find the value of r, which can be obtained by using the condition that in that exact time
Simplifying and isolating r
![\displaystyle r=\sqrt[3]{512}=8\ cm](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Csqrt%5B3%5D%7B512%7D%3D8%5C%20cm)
Replacing in the rate of change
