A tank with some water in it begins to drain. The function v(t)=53−2.7t determines the volume of the water in the tank (in gallons) given a number of minutes t since the water began draining. What is the value of the vertical intercept of the function v, and what does this value represent in the context of the problem? The vertical intercept is 53, and it represents the number of gallons of water in the tank when it starts draining. The vertical intercept is 53, and it represents how many minutes it takes for all of the water to drain from the tank. The vertical intercept is 19.63, and it represents the number of gallons of water in the tank when it starts draining. The vertical intercept is 53, and it represents the weight of the tank when it is empty. The vertical intercept is −2.7 and it represents the time value when the tank is full.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
A tank with some water in it begins to drain. The function v(t)=53−2.7t determines the volume of the water in the tank (in gallons) given a number of minutes t since the water began draining.
What is the value of the vertical intercept of the function v, and what does this value represent in the context of the problem?
- The vertical intercept is 53, and it represents the number of gallons of water in the tank when it starts draining.
- The vertical intercept is 53, and it represents how many minutes it takes for all of the water to drain from the tank.
- The vertical intercept is 19.63, and it represents the number of gallons of water in the tank when it starts draining.
- The vertical intercept is 53, and it represents the weight of the tank when it is empty.
- The vertical intercept is −2.7 and it represents the time value when the tank is full.
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