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What is cubic growth and how does it differ from exponential growth?
Cubic Growth is x^a, a being some constant, while exponential growth is a^x. Exponential growth ends up growing MUCH faster than cubic growth.
What characteristics of the graph of a function by using the concept of differentiation first and second derivatives?
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
Three angles of a triangle always add up to how many degrees?
The sum of the three angles of a triangle is always 180º
Can a triangle add up to 190 degrees?
No, always 180 degrees.
Are two angles that are supplementary congruent?
They can be but not always because supplementary angles add up to 180 degrees.
How are the graphs of exponential growth and exponential decay functions different?
Exponential growth goes infinitely up. Exponential decay goes infinitely over always getting closer to the x axis but never reaching it. ADDED: An exponential decay trace's flat-looking region has its own special name: an "asymptote".
What math book did Rudiger Gamm learn math from?
He memorized tables of functions, exponential functions, logarithmic functions, etc, ... try looking up "handbook of mathematical functions"
What does 'concave up' mean in physics terms?
In physics, 'concave up' refers to the shape of a curve or surface that opens upward, resembling a cup that faces upwards. This typically signifies a region where the rate of change of a function is increasing. It is often associated with the idea of a positive second derivative.
Is a spoon concave or convex?
A spoon is concave, as its bowl-like shape curves inward. This concave shape allows the spoon to hold and scoop up food effectively.
A film artists use concave mirror when applying make up?
A film artist typically uses a concave mirror when applying make-up. The reason for this is that a concave mirror produces an erect, virtual and highly magnified image.
Can exponential graphs be concave up decreasing?
Yes. A simple example is the graph of the function y=e-x This is a simple manipulation of a basic exponential function, y=ex. Graphically it is obvious that this function is decreasing and concave upward across it entire domain, but it is easy to show this mathematically as well For, the function y=e -x, the basic pattern for exponential derivatives, as well as the chain rule, will supply the first and second derivatives of this function, which will be necessary to mathematically determine the concavity and "slope" of this function. I will assume you know how to do basic derivatives since you are asking this question. You seem to be well entrenched in typical curriculum for a derivative calculus course. I will list the original function and its first and second derivatives below: f(x)=e-x f'(x)=-e-x f''(x)=e-x When the first derivative is examined, you will notice that regardless of what number is input for the variable "x", the result will always be negative, which proves that the function will remain decreasing for its entirety. When the second derivative is examined, you will notice that regardless of what number is input for the variable "x", the result will always be positive. This proves that the function will remain upwardly concave for its entirety. You can also use the fact that if f(x)=ex then f(-x) = e-x and we have created a reflection across the y axis since that is what f(-x) does. The reflection does not change the fact the graph is concave up, but it does show it is decreasing. The fact that the second derivative is greater than 0 confirms this. As you remember, is says if f"(x) is greater than 0 for all x on some interval I, then f(x) is concave up on I.
How are exponential growth patterns similar to and different from linear growth patterns?
They are similar because the population increases over time in both cases, and also because you are using a mathematical model for a real-world process. They are different because exponential growth can get dramatically big and bigger after a fairly short time. Linear growth keeps going up the same amount each time. Exponential growth goes up by more each time, depending on what the amount (population) is at that time. Linear growth can start off bigger than exponential growth, but exponential growth will always win out.
Is a virtual and inverted image formed by a concave mirror?
Your right! You see technically we see up side down but with the light we see right side up so what that means is yes it is upside down. Well, since the brain doesn't turn it "right side up" it could be either way that you look at it.
What is mellow concave?
First you have to understand concave. Concave is a term of the curve of the deck. Not from nose to tail, but from side to side. You will notice the board dips down in the middle (or comes up on the sides, however you want to look at it). This allows your heels/toes to flick the board for kickflips and heelflips. The deeper the groove (or the more the side come up) the more the concave. So, for a board to have mellow concave it is more flat.
Why not concave mirrors are suitable for make up?
Both concave and convex mirrors will distort the image of the face if used when applying make-up. Which is why flat mirrors are used instead.
What is a make up mirror Concave or Convex?
A makeup mirror is typically concave. Concave mirrors curve inward and are used to magnify reflections, making them useful for applying makeup. The concave shape helps to focus light on the face for detailed and accurate application.
If the acceleration is increasing with time will the velocity graph be a straight line concave up or concave down?
If acceleration is increasing with time, the velocity graph will be concave up. This is because a positive acceleration causes the velocity to increase over time, resulting in a curve that opens upward on the velocity-time graph.
