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Leno4ka [110]
3 years ago
11

What is the answer to question 4,5,6

Mathematics
1 answer:
alex41 [277]3 years ago
7 0
4:polygon
5:heptagon and trapoziod or parallelogram
You might be interested in
What is the essence of calculus? <br>*friendship​
iragen [17]

Differential Calculus, or Differentiation

If we have a function of one variable, ie of the form y=f(x), then in its most basic form differentiation is the study of how a small change in one variable x affects the other variable y.

As an real life example, consider the average speed of a moving car:

average speed = distance travelled/ time taken

Obviously, this is an average by definition, but if there existed a formal mathematical link between distance and time, could we build a function that would tell us the instantaneous velocity at every given moment? The study of differential calculus gives strategies for calculating the ratio of a little change in distance to a small change in time, and then calculating the real instantaneous speed by making the small change infinitely small.

Similarly if we wanted to find the gradient of the tangent to a curve at some particular point A we would estimate the gradient by using a chord to a nearby point B. As we move this nearby point B  closer to the tangent point A the slope of the chord approaches the slope of the tangent with more and more accuracy. Again differential calculus provides techniques for us to make the point B infinitesimally close to the point A o that we can calculate the actual gradient of the tangent.

Integral Calculus, or Integration

Suppose we wanted to calculate the area under a curve, y=f(x),  bounded the x =axis, and two points a and b. We could start by splitting the interval  [a,b]  into n regular strips, and estimating the area under the curve using trapezia (this is the essence of the trapezium rule which provides an estimate of such an area). If we increase n then generally we would hope for a better approximation. The study of integration provides techniques for us to take an infinitely large number of infinitesimally small strips to gain an exact solution.

The Fundamental Theorem of Calculus

Given the above two notions, it would appear that there is no connection between them at first., The Fundamental Theorem of Calculus, on the other hand, is a theorem that connects the rate of change of the area function (which determines the area under a curve) to the function itself. In other words, the area function's derivative equals the function itself.

Visual for  Fundamental Theorem of Calculus for integrals:

\int\limits^b_af {(x)} \, dx =F(b)-F(a).

where F is an antiderivative of f

Physics, Chemistry, all engineering sciences, statistics, economics, finance, biology, computer science, linguistics, to name but a few, are all areas that would be a desert without the use of calculus.

Leibnitz and Newton worked to define the velocity of a planet moving on a curved trajectory. That was not possible without calculus, and both had to invent differential calculus. Differential calculus allows to compare quantities along a curve, and thus their time rate of change.

All of classical physics can be summarized in this operation. Given second derivative (which is Force/mass), find the position as a function of time. This process is called integration. Half of calculus is made with integration, the other half with derivation. All of classical physics rests on these two parts of the calculus.

Quantum mechanics, quantum field theory, electromagnetism, fluid mechanics all use integration and derivation and much more. I rest my case. I hope this helps you gauge the place that calculus occupies in science.

4 0
2 years ago
Read 2 more answers
Which expression is equivalent to 2 (t-4) +1. A 2t-5 B.2t-7 C. 2t-9 D. 2t -3
seraphim [82]

Answer: 2t + -8

Step-by-step explanation: Let's simplify this problem using the distributive property.

The first thing we want to do is change this minus to plus a negative.

Now we can distribute or multiply this 2 times

each of the terms inside the set of parentheses.

So we get 2(t) + 2(-4) and this simplifies to 2t + -8.

2t + -8 is the same thing as 2t -8.

8 0
3 years ago
when two trucks traveling in different directions approach each an intersection at the same time , on of the trucks must change
torisob [31]

This happens because the trucks move in one-dimension, while the airplanes move in 3 dimensions.

<h3></h3><h3>Why the trucks need to change direction or speed while the airplanes don't?</h3>

Well, the trucks move along a street. Thus, we can think that this is an one-dimensional kind of motion.

Where the trucks can go forward, backward, or get out of the line.

In the case of the airplanes, they can move actually in 3 dimensions (the airplane can go upwards, downwards, left, right, etc).

Now, in the one-dimensional case of the trucks there are only two directions (which are opposite) so if the trucks travel in different directions, then the trucks travel into each other, which would cause the collision.

While in the case of the airplanes more directions exists, so there isn't (necessarily) a collision.

If you want to learn more about motion:

brainly.com/question/26048315

#SPJ1

4 0
2 years ago
(6 x2 - 6x + 4) - (x2 – 5x – 9)
DedPeter [7]
The answer is 9x+13
4 0
3 years ago
What is 12.31 as a mixed fraction
VashaNatasha [74]
12 31/100 is the mixed fraction because in a decimal all the numbers to the left are whole numbers and all the numbers to the right are numbers that are part of a whole. Just like in a mixed fraction there is a whole number and a fraction in a mixed number. Since 12 is in the left it is the whole number and since 31 is to the right and in the place value 31 is ending in the hundredths place so that's why the fraction is, 31/100. That's how you came to know that 12 31/100 is the fraction for 12.31.
4 0
3 years ago
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