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Amanda [17]
3 years ago
14

The radius of a circle is the distance from its center to the edge of the circle. The diameter is the length of a line segment t

hat passes through the center and has endpoints on the edge of the circle. How are the radius and the diameter of a circle related? If needed, draw a picture on a piece of paper to help you explain.

Mathematics
2 answers:
katovenus [111]3 years ago
5 0

The relation is that the diameter is twice the length of the radius.

To make more proof, look at the attached image below.

mote1985 [20]3 years ago
5 0

Answer:

Step-by-step explanation:

hello :

the radius and the diameter of a circle related by this expression : d= 2r

d : diameter      r : radius

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If [infinity] cn8n n = 0 is convergent, can we conclude that each of the following series is convergent? (a) [infinity] cn(−3)n
pashok25 [27]

Answer:

a) we know that this is convergent.

b) we know that this might not converge.

Step-by-step explanation:

Given the \sum^\infty_{n=0}C_n8^n is convergent

Therefore,

(a)  \sum^\infty_{n=0}C_n(-3)^n The power series \sum C_nx^n has radius of convergence at least as big as 8. So we definitely know it converges for all x satisfying -8<x≤8. In particular for x = -3

∴ \sum^\infty_{n=0}C_n(-3)^n  is convergent.

(b) \sum^\infty_{n=0}C_n(-8)^n -8 could be right on the edge of the interval of convergence, and so might not converge

8 0
3 years ago
Provide an example of optimization problem
Mashutka [201]

Answer:

a. Convex solutions ,GO Methods

b. market efficiency

Explanation :

Step-by-step explanation:

A globally optimal solution is one where there are no other feasible solutions with better objective function values. A locally optimal solution is one where there are no other feasible solutions "in the vicinity" with better objective function values. You can picture this as a point at the top of a "peak" or at the bottom of a "valley" which may be formed by the objective function and/or the constraints -- but there may be a higher peak or a deeper valley far away from the current point.

In convex optimization problems, a locally optimal solution is also globally optimal. These include LP problems; QP problems where the objective is positive definite (if minimizing; negative definite if maximizing); and NLP problems where the objective is a convex function (if minimizing; concave if maximizing) and the constraints form a convex set. But many nonlinear problems are non-convex and are likely to have multiple locally optimal solutions, as in the chart below. (Click the chart to see a full-size image.) These problems are intrinsically very difficult to solve; and the time required to solve these problems to increases rapidly with the number of variables and constraints.

GO Methods

Multistart methods are a popular way to seek globally optimal solutions with the aid of a "classical" smooth nonlinear solver (that by itself finds only locally optimal solutions). The basic idea here is to automatically start the nonlinear Solver from randomly selected starting points, reaching different locally optimal solutions, then select the best of these as the proposed globally optimal solution. Multistart methods have a limited guarantee that (given certain assumptions about the problem) they will "converge in probability" to a globally optimal solution. This means that as the number of runs of the nonlinear Solver increases, the probability that the globally optimal solution has been found also increases towards 100%.

Where Multistart methods rely on random sampling of starting points, Continuous Branch and Bound methods are designed to systematically subdivide the feasible region into successively smaller subregions, and find locally optimal solutions in each subregion. The best of the locally optimally solutions is proposed as the globally optimal solution. Continuous Branch and Bound methods have a theoretical guarantee of convergence to the globally optimal solution, but this guarantee usually cannot be realized in a reasonable amount of computing time, for problems of more than a small number of variables. Hence many Continuous Branch and Bound methods also use some kind of random or statistical sampling to improve performance.

Genetic Algorithms, Tabu Search and Scatter Search are designed to find "good" solutions to nonsmooth optimization problems, but they can also be applied to smooth nonlinear problems to seek a globally optimal solution. They are often effective at finding better solutions than a "classic" smooth nonlinear solver alone, but they usually take much more computing time, and they offer no guarantees of convergence, or tests for having reached the globally optimal solution.

5 0
3 years ago
How to make an equation with numbers 0.25, 7.00, and 27
shepuryov [24]
There are many ways to do this.

One way could be 0.25x+7.00=27
8 0
3 years ago
Solve the system using substitution.<br> 2x = 5y + 14<br> x = 5y
andrew-mc [135]

Answer:

<h2>y = 2.8</h2><h2>x = 14</h2>

Step-by-step explanation:

To solve an equation, we can only have one variable. In this case, we are given the system 2x = 5y + 14. However, we are given the value of x in terms of y. We can substitute 10y in for 2x and solve.

10y = 5y + 14

First, we need to get all the variables on one side of the equation, so we subtract 5y.

5y = 14

Divide by 5

y = 14/5 or 2 4/5 or 2.8

Now for the x part.

2x = x + 14

Subtract 1x

x = 14

Now we check our answer.

2(14) = 5(2.8) + 14

28 = 14 + 14

28 = 28

Because 28 equals 28, our solutions are correct.

7 0
3 years ago
Simplify 2(5x – 4) + 3x
guapka [62]
To simplify, you must distribute the 2 into the 5x and -4 by multiplying 2 with 5x and 2 with -4.

<span>2(5x – 4) + 3x

2 x 5x = 10x

2 x -4 = -8

 You will get 10x - 8 + 3x

Now you must combine like terms or add like terms. In this case we must add 10x and 3x

10x + 3x = 13x

Finally the answer would be 13x - 8</span>
6 0
3 years ago
Read 2 more answers
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