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Alexxandr [17]
3 years ago
5

A cylinder has radius r and height h. a. How many times greater is the surface area of a cylinder when both dimensions are multi

plied by a factor of 2? 3? 5? 10? b. Describe the pattern in part (a). How many times greater is the surface area of a cylinder when both dimensions are multiplied by a factor of 20?
Mathematics
1 answer:
kondor19780726 [428]3 years ago
3 0
To find it directly

A = 2 pi r h

A is proportional to rh

factor 2

A is multiplied by 2 * 2 = 4

factor 3

3 * 3 =9

factor 5

5 * 5 = 25

factor 10 

10 * 10 = 100

(b) the increase in A by factor x is x^2

c(20)^2 = 400 
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How do I solve polynomials
spin [16.1K]

Answer:

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

Also they can have one or more terms, but not an infinite number of terms.

These are polynomials:

3x

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512v5 + 99w5

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(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)

 

These are not polynomials

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2/(x+2) is not, because dividing by a variable is not allowed

1/x is not either

√x is not, because the exponent is "½" (see fractional exponents)

 

But these are allowed:

x/2 is allowed, because you can divide by a constant

also 3x/8 for the same reason

√2 is allowed, because it is a constant (= 1.4142...etc)

Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

monomial, binomial, trinomial

Variables

Polynomials can have no variable at all

Example: 21 is a polynomial. It has just one term, which is a constant.

Or one variable

Example: x4 − 2x2 + x   has three terms, but only one variable (x)

Or two or more variables

Example: xy4 − 5x2z   has two terms, and three variables (x, y and z)

What is Special About Polynomials?

Because of the strict definition, polynomials are easy to work with.

For example we know that:

If you add polynomials you get a polynomial

If you multiply polynomials you get a polynomial

So you can do lots of additions and multiplications, and still have a polynomial as the result.

Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines.

Example: x4−2x2+x

x^4-2x^2+x  

See how nice and

smooth the curve is?

You can also divide polynomials (but the result may not be a polynomial).

Degree

The degree of a polynomial with only one variable is the largest exponent of that variable.

Example:

4x3-x-3 The Degree is 3 (the largest exponent of x)

For more complicated cases, read Degree (of an Expression).

Standard Form

The Standard Form for writing a polynomial is to put the terms with the highest degree first.

Example: Put this in Standard Form: 3x2 − 7 + 4x3 + x6

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x6 + 4x3 + 3x2 − 7

You don't have to use Standard Form, but it helps.

5 0
3 years ago
Use a double angle identity to rewrite the formula r(Θ)=<img src="https://tex.z-dn.net/?f=1%2F16v%5E2sin%28theta%29cos%28theta%2
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Answer:

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Given the expression r(theta) = 1/16v²sinθcosθ

According to double angle of trigonometry identity;

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Sin2θ = sinθcosθ + cosθsinθ

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Substituting equation ** into the question

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Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ

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I’m having trouble. Help me please!!!
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Hopes this helps:

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