Find the unknown angle

tresset_1 [31]

3.14?

or do you want more digits?

3.141592653589793238462643383279502884197169399375105820974944592307816406286<span> </span>

3 0

3 years ago

Read 2 more answers

What is the difference between a factor of a number and a multiple of a number? use the number 25 has an example

Ne4ueva [31]

Answer:

factor: a submultiple; an integer value that gives an integer quotient when the number is divided by it.
multiple: the product of the number and another integer

Step-by-step explanation:

<h3>Factors</h3>

A set of factors of a number (N) is a set of integers {f1, f2, f3, ...} whose product is the number:

f1 × f2 × f3 × ... = N

Often the term "factors" is used to mean "prime factors," the set of prime numbers whose product is N.

When N = 25, the prime factors are {5, 5}. That is ...

5×5 = 25

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<h3>Divisors</h3>

A "divisor" of a number is a sub-multiple of N. That is, the quotient N/k is an integer for some divisor k of N. Usually, we're interested in integer divisors. All prime factors will be integer divisors of N. The term "factor" is often used when the term "divisor" is meant.

Divisors of N = 25 include 1, 5, and 25. There will be an odd number of integer divisors (as here) if the number N is a perfect square.

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<h3>Multiples</h3>

For an integer k, the value k×N is called a <em>multiple</em> of N, often, the <em>k-th multiple</em> of N.

Multiples of 25 include 25, 50, 75, 100, 125, and any other decimal number ending in 25, 50, 75, or 00.

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<em>Another example</em>

When N=30, the prime factors are {2, 3, 5}. The divisors are {1, 2, 3, 5, 6, 10, 15, 30}. (Note there are an even number of divisors.) Multiples of 30 include 30, 60, 90, 120, ....

6 0

2 years ago

Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be

Travka [436]

Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

dA/dt = in flow - out flow

Since litter falls at a constant rate of L grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

1/k∫-kdA/(L - Ak) = ∫dt

1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C' (C' = kC)

taking exponents of both sides, we have

$L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}$

When t = 0, A(0) = 0 (since the forest floor is initially clear)

$A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L$