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Eva8 [605]
2 years ago
9

For positive integer n, the factorial notation n! represents the product of the integers from n to 1. (For example, 6! = 6*5*4*3

*2*1.) What value of n satisfies the following equation?
5! X 9! = 12! x N
Mathematics
1 answer:
Novay_Z [31]2 years ago
8 0

Answer:

The value of N that satisfies the equation is \frac{1}{11}

Step-by-step explanation:

First we open the factorial of 12, to simplify the expression:

12! = 12*11*10*9!

So

5!*9! = 12!*N

5!*9! = 12*11*10*9!N

12*11*10N = 5!

Now we open the factorial of 5. So

12*11*10*N = 5*4*3*2*1

Since 5*2 = 10, 4*3 = 12, we have that:

12*11*10*N = 10*12*1

Now, simplifying by 10*12

11N = 1

N = \frac{1}{11}

This is the value of N that satisfies the equation

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Let f (x, y) = x3 + y3 x2 + y2 . (a) Show that |x3|≤|x|(x2 + y2), |y3|≤|y|(x2 + y2) (b) Show that |f (x, y)|≤|x|+|y|. (c) Use th
GarryVolchara [31]

Answer and Step-by-step explanation:

a.)x^2 and y^2 are always greater than zero.(assuming real x and y).

=>x^2<=x^2+y^2

=>|x|(x^2)<=|x|(x^2+y^2)

=>|x^3|<=|x|(x^2+y^2)

b. similarly, |y^3|<=|y|(x^2+y^2)

=>|f(x,y)|=|x^3+y^3|/(x^2+y^2)=|x|+|y|

c. let h is very small number (close to zero but positive)

lim (x,y)-> (0,0) f(x,y)=(x^3+y^3)/(x^2+y^2)

putting x=h and y=h and approaching h->0

lim h->0 f(h)=2h=0

There is another explanation attached below

4 0
2 years ago
I need help with this question
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Answer:

  1024

Step-by-step explanation:

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3 divisions: 2×(2×2) = 8

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After 10 divisions, there are 2^10 = 1024 viruses.

4 0
2 years ago
Find the angle θ between u = &lt;7, –2&gt; and v = &lt;–1, 2&gt;.
Dmitry_Shevchenko [17]

The angle between two vectors is:

CosФ = u - v / Magnitude(u) x magnitude(v)

Magnitude of u = SQRT(7^2 + -2^2) = SQRT(49 +4) = SQRT(53)

Magnitude of v = SQRT(-1^2 +2^2) = SQRT(1 +4) = SQRT(5)

u x v = (7 x -1) + (-2 x 2) = -7 + -4 = -11

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7 0
3 years ago
Read 2 more answers
Of the people who fished at Clearwater Park today, 48 had a fishing license, 32and did not. Of the people who fished at Mountain
horrorfan [7]

Answer:

The probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

Step-by-step explanation:

Denote the events as follows:

<em>X</em> = a fisher at Clearwater Park had a fishing license

<em>Y</em> = a fisher at Mountain View Park had a fishing license

The two events are independent.

The information provided is:

n (X) = 48

n (X') = 32

n (Y) = 72

n (Y') = 18

Then,

N (X) = n (X) + n (X')

        = 48 + 32

        = 80

N (Y) = n (Y) + n (Y')

        = 72 + 18

        = 90

Compute the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license as follows:

P(X'\cap Y)=P(X')\times P(Y)

                 =\frac{n(X')}{N(X)}\times \frac{n(Y)}{N(Y)} \\\\=\frac{32}{80}\times\frac{72}{90}\\\\=0.32

Thus, the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

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