All categories

3 years ago

What is the value of largest integers x such that 112/2^x is an integer.

Mathematics

1 answer:

Gennadij [26K]3 years ago

6 0

Answer:

x = 4

Step-by-step explanation:

16 × 7 = 112

2^4 = 16

so that is the answer

You might be interested in

A polynomial is graphed. What could the equation of p?<br> P(c)=(x+3)(c+1)(2x+1)

anygoal [31]

Answer:

penis

Step-by-step explanation:

big penis

8 0

3 years ago

Read 2 more answers

GIVING BRAINLIEST AND 100-50 POINTS

zloy xaker [14]

3. the greatest amount is 3

4. the least amount is 1 4/6
5. 3 + 1 4/6= 4 2/3
6. 3 - 1 4/6= 1 1/3

3 0

2 years ago

Read 2 more answers

Help me please!<br><br><br> I will give Brainliest!

STALIN [3.7K]

Answer:

Step-by-step explanation:

-3+4=1

negative 3 - negative 4

4 0

3 years ago

The following is a Markov (migration) matrix for three locations

mel-nik [20]

Answer:

(a) $\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}$

(b) After an infinite period of time; we will get back to a result similar to after the two time period which will be $= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}$

Step-by-step explanation:

The Markov Matrix can be interpret as :

$M = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right]$

From (a) ; we see that the initial population are as follows: 130 individuals in location 1, 300 in location 2, and 70 in location 3.

Le P represent the Population; So ; $P = \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right]$

The objective is to find How many are in each location after two time periods;

So, after two time period ; we have the population $P_2 = [M]^2 [P]$

where;

$[M]^ 2 = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right] \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right]$

$[M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc} 1+2+4 & 1+2+4 &1+2+4 \\ \\ 2+2+4&2+2+4&2+2+4\\ \\ 2+4+4&2+4+4& 2+4+4 \end{array}\right]$

$[M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right]$

Now; Over to after two time period ; when the population $P_2 = [M]^2 [P]$

$P_2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right] \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right]$

$\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}$

(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?

After a long time; that is referring to an infinite time (n)

So; $P_n = [M]^n [P]$

where ;

$[M]^n \ can \ be \ [M]^2 , [M]^3 , [M]^4 .... \infty$

; if we determine the respective values of $[M]^2 , [M]^3 , [M]^4 .... \infty$ we will always result to the value for $[M]^n$ ; Now if $[M]^n$ is said to be a positive integer; then :

After an infinite period of time; we will get back to a result similar to after the two time period which will be $= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}$

8 0

3 years ago

Help me pls w dis question

Harman [31]

Answer:

x = 2 and x = 5

Step-by-step explanation:

What are the roots of an equation?

In simple terms, the roots are simply the x intercepts of an equation.

How to find the roots of a quadratic equation:

We can find the roots of a quadratic equation one of three ways. Here you will learn how to do all three ways.

The first way (easiest way) :

The first way to find the roots of a quadratic equation is to graph the equation on a calculator and find where the equation crosses the x axis ( these are the x intercepts )

If you look at the attached image, you see the given equation x² - 7x + 10 = 0 graphed. The equation passes the x axis at (2,0) and (5,0) meaning the roots are x = 2 and x = 5.

Second way : Using the quadratic formula:

If you don't have a calculator or don't know how to graph the equation this is the best alternative way to find the roots.

The quadratic formula is : $\frac{-b\pm\sqrt{b^2-4(a)(c)} }{2(a)}$

Where the values of a,b and c are derived from the quadratic equation which should be written in quadratic form : ax² + bx + c = 0

This is the case here so we can easily define our variables and plug them into our formula

We have "ax² + bx + c = 0" = x² - 7x + 10 = 0 so we can say a = 1 , b = -7 and c = 10

We now plug these into the formula

Recall formula : $\frac{-b\pm\sqrt{b^2-4(a)(c)} }{2(a)}$

==> plug in a = 1 , b = -7 and c = 10

$\frac{-(-7)\pm\sqrt{(-7)^2-4(10)(1))} }{2(1)}$

==> remove parenthesis from -(-7)

$\frac{7\pm\sqrt{(-7)^2-4(10)(1))} }{2(1)}$

==> simplify exponents

$\frac{7\pm\sqrt{(49-4(10)(1))} }{2(1)}$

==> simplify all multiplication

$\frac{7\pm\sqrt{49-40} }{2}$

==> subtract 40 from 49

$\frac{7\pm\sqrt{9} }{2}$

==> simplify sqrt

$\frac{7\pm3 }{2}$

==> simplify +/-

$\frac{7+3 }{2},\frac{7-3 }{2}\\\frac{10 }{2},\frac{4 }{2}$

==> simplify division

5 , 2

The roots are x = 5 and x = 2

( Note that we used BPEMDAS to evaluate the formula when the values of a,b and c were plugged in. BPEMDAS is simply folllowing an order of operations to ensure you get the right answer. The order is as follows : Brackets , Parenthesis (any operations inside of parenthesis) , Exponents , Multiplication and Division ( do in order going left to right ) , Addition and Subtract ( do in order going left to right )

Also note that the quadratic formula ALWAYS WORKS.

Last way: Factoring

Finally, we can also find the roots by factoring.

We have x² - 7x + 10 = 0

We must first find a number that multiplies to 10 and adds to -7

We can do so by listing the factors of 10

Factors of 10 include , 10 and 1 , -10 and -1 , -5 and -2, and 5 and 2

Out of these we want to find the multiples that add to -7

10 + 1 = 11

-10 + -1 = -11

-5 + - 2 = -7

5 + 2 = 7

The multiples that add to -7 are -5 and -2 .

From there we want to split the -7 and x² to get (x-5)(x-2)

We then solve the roots by setting the individual factors to 0

x - 5 = 0

==> add 5 to both sides

x = 5

x - 2 = 0

==> add 2 to both sides

x = 2

8 0

2 years ago

What is the value of largest integers x such that 112/2^x is an integer.​

What is the value of largest integers x such that 112/2^x is an integer.