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3 years ago

What is the absolute value of 91?

1 answer:

7 0

$|a|= \left\{\begin{array}{ccc}a&if\ a\geq0\\-a&if\ a < 0\end{array}\right\\\\\\|91|\Rightarrow91 > 0\ therefore\ |91|=91\\\\Other\ examples:\\\\|4|\\4 > 0\Rightarrow|4|=4\\\\|-4|\\-4 < 0\Rightarrow|-4|=-(-4)=4$

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he half-life for a link on a social network website is 2.6 hours. Write an exponential function T that gives the percentage of

pychu [463]

Answer:

% Remaining $= [1-(1/2)^{\frac{t}{2.6}}]x100$

And replacing the value t =5.5 hours we got:

% Remaining $= [1-(1/2)^{\frac{5.5}{2.6}}]x100 =76.922\%$

Step-by-step explanation:

Previous concepts

The half-life is defined "as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not".

Solution to the problem

The half life model is given by the following expression:

$A(t) = A_o (1/2)^{\frac{t}{h}}$

Where A(t) represent the amount after t hours.

$A_o$ represent the initial amount

t the number of hours

h=2.6 hours the half life

And we want to estimate the % after 5.5 hours. On this case we can begin finding the amount after 5.5 hours like this:

$A(5.5) = A_o (1/2)^{\frac{5.5}{2.6}}$

Now in order to find the percentage relative to the initial amount w can use the definition of relative change like this:

% Remaining = $\frac{|A_o - A_o(1/2)^{\frac{5.5}{2.6}}|}{A_o} x100$

We can take common factor $A_o$ and we got:

% Remaining $= [1-(1/2)^{\frac{t}{2.6}}]x100$

And replacing the value t =5.5 hours we got:

% Remaining $= [1-(1/2)^{\frac{5.5}{2.6}}]x100 =76.922\%$

5 0

4 years ago

Find two unit vectos that are orthogonal to both [0,1,2] and [1,-2,3]

alekssr [168]

Answer:

Let the vectors be

a = [0, 1, 2] and

b = [1, -2, 3]

( 1 ) The cross product of a and b (a x b) is the vector that is perpendicular (orthogonal) to a and b.

Let the cross product be another vector c.

To find the cross product (c) of a and b, we have

$\left[\begin{array}{ccc}i&j&k\\0&1&2\\1&-2&3\end{array}\right]$

c = i(3 + 4) - j(0 - 2) + k(0 - 1)

c = 7i + 2j - k

c = [7, 2, -1]

( 2 ) Convert the orthogonal vector (c) to a unit vector using the formula:

c / | c |

Where | c | = √ (7)² + (2)² + (-1)² = 3√6

Therefore, the unit vector is

$\frac{[7,2,-1]}{3\sqrt{6} }$

[ $\frac{7}{3\sqrt{6} }$ , $\frac{2}{3\sqrt{6} }$ , $\frac{-1}{3\sqrt{6} }$ ]

The other unit vector which is also orthogonal to a and b is calculated by multiplying the first unit vector by -1. The result is as follows:

[ $\frac{-7}{3\sqrt{6} }$ , $\frac{-2}{3\sqrt{6} }$ , $\frac{1}{3\sqrt{6} }$ ]

In conclusion, the two unit vectors are;

[ $\frac{7}{3\sqrt{6} }$ , $\frac{2}{3\sqrt{6} }$ , $\frac{-1}{3\sqrt{6} }$ ]

and

[ $\frac{-7}{3\sqrt{6} }$ , $\frac{-2}{3\sqrt{6} }$ , $\frac{1}{3\sqrt{6} }$ ]

<em>Hope this helps!</em>

7 0

3 years ago

Domestic bees make their honeycomb by starting with a single hexagonal cell, then forming ring after ring of hexagonal cells aro

maw [93]

Answer:

aₙ= 6 n

Step-by-step explanation:

A honey comb cell contain 6 cells

a₁ = 6

d=6

aₙ = 6 + (n-1)6

= 6 n

7 0

4 years ago

The Jones family has saved a maximum of $750 for their family vacation to the beach. While planning the trip, they determine tha

stiks02 [169]

Answer:

Step-by-step explanation:

The Jones family has saved a maximum of $750 for their family vacation to the beach. It means that whatever they would do during the vacation, they cannot spend more than $750.

The inequality can be used to determine the number of nights the Jones family could spend at the hotel is

750 ≥ 75 + 125h

This can also be written as

75 + 125h ≤ 750

We would solve the inequality for the value of h.

125h ≤ 750 - 75

125h ≤ 675

h ≤ 675/125

h ≤ 5.4

For any value of h greater than 5.4 hours, the inequality will not be true.

4 0

3 years ago

The teacher decides that no student can win twice, so she removes the tickets of the first winner before drawing the second winn

trasher [3.6K]

Answer:

3/4

Step-by-step explanation:

Take Kitzen's number of raffle tickets and put them over Ava's tickets to give you 12/16 and the simplify which gives you 3/4 because the fraction is divisible by 4.

4 0

3 years ago