Mathematics, 17.09.2019 00:20 Arealbot

Athief steals a number of rare plants from a nursery. on the way out, the thief meets three security guards, one after another. to each security guard, the thief is forced to give one dash half of the plants that he still had, plus 2 more. finally, the thief leaves the nursery with 15 plants. how many plants were originally stolen?

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Answer from: azzyla2003

181 plants were originally stolen.

Step-by-step explanation:

To get the solution to this problem, We must go from the end to the beginning.

When the thief left the nursery, he had 15 plants left. That is equivalent to half of the plants he gave to the third guard plus two more plants. That's:

$\frac{x_1}{2} +2 = 15$

Where X3 is the amount of plants given to the 3rd. guard

Isolating x3

$\frac{x_3}{2}=15-2$

$\frac{x_3}{2}=13$

X3= 26 plants

When the thief met the third guard, he had 26 plants. From this amount we can calculate the amount of plants that the thief had when he met the second guard.

$\frac{x_2}{2} +2 = 26$

Where X2 is the amount of plants given to the 2nd. guard

Isolating x2

$\frac{x_2}{2}=26-2$

$\frac{x_2}{2}=24$

X2= 48 plants

When the thief met the second guard, he had 48 plants. From this amount we can calculate the amount of plants that the thief had when he met the first guard.

$\frac{x_1}{2} +2 = 48$

Where X1 is the amount of plants given to the 1st. guard

Isolating x1

$\frac{x_1}{2}=48-2$

$\frac{x_2}{2}=46$

X1= 92 plants

So, if we already know the amount of plants that the thief gave each guard, and also knowing that when he left the nursery he had 15 plants left, we can calculate the initial amount.

X_i - X_1 -X_2-X_3=15

Where Xi is the initial amount of plants.

Isolating Xi from the equation:

X_i= 15+ X_1+X_2+X_3

X_i=15+92+48+26

X_i= 181

So, 181 plants were originally stolen.

Answer from: Quest

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

= 2×(-2)+(-8)×(6)+(-8)×(-5)

= -4-48+40

= -12

hence, v.w= -12

Answer from: Quest

answer is 33

step-by-step explanation:

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