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Ostrovityanka [42]

3 years ago

9

A student wants to conduct an experiment to see how quickly information can travel. On Day 1 of the experiment, the student tell

s three friends a personal fact. On Day 2, those three friends share the fact with three new people each. Assuming this pattern continues, how many people will hear the fact on Day 7 of the experiment?

1 answer:

Aliun [14]3 years ago

7 0

3 people know a fact in 1st day.
In 2nd day they share it with 3 people each=3×3
Now 3×3 people shares it with 3 people each. and so on...
So,
3+3²+3³+3⁴+3^5+3^6+3^7
=3279 no of people altogether , will hear from 1st day to 7th day...
On the day 7,no of people who will hear the fact=3^7=2187

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A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

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Answer:

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Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

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$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

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This our equation of the arch!

5 0

3 years ago

Marcy wants to paint the sides of the wooden storage chest shown below gray except the white lid. What is the surface area?

arlik [135]

Answer:

Surface area = 2,160 in²

Step-by-step explanation:

Given:

Length of box = 15 in

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Height of box = 24 in

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Surface area = 2,160 in²

7 0

2 years ago