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d1i1m1o1n [39]
3 years ago
9

An ant went 2 meters away from its nest searching for food. The next time, the ant went 3 meters away. Each successive time the

ant leaves the nest to search for food, the ant travels the sum of the two previous times. How far will the ant travel on his fifth trip?
Mathematics
1 answer:
seropon [69]3 years ago
8 0

Answer:

The first time, the ant went 2m away, then we have a₁ = 2m

The second time, the ant went 3m away, then we have a₂ = 3m

The next time, the ant went a distance equal to the sum of the two previous ones, so we can write it in a general case as:

aₙ = aₙ₋₁ + aₙ₋₂

Only if n > 2.

then the third time, we have n = 3.

a₃ = a₂ + a₁ = 2m + 3m = 5m

a₄ = a₃ + a₂ = 3m + 5m = 8m

a₅ = a₄ + a₃ = 5m + 8m = 13m

This means that in the fifth trip, the ant went 13 meters away from its nest.

And if we consider the fact that the ant must go and return, then it will move a total distance of 13 meters two times, or 2*13m = 26 meters.

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Answer:

22.4 hours

Step-by-step explanation:

The population of bacteria is modelled by the equation:

P=P_0e^{rt}

From the the question, the initial population of bacteria is 720.

So after 26 hours, we have:

P=2P_0

This implies that:

2P_0=P_0e^{26r}

2=e^{26r}

26r =  ln(2)

r =  \frac{ ln(2) }{26}

r = 0.0267

We want to find how long it will take for there to be 1310 bacteria present.

1310=720e^{0.0267t}

\frac{1310}{720}  =  {e}^{0.0267t}

\ln(\frac{1310}{720})  = {0.0267t}

0.59853= {0.0267t}  \\ t =  \frac{0.59853}{0.0267}

t = 22.417

To the nearest tenth , it will take 22.4 hours

6 0
3 years ago
What is the area of the triangle below?
Novay_Z [31]
The answer is B:68

All you have to do is base times height and divide by 2

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4 0
3 years ago
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Dennis_Churaev [7]
Our current equation is:
-8r -31 = -3(5r -6)
To solve for this, we need to get r on one side of the equation and then simplify if needed.
On the right side of the equation, we have a pending Distributive Property, which is when you multiply the number/variable outside of the parenthesis by all numbers/variables in the parenthesis.
Let's simplify this Distributive Property to help understand our equation better.
-3(5r -6)
Multiply -3 by each number/variable separately (unless they are already being multiplied, like 2x, 1/2x, etc).
-3(5r) + -3(-6).
-3(5r) = -15r
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Your equation now is:
-8r -31 = -15r + 18
Add 15r to both sides to get r on one side.
7r -31 = 18 is now our current equation.
Add 31 to both sides to get 7r by itself.
7r = 49 is now our equation.
r is still being multiplied by 7, so we need to do the opposite of multiplying by 7.
Divide both sides by 7.
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I hope this helps!
8 0
3 years ago
Someone please show me how to do this
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The 1 represents the y intercept so a point is (0,1). To find other points, plug in values for x. For example, plus in x and you get a y value of 2. So just plot a number of points and then connect them with a curved line( called a parabola).
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