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Veronika [31]
3 years ago
14

Round 2,461,612,242 to the nearest billion

Mathematics
2 answers:
beks73 [17]3 years ago
7 0

Answer:

2 billion

Step-by-step explanation:

if the # is 4 or brow you round down

Gre4nikov [31]3 years ago
6 0

Answer:

2,000,000,000.

Step-by-step explanation:

We know that when rounding, we take a look at the digit next to the digit we are rounding. So if I were to ask for you to round 122 to the nearest hundred, then the answer would be 100.

Remember that we round down if the digit next to it is 0-4. If the digit is 5-9, then we round up.

In this case, the digit next to the 2 is a 4. We know that we round down with a 4, so we go to the nearest whole billion, in this case 2 billion.

I hope this helps!

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Do 80 divided by 44%
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3 years ago
the expression 4(1.5g+ 3.5) is equal to 6g plus a constant term what is the value of the constant term
riadik2000 [5.3K]
4*3.5 =14.0
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3 0
3 years ago
Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.
Fantom [35]

Part 1: You can simplify a_n to

\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}

Presumably, the sequence starts at <em>n</em> = 1. It's easy to see that the sequence is strictly decreasing, since larger values of <em>n</em> make either fraction smaller.

(a) So, the sequence is bounded above by its first value,

|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}

(b) And because both fractions in a_n converge to 0, while remaining positive for any natural number <em>n</em>, the sequence is bounded below by 0,

|a_n| \ge \boxed{0}

(c) Finally, a_n is bounded above and below, so it is a bounded sequence.

Part 2: Yes, a_n is monotonic and strictly decreasing.

Part 3:

(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.

(b) Since a_n is decreasing and bounded below by 0, its limit as <em>n</em> goes to infinity is 0.

Part 4:

(a) We have

\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10

and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.

(b) Taking the limit gives

\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty

so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.

For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".

(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge

(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.

(e) does : this is true and is known as the monotone convergence theorem.

5 0
3 years ago
Please help me please
hram777 [196]

Answer:

detailed explanation is in image

Step-by-step explanation:

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4 0
2 years ago
Read 2 more answers
A thermometer is taken from a room where the temperature is 24oc to the outdoors, where the temperature is −15oc. After one minu
kap26 [50]

Solution:

Use Newton's Law of Cooling.  


T = T_s + (T_0 - T_s)*e^(-kt)  


where  

T = temperature at any instant  

T_s = temperature of surroundings  

T_0 = original temperature  

t = elapsed time  

k = constant  


Now, we need to find this constant. We are given that after one hour, the temperature drops to 13° C in a 7°C Environment.  

T = 14, T_0 = 24, T_s = -15, t = 1, k = ?  

T = T_s + (T_0 - T_s)*e^(-kt)  

==> 14 = -15 + (24 - 7)*e^(-k)  

==> 14 = 7 + 17*e^(-k)  

==> 7 = 17*e^(-k)  

==> 7/13 = e^(-k)  

==> -k = ln(7/17)  

==> k = -ln(7/17) ≈ 0.774  

Now,


Let's calculate temperatures!  

T = ?, T_0 = 24, T_s = -15, k = 0.773, t = 3  

T = T_s + (T_0 - T_s)*e^(-kt)  

==> T = -15 + (24 –(-15))*e^[ -(0.774)(2) ]  

==> T = -15 + 39*e^(-1.548)  

==> T ≈ 15.72° C  

This the required answer.


7 0
3 years ago
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