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MA_775_DIABLO [31]
3 years ago
5

Sarah lives 1,493 miles from her grandmother. One year, sarah's family made 4round trips to visit her grandmother. How many mile

s dis they travel in all?
Mathematics
2 answers:
UkoKoshka [18]3 years ago
4 0
Since it says round trip, you have to multiply the number of miles it gave you by two and then by four since they made four trips. this means that the answer is 11,944.
Viefleur [7K]3 years ago
4 0
4 round trips = 8 total trips (back and forth)

8 * 1493 = 11,944 miles <==
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What is the length of the arc intercepted by an angle of 10 degrees on a circle with a radius of 10 meters?
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\displaystyle\\&#10;\texttt{Length of the arc }= 2\pi R\times  \frac{10}{360} = \frac{2\pi \times 10}{36} = \frac{20\pi}{36} =  \boxed{\frac{5\pi}{9}~m}



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3 years ago
Help, i will give brainliest
andrey2020 [161]

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8 0
3 years ago
Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

so that \{b_n\} = \{4, 6, 8, 10, 12, \ldots\}.

Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

and we see that this is a constant sequence, \{c_n\} = \{2, 2, 2, 2, \ldots\}. In other words, \{b_n\} is an arithmetic sequence with common difference between terms of 2. That is,

2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2

and we can solve for b_n in terms of b_1=4:

b_{n+1} = b_n + 2

b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2

b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2

and so on down to

b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)

We solve for a_n in the same way.

2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

6 0
2 years ago
I NEED THE CORRECT ANSWER TO THIS ASAP FOR A TEST!!!!! What is the solution to the inequality?
garik1379 [7]
The correct answer is c , m<6
6 0
3 years ago
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