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storchak [24]
3 years ago
10

Alberta is going to have dinner at her grandmother's house, but she is running a bit behind schedule. as she gets onto the highw

ay, she knows that she must exit the highway within 58 min if she is not going to arrive late. her exit is 43 mi away. how much time would it take at the posted 60 mph speed?
Mathematics
1 answer:
garri49 [273]3 years ago
4 0
<span>If there are 60 seconds in a minute and 60 minutes in an hour, while you're traveling 60 miles an hour, that should reduce to 6 miles every 6 minutes. That's equivalent to 1 minute per mile. so if you're travelling 60 miles for 60 minutes, it means that it takes 1 minute to travel 1 mile. so the answer is 60 min


</span>
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18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:
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a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}

S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525

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