Answer:
0.448 seconds
Step-by-step explanation:
d = -16t² -4t + 412
find t when d = 407
substituting d = 407 into the equation:
407 = -16t² -4t + 412 (subtract 407 from both sides)
-16t² -4t + 412 - 407 = 0
-16t² -4t + 5 = 0 (multiply both sides by -1)
16t² + 4t - 5 = 0
solving using your method of choice (i.e completing the square or using the quadratic equation), you will end up with
t = (-1/8) (1 + √21)= -0.70 seconds (not possible because time cannot be negative)
or
t = (-1/8) (1 -√21) = 0.448 seconds (answer)
Answer:
irrational
are the numbers like 7.55782902..where the numbers aren't repeated
The sequence is given as follow
![3a](https://tex.z-dn.net/?f=3a)
,
![3 a^{2}b,3 a^{3} b^{2} , 3 a^{4} b^{3}](https://tex.z-dn.net/?f=3%20a%5E%7B2%7Db%2C3%20a%5E%7B3%7D%20b%5E%7B2%7D%20%2C%203%20a%5E%7B4%7D%20b%5E%7B3%7D%20)
When finding the pattern of a sequence, we can try to work out whether there is a common difference or a common ratio between each term. We try by finding a common ratio
![\frac{3 a^{2}b }{3a} =ab](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%20a%5E%7B2%7Db%20%7D%7B3a%7D%20%3Dab)
![\frac{3 a^{3 b^{2} } }{3 a^{2}b }=ab](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%20a%5E%7B3%20b%5E%7B2%7D%20%7D%20%7D%7B3%20a%5E%7B2%7Db%20%7D%3Dab%20)
![\frac{3 a^{4} b^{3} }{3 a^{3} b^{2} }=ab](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%20a%5E%7B4%7D%20b%5E%7B3%7D%20%7D%7B3%20a%5E%7B3%7D%20b%5E%7B2%7D%20%7D%3Dab%20)
The term to term rule is multiplied by
![ab](https://tex.z-dn.net/?f=ab)
The
![5^{th}](https://tex.z-dn.net/?f=%205%5E%7Bth%7D%20)
term is given
![3 a ^{4} b^{3}](https://tex.z-dn.net/?f=3%20a%20%5E%7B4%7D%20b%5E%7B3%7D%20)
×
![ab=3 a^{5} b^{4}](https://tex.z-dn.net/?f=ab%3D3%20a%5E%7B5%7D%20b%5E%7B4%7D%20%20)
The
![6^{th}](https://tex.z-dn.net/?f=%206%5E%7Bth%7D%20)
term is given by
![3 a^{5} b^{4}](https://tex.z-dn.net/?f=3%20a%5E%7B5%7D%20b%5E%7B4%7D%20%20)
×
Answer:
648,294,565,652
Step-by-step explanation:
Answer:
30 revolutions
Step-by-step explanation:
to calculate the revolution of the wheels in 66 metres we need to get the circumference
circumference = 2πr, r = radius (diameter divided by 2) but from the formula of circumference we ca rewrite it as πd= 3.14 x 70 = 219.8cm
next convert 66 metres to cm
100cm = 1m
x= 66m
cross multiply
x= 66m x100cm/1m= 6600cm
revolutions in 66metres = 6600cm/219.8cm = 30.0272975 ≅30 revolutions