Answer:
A = 100 pi cm^2
Step-by-step explanation:
A = pi(r^2)
A = pi(10^2)
A = pi(100)
A = 314.16 '
Convert to pi units.
314.16 ---> 100pi cm^2
Answer:
n = 60.22
Step-by-step explanation:
Hello
To find Sn, we need to draw out equations for each a₇ and a₁₉
In an arithmetic progression,
Sn = a + (n-1)d
Where Sn = sum of the A.P
a = first term
d = common difference
a₇ = 32
32 = a + (7-1)d
32 = a + 6d ........equation (i)
a₁₉ = 140
140 = a + (19-1)d
140 = a + 18d .........equation (ii)
Solve equation (i) and (ii) simultaneously
From equation (i)
32 = a + 6d
Make a the subject of formula
a = 32 - 6d .....equation (iii)
Put equation (iii) into equation (ii)
140 = (32 - 6d) + 18d
140 = 32 - 6d + 18d
Collect like terms
140 - 32 = 12d
12d = 108
d = 108 / 12
d = 9
Put d = 9 in equation (i)
32 = a + 6(9)
32 = a + 54
a = 32 - 54
a = -22
When Sn = 511
Sn = a + (n - 1)d
Substitute and solve for n
511 = -22 + (n-1) × 9
511 = -22 + 9n - 9
511 = -31 + 9n
511 + 31 = 9n
542 = 9n
n = 542 / 9
n = 60.22
To simplify combine like terms:
8m + 7m = 15m
4n - 2n = 2n
Simplified: 15m + 2n
This isn’t easy due to fractions but you just need to find a common denominator, what goes into 9 evenly and also goes into 4 evenly. 36 works and it is the lowest common denominator. What number multiplied by 9 gets you 36? (36/9) 4. So Emma uses 4/36ths of a gallon of gas to get 9/36ths of the way to work. So you take (4/36) or .25 and multiply that by 9 to get...
2.25 trips
Answer:
Step-by-step explanation:
multiply both sides by 36
