These are two questions and two answers.
1) Problem 17.
(i) Determine whether T is continuous at 6061.
For that you have to compute the value of T at 6061 and the lateral limits of T when x approaches 6061.
a) T(x) = 0.10x if 0 < x ≤ 6061
T (6061) = 0.10(6061) = 606.1
b) limit of Tx when x → 6061.
By the left the limit is the same value of T(x) calculated above.
By the right the limit is calculated using the definition of the function for the next stage: T(x) = 606.10 + 0.18 (x - 6061)
⇒ Limit of T(x) when x → 6061 from the right = 606.10 + 0.18 (6061 - 6061) = 606.10
Since both limits and the value of the function are the same, T is continuous at 6061.
(ii) Determine whether T is continuous at 32,473.
Same procedure.
a) Value at 32,473
T(32,473) = 606.10 + 0.18 (32,473 - 6061) = 5,360.26
b) Limit of T(x) when x → 32,473 from the right
Limit = 5360.26 + 0.26(x - 32,473) = 5360.26
Again, since the two limits and the value of the function have the same value the function is continuos at the x = 32,473.
(iii) If T had discontinuities, a tax payer that earns an amount very close to the discontinuity can easily approach its incomes to take andvantage of the part that results in lower tax.
2) Problem 18.
a) Statement Sk
You just need to replace n for k:
Sk = 1 + 4 + 7 + ... (3k - 2) = k(3k - 1) / 2
b) Statement S (k+1)
Replace
S(k+1) = 1 + 4 + 7 + ... (3k - 2) + [ 3 (k + 1) - 2 ] = (k+1) [ 3(k+1) - 1] / 2
Simplification:
1 + 4 + 7 + ... + 3k - 2+ 3k + 3 - 2] = (k + 1) (3k + 3 - 1)/2
k(3k - 1)/ 2 + (3k + 1) = (k + 1)(3k+2) / 2
Do the operations on the left side and you will find it can be simplified to k ( 3k +1) (3 k + 2) / 2.
With that you find that the left side equals the right side which is a proof of the validity of the statement by induction.
Answer:
D
Step-by-step explanation:
It might be wrong tho sorry
Answer:
Nine million nine thousand, is written 9,009,000.
Answer:
Carly
Step-by-step explanation:
to figure out what the ratio is you need to put it in fraction form
zoe's team is 8/14
carly's team is 7/17
you need to find a common denominator to figure out who has the higher number of wins
in this case, the common denominator would be 238 or 14 times 17
you multiply both the numerator and the denominator by 17/17 for zoe's fractions
zoe's team has 136/238
carly's team would be multiplied by 14/14
this would give you 98/238
now that both fractions have the same denominator you can determine that carly's team lost more games
Answer:
The correct option is;
C. The panthers lost 3 yards on the 3rd play
Step-by-step explanation:
Given that the graph's y-axis represents the number of yards the Panthers traveled, and the x-axis represents the play number, then we have;
The coordinates of the point A are (3, -3) which shows the following;
x-coordinate = Number of play = 3rd play
y-coordinate = Number of yards the Panthers traveled = -3 yards = Loss of 3 yards
The combined meaning of the point A is that the Panthers went back (lost) 3 yards on the 3rd play.
