Answer:
The first one
Step-by-step explanation:
Step-by-step explanation:
Just use a calculator it helps, when I use the calculator it helps me alot
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:
, ](https://tex.z-dn.net/?f=%5B16%20%2B%20%28-18%29%5D%28-4%29)
Step-by-step explanation:
Given: The low temperature on Monday was 16°F. The low temperature on Tuesday was 18°F cooler. The low temperature on Wednesday was –4 times Tuesday’s temperature.
To find: expression that can be used to describe the low temperature on Wednesday
Solution:
Temperature on Monday = 16°F
So,
Temperature on Tuesday = 
Temperature on Wednesday = 
So, expression 
can be used to describe the low temperature on Wednesday.
Also,
\,\,\left \{\because (a-b)=\left [ a+(-b) \right ] \right \}](https://tex.z-dn.net/?f=%2816-18%29%28-4%29%3D%5B16%20%2B%20%28-18%29%5D%28-4%29%5C%2C%5C%2C%5Cleft%20%5C%7B%5Cbecause%20%20%28a-b%29%3D%5Cleft%20%5B%20a%2B%28-b%29%20%5Cright%20%5D%20%5Cright%20%5C%7D)
So, expression also represent temperature on Wednesday.
Answer:
The point of intersection is (3,1)
Step-by-step explanation:
Manipulate these equations to achieve the form of y = mx + c
1) y + 5 = 2x
Y = 2x - 5
2) y = 7 - 2x
Y = -2x + 7
Point of intersection is (3,1) on the graph attached
To check algebraically:
2x - 5 = -2x + 7
4x = 12
X = 3
Substitute to get y
Y = 2x - 5
Y = 2 x 3 - 5
Y = 1
Therefore (3,1)
