Answer:
Step-by-step explanation:
<u>To make the given piecewise function continuous we need:</u>
- ax² - b = 6 and 5ax + b = 6 at x = 1
<u>It gives us the system:</u>
- a(1²) - b = 6 ⇒ a - b = 6
- 5a(1) + b = 6 ⇒ 5a + b = 6
<u>Sum of the two:</u>
- a - b + 5a + b = 6 + 6
- 6a = 12
- a = 2
<u>Then b is:</u>
Answer:
1. The 
is between 3 and 4.
2. The 
is between 7 and 8.
3. The 
is between 4 and 5.
4. The 
is between 9 and 10.
5. The 
is between 6 and 7.
Step-by-step explanation:
1. : 10 is near the perfect squares 9 and 16, which would mean its answer is between their square roots which are 3 and 4.
2. : 10 is near the perfect squares 49 and 64, which would mean its answer is between their square roots which are 7 and 8.
3. : 10 is near the perfect squares 16 and 25, which would mean its answer is between their square roots which are 4 and 5.
4. : 10 is near the perfect squares 81 and 100, which would mean its answer is between their square roots which are 9 and 10.
5. : 10 is near the perfect squares 36 and 49, which would mean its answer is between their square roots which are 6 and 7.
Answer:
The average rate of change of f(x) is greater than g(x) on the interval [0,3]
Step-by-step explanation:
:)) Hope it helps!!
Answer:
a = 13 and b = 12-5i
Step-by-step explanation:
We need a common denominator
3+2i 5-i
---------- + ---------
3-2i 2+3i
(3+2i) (2+3i) (5-i)(3-2i)
------------------ + --------------------
(3-2i) (2+3i) (2+3i) (3-2i)
Foil the numerators
6 +4i+9i+6i^2 +15-3i-10i+2i^2
------------------ --------------------
(2+3i) (3-2i)
Combine like terms
21 +8i^2
------------------
(2+3i) (3-2i)
We know that i^2 = -1
21 +8(-1)
------------------
(2+3i) (3-2i)
21 -8
------------------
(2+3i) (3-2i)
13
------------------
(2+3i) (3-2i)
Foil the denominator
13
---------------
6 +9i -4i -6i^2
Combine like terms
13
----------------
6+ 5i -6(-1)
13
----------
12 +5i
We know have
13
-------------
12 + 5i
Multiply by the conjugate
13 ( 12-5i)
------------- * -------------
12 + 5i 12 -5i
13 (12-5i)
--------------
144 +25
13(12-5i)
-------------
169
12-5i
------------
13
The parentheses are (12-5i)/13
We need the reciprocal to make the equation become 1
which is 13/ 12-5i
a = 13 and b = 12-5i
