9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
__
The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
__
This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
_____
<em>Additional comment</em>
With these values, the function becomes ...
A) Use the distance formula to find the length of each side, and then add the lengths.
Answer:
135°
Step-by-step explanation:
Answer:
Step-by-step explanation:
x (3,7,11,15)
y (4,6,8,10)
A. This IS a function because u have no repeating x values
B. Data in table :
when x = 11, y = 8
relation : f(x) = 5x - 21....when x = 11
f(11) = 5(11) - 21
f(11) = 55 - 21
f(11) = 34.....so when x = 11, y = 34
therefore, the relation f(x) = 5x - 21 has a greater value then the table
C. f(x) = 5x - 21......f(x) = 99
99 = 5x - 21
99 + 21 = 5x
120 = 5x
120/5 = x
24 = x <====
Answer:
Part a) 3.5 weeks
Part b) 185 tickets
Step-by-step explanation:
Part a) After how much time have the same number of tickets been sold for both festivals?
Let
x -----> the number of weeks
y ----> the number of tickets sold
we have
<em>Country Music Festival</em>
----> equation A
<em>Pop Music Festival</em>
----> equation B
Equate equation A and equation B
solve for x
Part b) What is the number of tickets sold at that time?
substitute the value of x=3.5 weeks in the linear equation A or linear equation B
