I am sorry I can help more but
Google can graph lines if that helps
You just look up graph of a line with your numbers
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 ...
3(2x/5)
Final result :
6x
——
5
Step by step solution :
Step 1 :
x
Simplify —
5
Equation at the end of step 1 :
x
3 • (2 • —)
5
Step 2 :
Final result :
6x
——
5
1. 3^3 = 27, 27 x 270 = 7,290m^3
2. original volume = 8 x 6 = 48 cm^3
new volume = 48 x (5/4)^3 = 93.75 cm^3