Answer:
sin(x)
- cos(x)
Step-by-step explanation:
The derivative for f(x) up to 4 terms is
f(x) = cos(x)
f'(x) = - sin(x)
f''(x) = - cos(x)
f'''(x) = -(-sin(x))
f'''(x) = sin(x)
f''''(x) = cos(x)
What this is tell you is that you need to go to 4 differentiations before you get back to where you started from.
The next step is to find out how many groups of 4 there are in 119 differentiations, and, more importantly, what the remainder is.
So you have to go through 29 differentiations to get to 116 times you have differentiated (119/4 = 29)
There are 3 more differentiations you have to do which will be f'''(x) = sin(x)
The answer is
===============
f(x) = sin(x)
f'(x) = cos(x)
f''(x) = -sin(x)
f'''(x) = -cos(x)
f''''(x) = sin(x)
The argument is going to be the same as you used above. 116 differentiations will get you back to sin(x). You need 3 more differentiations so f'''(x) = - cos(x)
Answer:
Step-by-sep explanation:
Given:
Diameter of circle = 20 units
Center of circle = (-1, 7)
Standard form of the equation of a circle is expressed in the center-radius form as:
,
Where,
h = -1
k = 7
r = ½ of diameter = ½(20) = 10 units
Plug in the values into the equation
This question is incomplete, the missing diagram is uploaded along this answer below;
Answer:
horizontal V₁ ( 141.37 in³ ) is less than vertical V₂ ( 235.62 in³ )
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
from the image,
We find the volume of the solid obtained by rotating the card around a horizontal line;
Volume of the cylinder V₁ = πr²h
given that; radii = 3 in and height = 5 in
we substitute
V₁ = π × (3)² × 5
V₁ = π × 9 × 5
V₁ = 141.37 in³
Next we find the volume of the solid obtained by rotating the card around a vertical line;
Volume of the cylinder V₂ = πr²h
given that; radii = 5 in and height = 3 in
we substitute
V₂ = π × (5)² × 3
V₂ = π × 25 × 3
V₂ = 235.62 in³
Hence horizontal V₁ ( 141.37 in³ ) is less than vertical V₂ ( 235.62 in³ )
