Answer:
10) f'(x) = (x² + 6x - 3)/(x + 3)²
11) g'(x) = 1 - csc²x
Step-by-step explanation:
10. f(x) = x(1 - (4/(x + 3))
Expanding gives;
f(x) = x - (4x/(x + 3))
Differentiating gives;
f'(x) = 1 - 4/(x + 3) + 4x/(x + 3)²
Simplifying this gives;
f'(x) = [(x + 3)² - 4(x + 3) + 4x]/(x + 3)²
f'(x) = (x² + 6x + 9 - 4x - 12 + 4x)/(x + 3)²
f'(x) = (x² + 6x - 3)/(x + 3)²
11. g(x) = x + cot x
Rewriting this gives;
g(x) = x + (1/tan x)
We know that derivative of tan x is sec x while derivative of (1/tan x) is -csc²x
Thus;
g'(x) = 1 - csc²x
This can be written as
Differentiating this gives;
g'(x) = 1 - csc²x
Answer: one Apple costs £ 0.20, and one banana costs £ 0.60
Step-by-step explanation:
let x = the amount of apples
let y = the amount of bananas
4x + y = 1.40
7x + y = 2
this is à system of equations
simplify the top equation to y = 1.4 - 4x
now plug that into the second equation and solve
7x + 1.4 - 4x = 2
3x + 1.4 = 2
3x = 0.6
x = 0.2
that means that one Apple costs £ 0.20
plug that back into the top equation
4x + y = 1.4
4(0.2) + y = 1.4
0.8 + y = 1.4
y = 0.6
so one banana costs £ 0.60
Answer:
<h2>54 in²</h2>
Step-by-step explanation:
Look at the picture.
The edge of the cube is equal to the diagonal of the sphere.
Therefore, the length of the cube's edge is 3 inches.
The formula of a surface area of a cube:
Substitute a = 3 in:
Answer:
density= mass/ volume
Step-by-step explanation:
d=m/v
