Simplify (sin^4(x) - cos^4(x)) / (sin^2(x) - cos^2(x))
1 answer:
You might be interested in
Answer:
The factor is 11x - 2y ⇒ 2nd answer
Step-by-step explanation:
* Lets explain how to factorize the difference of two cubes
- If we want to factorize x³ - y³
- The binomial x³ - y³ is different of two cubes, because x³ is cube x
and y³ is cube y
- The difference of two cubes has two factors one two two terms and
the other is three terms
- To factorize it we find the ∛x³ and ∛y³
→ ∛x³ = x and ∛y³ = y
→ Then the first factor is (x - y)
→ We find the second factor from the first factor
→ square x
→ square y
→ Multiply x and y and put them between x² and y² with opposite sign
of the first factor
→ The second factor is (x² + xy + y²)
* Lets do the same with 1331x³ - 8y³
∵
∵
∴ The first factor is (11x - 2y)
∵ (11x)² = 121x²
∵ (2y)² = 4y²
∵ 11x × 2y = 22xy
∵ The sign of first factor is (-)
∴ The second factor is (121x² + 22xy + 4y²)
∴ <em>The factor is 11x - 2y </em>
Answer:
-3.47 inches per minute
Step-by-step explanation:
Let the height be 'h' for any time 't'.
Given:
Length of the prism (L) = 10 in
Width of the prism (w) = 16 in
The rate of change of volume of prism is, (The negative sign implies the volume decreases with time.)
Now, rate of change of height of prism =
Length and width remains constant.
Now, we know that, volume of a rectangular prism is given as:
Volume = Length × width × Height
Now, differentiating both sides with respect to time 't', we get:
Plug in the given values and solve for . This gives,
The negative sign implies the height decreases with time.
Therefore, the the rate of change, in inches per minute, of the height when the height is 3 inches is -3.47 inches per minute.