Answer:
∫₁⁵ 2t (t² + t³) dt
Step-by-step explanation:
The area is ∫ₓ₁ˣ² y dx. To parameterize, replace x₁ and x₂ with t₁ and t₂. Replace y = f(x) with y = f(t), and replace dx with (dx/dt) dt.
x = 5 + t², so dx = 2t dt.
∫₁⁵ (t² + t³) (2t dt)
∫₁⁵ 2t (t² + t³) dt
Answer:
-10
Step-by-step explanation:
In multiplying and dividing if there is 2 negatives it is always a positive but if it is 1 negative and a positive it is always a negative. This is only for multiplying and dividing. So the answer is negative 10.
the unscented candles burn faster at a rate of (1/3) inches/ hour
Step-by-step explanation:
scented candles:
(1/12) / (20/60) = 1/4 inches/ hour
unscented candles:
(1/6) / (30/ 60) = 1/3 inches/ hour
hope it helps!
Consider the attached figure. The whole rectangle is ABCD, while AEGF is the part located in the third quadrant. In fact, this quadrant is composed by all the points with both coordinates negative.
To answer the question, let's compute the area of the two rectangles and see what part of ABCD is AEGF.
A and B have the same x coordinate, so the length of AB is given by the absolute difference of their y coordinates:

Similarly, but exchanging the role of x and y, we compute the length of BC:

So, the area of the rectangle is 
The same procedure allows us to compute width and height of the sub-rectangle in the third quadrant:


So, the area of the portion located in the third quadrant is 
This means that the ratio between the two area is

If we want this ratio to be a percentage, just make sure that the denominator is 100:
