To evaluate 17 int (sin^2 (x) cos^3(x))
From Trig identity. Cos^2(x) + sin^2(x) =1. Cos^2(x) = 1 - sin^2 (x)
Cos^3(x) = cosx * (1 - sin^2 (x)) = cosx - cosxsin^2x
So we have 17 int (sin^2x(cosx - cosxsin^2x))
int (sin^2x(cosx)dx - int (sin^4xcosx)dx. ----------(1)
Let u = sinx then du = cosxdx
Substituting into (1) we have
int (u^2du) - int (u^4du)
u^3/3 - u^5/5
Substitute value for u we have
(sinx)^3/3 - (sinx)^5/5
Hence we have 17 [ sin^3x/3 - sin^5x/5]
Applying the rule for dilation, we will multiply the scale factor to its coordinates.
Having Q (0,2) and DO 0.5(x.y), the coordinates of Q' will be:
x = (.5)(0) = 0
y = (.5)(2) = 1
Therefore coordinates of Q' is (0,1)
*Having a scale factor of >1, the figure is said to be reduced.
The correct answer is C. A 2-column table with 3 rows. Column 1 is labeled x with entries negative 5, 0, 3. Column 2 is labeled y with entries negative 18, negative 2, 10.
Explanation:
The purpose of an equation is to show the equivalence between two mathematical expressions. This implies in the equation "–2 + 4x = y" the value of y should always be the same that -2 + 4x. Additionally, if a table is created with different values of x and y the equivalence should always be true. This occurs only in the third option.
x y
5 -18
0 -2
3 10
First row:
-2 + 4 (5) = y (5 is the value of x which is first multyply by 4)
-2 + 20 = -18 (value of y in the table)
Second row:
-2 + 4 (0) y
-2 + 0 = -2
Third row:
-2 + 4 (3) = y
-2 + 12 = 10
