Hi there!
To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine:
Answer:
The rate is the distance divided by the time.
60 feet in 10 seconds = 60 ft / 10 sec = 6 ft / sec
42 feet in 6 seconds = 42 ft / 6 sec = 7 ft / sec <--- We have a winner!
Step-by-step explanation:
1: I can’t see one it’s cut out sorry :(
2:go down four horrizontal for each line making a rhombus
3: 3a:true 3b:true 3c:false 3D: false
4.PART A: Draw a square in the middle.
4. PART B: Say there are four right angles
5: Line, point, ray, line segment
6. There are 2 acute and 1 right
7. A B C
8: 1/4 1/6 1/8
9: 9a 9c and 9d
10: square and polygons first, then triangles because they have 4 sides while a triangle has 3
10 PART B: rectangles second, then the pentagons are third, the parallelogram is first, then the triangles because a rectangle has all right angles
11: she drew a square!
12: polygons without right angles
13: I can’t draw on your paper just draw three lines in the trapezoid
13: a c and d
Cost of the 3 shirts before tax = 2*49.96 + 1/2 * 49.96
= $124.90
After adding 7.1% tax total cost = 124.90 * 1.071 = $133.77
So the cost od each shirt = 133.77 / 3 = $44.59 (answer)
