Yolo has 2 pieces of string. One is 32 inches long, the other is 48 inches long. She wants to make as many necklaces as she can,
2 answers:
You might be interested in
The length of the rug is 4 ft.
The width of the rug is 2.5 ft.
Explanation:
The area of the rug is 10 ft.
The length of the rug be l.
Let us convert the inches to feet.
Thus,
Thus, the length of the rug is
Let the width of the rug be w.
Substituting these values in the formula of area of the rectangle, we get,
Solving the expression using the quadratic formula,
Substituting the values, we have,
Thus,
and
Since, the value of w cannot be negative, the value of w is 2.5ft
Thus, the width of the rug is 2.5ft
Substituting in
, we get,
Thus, the length of the rug is 4 ft.
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: