Answer:
A) When using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. True.
The Shell method is a technique used to find the volume of a solid of revolution. Here, we take thin shells with axis coinciding with the axis about which the region whose volume is to be found, is revolved.
B) If a region is revolved about the y-axis, then the shell method must be used. False.
This method can be used with any axis of rotation.
C) If a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y. True.
The washer method uses thin disks with infinite width but the shell method uses thin concentric shells with infinite width about the axis of revolution. So, the statement is true.
Unclear of the question, but the value is already as a mixed fraction. The value of absolute value is just the distance from zero. So, |-4|=4 or |6|=6
Answer:
Step-by-step explanation:
The attached diagram shows the triangle ABC formed by the ladder with the wall of the house.
Triangle ABC is a right angle triangle. It has a 90 degree angle. The length of the ladder forms the hypotenuse(AC)of the triangle. This length can be determined by applying Pythagoras theorem
Hypotenuse^2 = opposite ^2 + adjacent^2
AC^2 = 22^2 + 5^2
AC^2 = 484 + 25 = 509
AC = √509
AC = 22.56
The slope of the ladder is
(change in y)/(change in x)
Slope = 22/5 = 4.4
If the roots of the equation f(x)=0 are -4,-1, 2 and 5, then binomials (x+4), (x+1), (x-2) and (x-5) are factors of needed polynomial.
Thus, the polynomial will have form
where a is real coefficient (positive or negative). This polynomial has degree 4 as needed.
The form of the graph depends on the sign of coefficient a. Attached diagrams show two different cases of possible forms of graphs (first one for positive coefficient a, second one for negative coefficient a).