Answer:
<6 = 60 degrees, <7 is 50 degrees, <8 is 70 degrees
Step-by-step explanation:
Angle 6 is 60 degrees because of the alternate interior angles theorem.
Angle 7 is 50 degrees, also because of the alternate interior angles theorem.
Now, the three interior angles of a triangle should add up to 180 degrees. That means:
60 + 50 + <8 = 180
<8 = 70 degrees
<6 = 60
<7 = 50
<8 = 70
If she does 10 a day she will do 520 after 52 weeks
The second function has a graph that is identical to that of the first function, except that it is shifted upward by 4 units.
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The thrust of this question is to get you to recognize that adding a constant to a function shifts its graph in the amount and direction of the constant value (positive ⇒ upward).
The region in question is the set
or equivalently,
Cross sections are taken perpendicular to the y-axis, which means each section has a base length equal to the horizontal distance between the curve y = x³ and the line x = 0 (the y-axis). This horizontal distance is given by
y = x³ ⇒ x = ∛y
so that each triangular cross section has side length ∛y.
The area of an equilateral triangle with side length s is √3/4 s², so each cross section contributes an infinitesimal area of √3/4 ∛(y²).
Then the volume of this solid is
I've attached some sketches of the solid with 16 and 64 such cross sections to give an idea of what this solid looks like.