The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,
<span>Sn </span>= (<span><span><span>a1</span>(1−<span>r^n</span>) / (</span><span>1−r)
Substituting the known terms,
Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
Sn = 26.5625
Thus, the sum of the first four terms is 26.5625. </span></span>
C because they are like giant engines that use warm moist air as fuel, that is why they form over warm ocean waters like the equator.
Point R is the midpoint of FE¯¯¯¯¯ , so the coordinates of point R are (3a, b).
In △DEF , the length of the base, DF¯¯¯¯¯ , is
4a, and the height is 2b, so its area is
1/2×4a×2b = 4ab.
In △QRP , the length of the base, QR¯¯¯¯¯ , is
3a-a = 2a, and the height is b, so its area is 1/2×2a×b = ab .
Comparing the expressions for the areas proves that the area of the triangle created by joining the midpoints of an isosceles triangle is one-fourth the area of the larger isosceles triangle.
Answer: The first diagram you selected is the correct visual representation.
Check out the diagram I posted below. The red vertical line is x = 0, aka the y axis. The blue parabola is 3x = y^2. The green horizontal line is y = 6. The region bounded by these curves is the gray shaded region.
Spinning that gray region around the y axis results in the first diagram in your answer choices. The disk in pink is a cross section to help find the volume (through the use of integral calculus).
