The sum of a geometric sequence is:
s(n)=a(1-r^n)/(1-r) in our case:
s(n)=3(1-4^n)/(1-4)
s(n)=-(1-4^n)
s(n)=(4^n)-1 and s=1023
(4^n)-1=1023
4^n=1024
n ln4=ln1024
n=(ln1024)/(ln4)
n=5
Answer:
b. about 91.7 cm and 44.6 cm
Step-by-step explanation:
The lengths of the diagonals can be found using the Law of Cosines.
Consider the triangle(s) formed by a diagonal. The two given sides will form the other two sides of the triangle, and the corner angles of the parallelogram will be the measure of the angle between those sides (opposite the diagonal).
For diagonal "d" and sides "a" and "b" and corner angle D, we have ...
d² = a² +b² -2ab·cos(D)
The measure of angle D will either be the given 132°, or the supplement of that, 48°. We can use the fact that the cosines of an angle and its supplement are opposites. This means the diagonal measures will be ...
d² = 60² +40² -2·60·40·cos(D) ≈ 5200 ±4800(0.66913)
d² ≈ {1988.2, 8411.8}
d ≈ {44.6, 91.7} . . . . centimeters
The diagonals are about 91.7 cm and 44.6 cm.
1) |−11| = 11, therefore Peter is at a distance of 11 feet
2) Jimmy, because each of the two points is fraction 5 over 8 unit away from 0
3) 36 + 28=64 4x4=36+4x7=28 36+28=64
7+9=16 4x16=64
Answer:
- Library 2 charges more for each book loaned.
- Library 1 has a cheaper subscription fee.
Step-by-step explanation:
Based on the table, we can write the equation for the cost of borrowing from Library 2 using the two-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
for (x1, y1) = (2, 15.50) and (x2, y2) = (8, 26) this equation becomes ...
y = (26 -15.50)/(8 -2)(x -2) +15.50 . . . . . fill in the values
y = (10.50/6)(x -2) +15.50 . . . . . . . . . . . . simplify a bit
y = 1.75x -3.50 +15.50 . . . . . . simplify more
In the above, we have x = number of books; y = cost. We can use "n" and "C" for those, respectively, as in the equation for Library 1. Then the monthly cost for Library 2 is ...
C = 12 + 1.75n . . . . . . . arranged to the same form as for Library 1
_____
Now, we can answer the questions.
Library 2 charges more for each book loaned. (1.75 vs 1.50 for Library 1)
Library 1 has a cheaper subscription fee. (10 vs 12 for Library 2)
_____
The numbers in the cost equations are ...
C = (subscription fee) + (cost per book loaned)·n
Answer:
<em>Answer</em><em> </em><em>B</em><em> </em><em>is</em><em> </em><em>correct</em><em>.</em>
