Sequences & Series
Is the following sequence geometric or arithmetic?
2, 4, 6, 8,...
Arithmetic
Solve
101-x=104
x=3
log3(x)=log3(14)
x=14
A four-meter-long ladder leans against a building. If the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? How far from the wall is the base of the ladder?
The ladder reaches at 3.46 meters.
The base of the ladder is 2 meters.
What is the first step to verify this equation:
cot(x)/csc(x)=cos(x)
Converting cotangent and cosecant into their alternative expressions.
Find the a101 term for:
3, 8, 13, 18, 23, 28,...
503
Solve
3x^2-3x=81
x=1, 4
log10(x2-30)=log10(x)
x=6
A five-meter-long ladder leans against a wall, with the top of the ladder being four meters above the ground. What is the approximate angle that the ladder makes with the ground?
About 53 degrees
Solve
2cos(theta)+1=0
theta= 4pi/3 or 2pi/3
Find the a7 term for the following geometric sequence:
3, 6, 12, 24, 48
192
Solve
4x+1=1/64
x=-4
2log10(x)=log10(4)+log10(x-1)
x=2
Two sides of a triangle are 8 units and 12 units long. The angle opposite the 8 unit long side is 35 degrees. What is the angle opposite the side that is 12 units long?
About 59.4 degrees
Simplify
cos2(x)-1/sin2(x)
tan2(x)
Find an equation for the nth partial sum of Sn
100+75+50+...
Sn=-25n2+225/2
8x-2= square root of 8
x=5/2
log2(x)=4.5
x=22.63
A triangle has sides measuring 3 units and 4 units, with an included angle of 57 degrees. What is the length of the side opposite the 57 degrees angle?
3.5 units
tan(x)+cot(x)/cot(x)
1
Find an equation for the nth partial sum of Sn and find S3
4(b)n-1
4+4b+4b2
2x=-4
No solution
log10(7x+2)+log10(9)=log10(2x)
No solution
Find the measure of C
a=29
c=24
B=101
C=36.322 degrees
tan(x)/tan(x)+cot(x)
sec2+1