How do you find the common difference in arithmetic sequences and the common ration in geometric sequences?
2nd term minus the 1st,
and
2nd term divided by the first
100
For exponential functions, f(x)=ab^x, what is the initial amount, what is the rate of exponential growth, and what is time?
a=initial amount
b=rate of growth
x=time
100
Find the parametrization for the curve:
The circle with center (3, 9) and radius 2.
x=3+2cosΘt
y=9+2sinΘt
100
Explain SOHCAHTOA
sin=O/H
cos=A/H
tan=O/A
100
f(x)=(x-6)/7, g(x)=7x+6. Find f(g(x)).
f(g(x))=x
200
How many terms are in the expansion of (a+b)^n
n+1 terms
200
There are currently 73 million cars in a certain country, increasing by 1.7% annually. How many years will it take for this country to have 91 million cars? Round to the nearest year.
91=73(1.017)^x
x=13.074
13 years
200
Eliminate the parameter:
X=√t, y=2t+5
y=2x^2+5
200
From a distance of 43 feet from the base of a building, the angle of elevation to the top of the building is 63 ̊. Estimate the height of the building to the nearest foot.
84 feet
200
Describe the end behavior as the function approaches the vertical asymptote:
f(x)=3/(x-4)
lim as x->4-=-infinity (down)
lim as x->4+=+infinity (up)
300
What equation is used for finding the sum a series converges to if r is between 0 and 1?
a/(1-r), where a=the first term, and r=the common ratio
300
If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 30 days?
$4.65
300
Estimate the maximum height reached by a baseball during its flight if it is thrown with a velocity of 102 feet per second at an angle of 58° relative to level ground.
117 Feet
300
From a distance of 1206 feet from a spotlight, the angle of elevation to a cloud base is 43 ̊. Find the height of the cloud base to the nearest foot.
1125 feet.
300
If a baseball is thrown with a velocity of 97 feet per second at an angle of 30° relative to level ground, at what length will the height of the ball and the distance travelled be the same?
255 ft
400
Identify the first term and the common ratio for the following geometric series:
2(2/5)^(2k)
a=2
r=2/5
400
18. The decay of 425 mg of an isotope is given by A(t)= 425e^-0.029t, where t is time in years. Find the amount left after 56 years.
84 mg
400
Find the vertices:
(x-2)^2-(y-4)^2=1
81 144
(11, 4)(-7 , 4)
(2, 16)(2, -8)
400
Solve for x:
sin39 ̊=20/x
x=31.78
400
Describe the end behavior of the function at its horizontal asymptote:
f(x)=(x+1)/(x^2-2x)
lim as x->-inf=0
lim as x->+inf=0
500
What is the sum of the next two terms in the following sequence?
-2, 5, 12, 19, 26, …
73
500
Given the following information, determine the formula for the exponential function:
(-1, 6)
(0, 9)
(1, 13.5)
(2, 20.25)
f(x)=9(1.5)^x
500
A Ferris wheel with a radius of 36 feet turns counter clockwise at the rate of one revolution every 15 sec. The lowest point of the Ferris wheel is 14 feet above ground
level at the point (0, 14) on a rectangular coordinate system. Find parametric equations for the position of a person on the Ferris wheel as a function of time (in seconds) if the Ferris wheel starts (t = 0) with the person at the point (36, 50).
x = 36 cos (24t)° ft
y = 36 sin (24t)° + 50 ft
500
Use Trig identities to simplify the following:
cotΘ secΘ sinΘ
1
500
Find all vertical asymptotes:
((x-4)(x+4))/(x^2-1)