Hooke's Law states that the force needed to keep a spring stretched x units beyond its natural length is directly proportinal to x.
Hooke's Law as an equation: F=______
If a spring has a natural length of 14 cm and a force of F=35 N is required to maintain the the spring stretched to a length of 19 cm, find the spring constant k=________
What force is needed to keep the spring stretched to a length of 16 cm? ___________
What is
F=kx
k=7
F=14
100
g(x)=2x^2+8x+11
Express g in standard form
What is
2(x+2)^2+3
100
Factor the polynomial and use the factored form to find the zeros.
P(x)=x^3+x^2-20x
What is -5,0,4?
200
The Domain of the function
f(x)=x/(x^2+x-6)
What is (-infinity,-3)U(-3,2)U(2,infinity)
200
f(x)=x^2+4x
f(0)
f(3)
f(a)
f(1/a)
What is
0, 21, a^2+4a, 1/a^2 + 4/a
200
A function whose graph is a parabola with vertex (2,-1) and passes through the point (3,1)
What is
f(x)=2(x-2)^2-1
200
r(x)=(x-5)/(x+1)^2
the x-intercept
What is (5,0)?
300
The Domain, Range and Asymptote of
f(x)=e^(x+2)-2
What is (-infinity,infinity), (-2,infinity) and y=-2
300
f(x)=x^2+4x
f(-3)
f(-a)
What is
-3, a^2-4a
300
If a ball is thrown upward with a velocity of 22 ft/s, its height in feet after t seconds is given by y=22t-16t^2
What is the maximum height attained by the ball? (Round to the nearest whole number)
What is 8 ft
300
r(x)=(x-5)/(x+1)^2
the y-intercept
What is (0,-5)?
400
The Domain, Range and asymptote of
f(x)=4lnx +1
What is (0,infinity), (-infinity, infinity) and x=0
400
f(x)=4x^2+10
f(x+2)
f(x) + f(2)
What is
4(x+2)^2+10
4x^2+36
400
Use synthetic division and the Remainder Theorem to evaluate P(c)
P(x)=6x^2+7x+8, c=1/2
What is 13?
400
Doctors use radioactive iodine as a tracer in diagnosing certain thyroid gland disorders. This type of iodine decays in such a way that the mass remaining after t days is given by the function m(t)=3e^(-0.08t)
Find the mass at t=0
How much of the mass remains after 3 days (Round to 3 decimal places)
What is 3 and 2.332
500
Solve the system
x - y=2
x+3y=10
What is (4,2)
500
f(x)=2x-7, g(x)=7-x^2
(fog)(x)
(gof)(x)
What is
2(7-x^2)-7
7-(2x-7)^2
500
A woman invests $5,600 in an account that pays 6% interest per year, compounded continuously.
What is the amount after 3 years? (nearest cent)
How long will it take for the amount to be $8,000? (2 decimals)
What is 6704.42, 5.94
500
Ebbinghaus' Law of Forgetting states that if a task is learned at a performance level Po, then after a time interval t the performance level P satisfies
log P = log Po - c log(t+1)
where c is a constant that depends on the type of task and t is measured in months.
Use Ebbinghaus' Law of Forgetting to estimate a student's score on a biology test two years after he got a score of 98 on a test covering the same material. Assume c=0.3 and t is measured in months. (round to the nearest whole number)