Calculus
Compute
limx->3 5x2-8x-13/x2-5
11/4
Slove sqrt(x-8)=3
IN 10 SECONDS COUNT DOWN
GO!!!
x=17
The triangle bounded by the lines y = 0, y = 2x and y = -0.5x + k, with k positive, is equal to 80 square units. Find k.
K=10
A gambler playing with 3 playing cubes wants to know weather to bet on sum 11 or 12. Which of the sums will occur more probably?
extra Credit +200 points
The gambler should bet on 11, as P(11) > P(12).
This famous flipper has cemented herself as the most successful gymnast in US history with 7 national titles, 5 world championship titles and 30 overall medals at world championship and Olympic competition.
Simone Biles
You are evaluating a line integral to find the total work done by moving a particle along a circle with radius 8 through a conservative vector field. What is the amount of work?
0
DIFFERENTIATE
4ln(ln(ln(sec x)))
4tan x/ln(ln(sec x))ln(sec x)
1/(x-3)+1/(x+3)=10/(x2-9)
x=5
If 3x−y=12, what is the value of 8x/2y?
212
Two coins are tossed, find the probability that two heads are obtained.
P(E) = 1 / 4
This famous US sprinter is credited with "single-handedly crushing Hitler's myth of Aryan supremacy" by winning 4 gold medals at the 1936 Berlin Olympics.
The award named after him is the highest honor given by USA Track and Field.
Who is Jesse Owens?
Write a vector parameterization of the line through the points (1, 2, 3) and (2, 4, 7)
<1+1t , 2+2t, 3+4t>
Integrate
sqrt(x)/(x-1) dx
2sqrt(x)+ln(sqrt(x)-1/(sqrt(x)+1))+C
At t = 0 there are 50 grams of a radioactive isotope. The isotope has a half-life of 16 minutes. Use the exponential decay model to write the amount A as a function of time t.
A = A0e −rt = 50e^( −0.04332t), where A is in grams and t in minutes.
C=5/9(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I.A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
| 5 |
| 9 |
degree Celsius.
II.A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III.A temperature increase of
| 5 |
| 9 |
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
ANSWER IS D
Which of these numbers cannot be a probability?
a) -0.00001
b) 0.5
c) 1.001
d) 0
e) 1
f) 20%
Name ONE of the three new swimming events being raced in the Tokyo Olympics.
Women's 1500 meters
Men's 800 meters
Mixed 400 Medley Relay
What is the Jacobian for the transformation from dxdy to polar coordinates?
rdrdtheta
A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5 m2/sec at what rate is the radius decreasing when the area of the sheet is 12 m2
rt=-0.040717
Slove 3tan(x/2)+3=0
x=2arctan(-1)
Four students about to purchase concert tickets for $18.50 for each ticket discover that they may purchase a block of 5 tickets for $80.00. How much would each of the 4 save if they can get a fifth person to join them and the 5 people equally divide the price of the 5-ticket block?
$2.50
The blood groups of 200 people is distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?
P(E)=70/200=.35
What is the location of the 2024 Summer Olympics?
Paris France
Find the equation of the plane through the points (0, 1, 0), (2, 3, 4), (1, 0, 1). (Simplify this equation to the form _x + _y + _z = _)
3x+y-2z = 2
Determine the area below this function and above the x-axis.
f(x)=3+2x-x2
32/3
Write down the equation of a circle with radius 8 and center (-4,7).
(x+4)2+(y-7)2=64
Ms. DiCicco can paint a wall in 90 minutes. Mr. Hanson can paint the same wall in 120 minutes. How long will it take the two of them to paint the wall together? (Assuming they stay out of each other's way!)
360/7 (about 51.4 minutes)
A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white?
P(E)=1/2
Name 3 of the 5 events in the Olympic pentathalon. (You may choose ancient or modern)
Ancient: Long Jump, Foot Race (Stadion), Discus Throw, Javelin Throw, Wrestling
Modern: Fencing, Swimming, Running, Show Jumping, and Shooting
Come up with SOME argument about why the multivariable calculus concept "curl" is essential in the sport of curling...
?