Algebra
what is the median of this data set
1, 52, 78, 67, 89
67
d/dx e5x
5e5x
What is Newtons 2nd Law of motion?
*hint it is an equation...
F = ma
This mathematician related the symmetries found in nature to the conservation laws found in physics.
Hint: She is known as the “mother of modern algebra” and has a famous theorem named after her.
Emmy Noether
What is the area of a rhombus with a diagonal length length of 6 and 7.
21
What is the relationship between velocity and total distance using Calculus.
*Hint distance is NOT displacement
∫|𝑣(𝑡)|𝑑𝑡
A ball is dropped from the top of the Eiffel Tower. What type of energy increases as it falls toward the ground?
kinetic energy
This mathematician is known as the “father of calculus,” having developed the fundamental ideas of differentiation and integration.
Isaac Newton or Gottfried Wilhelm Leibniz
A rectangle has a length of 3x and a width of 2x.
If x = 4 what is the area of the rectangle?
96 units2
∫(4x3+2)dx
x4+2x+C
Given a box is stationary, has a mass of 20 kilograms and is on an incline with an angle of 60 at its base, what is the box's weight perpendicular to the incline?
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F = m*g*cos(60) --> 20kg*9.8m/s2*0.5
F = 98N
This mathematician discovered that objects fall at the same rate regardless of mass. He is also famous for discovering the rings around Saturn in the 1600's.
Galileo Galilei
factor this: 6x2−11x−10
(3x+2)(2x−5)
The graph of a differentiable function f(x) has a horizontal tangent at x=2.
What does this mean about the derivative f′(2)?
f'(2)=0
if a linear line is shown on a graph with distance (m) in the x-axis and force (N) in the y-axis, what does the area under the curve represent. include units.
Area represents work measured in joules (J)
Area represents change in energy (J)
This famous mathematician discovered the relationship between mathematical ratios in musical ratios. For example, an identical string that is half the length will produces a note one octave higher.
Pythagoras
A number is tripled, then increased by 12, and the result is the same as doubling the original number plus 27.
What is the number squared?
3x+12 = 2x+27
x=15
152 = 225
A particle moves along a line with position function
s(t)= t3−6t2+9t
Find the velocity v(t) and determine at what time(s) the particle is at rest.
s′(t) = 3t2−12t+9
t = 1, 3
A roller coaster starts from rest at the top of a hill and moves down without friction.
Ignoring air resistance, how does the total mechanical energy (potential + kinetic) change as it moves?
Energy is conserved so it stays the same.
She was mathematician that worked at NASA and helped calculate trajectories for early space missions, including the Apollo 11 moon landing.
Katherine Johnson