Mathmatics Flashcards
Which of the following equations correctly describes the shaded area of the x-y plane?
Find Slope of the line using:
m = (Y2 - Y1) / (X2 - X1 )
Put into slope form
y = mx + b
Isolate “b”
What is most nearly the slop of the line tangent to the parabola y = 12x2 + 3 at a point where x = 5?
Take the derivative of y = 12x2 + 3 with respect to x.
Substitute 5 for x.
Solve.
Which field has a positive vector curl?
Which one of the 4 figures shown has rotation?
If there are more than one field that has rotation use the Right Hand Rule and pick the one that has a positive Z.
x = -2 is one of the roots of the equation x3 + x2 -22x - 40 = 0. What are the other two roots?
Use “poly-solve” on calculator.
What is the unit vector of R = 12i - 20j - 9k?
To find a unit vector, take the magnitude.
Divide vector R by the magnitude.
Which of these vector identities is INCORRECT?
(A) A · A = 0
(B) A x A = 0
(C) A · B = B · A
(D) A x B = -B x A
If the dot product of two vectors is zero, either one or both of the vectors is zero or two vectors are perpendictular. The equation A · A = 0 is, therefore, true only when A = 0, and it is not an identity. the other three option are identities.
For the three vectors A, B, and C,
A = 6i + 8j + 10k
B = i + 2j + 3k
C = 3i +4j + 5k
What is most nearly the product A • (B x C)?
Place into calculator by pressing “2nd” & “EE”.
Solve.
Evaluate the following indefinite integral.
Use “u” substitution
u = cos2x.
du = (- sin x) dx.
What is the decimal equivalent of the 8 - bit binary number 1011 1101?
The decimal equivalent is found by using the following formula,
D = ak2k - ak-12k-1 + … a0 + a-12-1….
= (1)(27) + (0)(26) + (1)(25) + (1)(24) + (1)(23) + (1)(23) + (1)(22) + (0)(21)+(1)(20)
= 189
The excluse OR is an associative operator, as are all Boolean operators, so
Put information in standard equation of the line y = mx + b (y=4/3x+b).
Insert (6,4) into equation to find y intercept (b).
To find the length take magnitude between two points.
To find the general form take the points given (4,-6)
Seperate them (4,0) & (0,-6)
Insert into point slope form y1 - y2 = m (x1-x2), solve for slope
Make equation of line y = mx + b
Isolate all figures to the left side (General Form) Ax + By + C = 0
Use Logarithmic property logx(A) - logx(B) = logx(A/B)
Then use Logarithmic property logx(A) + logx(B) = logx(AB)
if csc(phi) = -8/5 then, sin(phi) = -5/8
Use identity cos(2phi) = 1 - 2 sin2(phi)
1 - 2[(-5/8)2] solve.
Use trig identity to convert everything to cos and sin.
simplify
use identiy cos2(x) = 1 - sin2(x)
Use U substitution to convert to a quadratic equation
solve
Plug into calculator
Find the EQ of a Circle (x-h)2 + (y-k)2 = r2
Complete the square (half the number then square it)
(x2 - 8x ) + (y2 - 10y ) + 25 = 0
(x2 - 8x + 16) + (y2 - 10y ) + 25 = 0 + 16
(x2 - 8x + 16) + (y2 - 10y + 25 ) + 25 = 0 + 16 + 25
(x2 - 8x + 16) + (y2 - 10y + 25 ) = 0 + 16 + 25 - 25
(x - 4)2 + (y - 5)2 = 16
(4,5)
Take the derivative
Find roots using quadratic formula
Evaluate the derivative using roots
Take the derivative of the function
find roots, choose which one agrees with conditions specified in problem.
Take derivative of top and bottom
find the limit as x -> 0
Take the partial derivative of each term individually
2xy3 + y4 + cos(x)+[-2sin(x)cos(x)] + 0
y3(2x + 1) + cos(x) - 2cos(x)sin(x)
y3(2x + 1) + cos(x)(1-2sin(x)
You dont even have to do the problem.
The integral of 1/x is ln|x| so the answer has to be A.
Use “U” substitution
u = cos(x)
du = -sin(x) dx
evaluate
