Math

Question 1

Hyperbola Equation

Answer 1

Ax²+2Bxy+Cy²+…=0

B²-AC>0

Question 2

Cos²θ+sin²θ

2Cosθ*sinθ

Answer 2

1

2sinθ

Question 3

Adjoint

adj|2 3|

  |-1 0|

Answer 3

|0 -3|

|1 2|

Question 4

Eigenvalues

|1 1|

|2 0|

Answer 4

|1-λ 1|

|2 0-λ|

Question 5

Particular Differential Equation

y+4y=3e^(-t)

Answer 5

replace y to solve the equation

y=Ae^(-t)

Question 6

Amplitude

of steady-state

y+4y+4y=8sin2t

Answer 6

replace y with some comon factor

y_p=Asin2t+Bcos 2t

Question 7

Volume of a parabola

Answer 7

V=∫πx²dy ,0,a

Question 8

the vector field is conservative is zero

Answer 8

The curl

the curl of a vectore field is zero if it is conservative

Question 9

the cross product AxB

A= (4i+2j)

B= (3i+5j)

Answer 9

(4*5)- (2*3)

Question 10

Dot Product

A*B

A=(4i+2j)

B(3i+5j)

Answer 10

A*B= (4*3)+(2*5)

Question 11

component of A in the direction B

A=i-4j and B= 2i-4j-4k

Answer 11

A*i_B=(A*B)/|B|

={(i-4j)*(2i-4j-4k)]

(2²+4²+4²)^1/2

(2+16)/6=3

Question 12

the diferential equation

y”+3x²y’+sinx=0

is?

Answer 12

x: nonhomogeneous

X²: variable coefficient

depends in Y:linear

if its in terms of Y will be nonlinear

Question 13

Taylor series

Cos2x

Answer 13

1-(2x)²/2!+(2x)⁴/4!-….

Question 14

intercept of the line tangent to the parabola

x=2y²

point: (2,1)

Answer 14

derivada de x

x=4y

y=1/4x+b

replce the point and find b

Question 15

i=

Answer 15

i=e^(πi/2)

Question 16

e^(πi/4)=

Answer 16

=cosπ/4 + i sinπ/4

Question 17

limx-0, f2/g2

f=sin2x

g=x

Answer 17

2sin2xcos2x)/x

2(2cos²2x-2sin²2x)/1=4

use differenatial in both sides

Question 18

dot product in polar form

(1+2i)(5+3i)

Answer 18

=x+yi

re^iθ

r=√(x²+y²)

θ=tan^-1 (y/x)

degree in polar

Question 19

∫(0,π), x sin2x dx

Answer 19

u=x dv=sin2xdx

du=dx v=-1/2cos2x

uv+vdu

Question 20

base 4 number 101.1 to base 10

Answer 20

1*4²+0*4¹+1*4⁰+1*4^-1

Question 21

base10 number 21.75

into binary form

Answer 21

1*2⁴+0*2³+1*2²+0*2¹+1*2⁰

Question 22

which integral be used to provide the socond moment about the x-axis of the area formed by the straight line, the x-axis and the y-axis?

Answer 22

∫₀³γ² x dy

Question 23

with **differentiation you can **

Answer 23

find concavity of curve,the location and number of inflection points