Math Answers

what is the importance of trigonometry in daily life?

use the Gaussian Elimination method to find the value of a so that the system of equations.
x+(a+4)y+(4a+2) z=0
2x+3ay+(3a+4) z=0
x+2(a+1)y+(3a+4) z=0
has (i) a unique solution ;
(ii) infinitely many solutions.
Further, find the solution set in each case.

An automobile dealership uses CODE = 1 for new automobiles, CODE = 2 for used automobiles, and CODE = 3 for separate accessories. A salesman’s commissions are as follows: on new automobile, 3% of the selling price but a maximum of $300; on used automobile, 5% of the selling price but with a minimum of $75; on accessories, 6% of selling price.

1. Draw a flowchart that inputs CODE and PRICE and outputs COMMISSION.
2. Write a pseudocode programme that inputs CODE and PRICE and outputs COMMISSION.

Given that
A
=
sin
t
i
+
cos
t
j
+
t
k
A=sin⁡ti+cos⁡tj+tk
, evaluate
∣
∣
∣
d
2
A
d
t
2
∣
∣
∣
|d2Adt2|

Determine the unit tangent at the point where t=2 on the curve
x
=
t
2
+
1
x=t2+1
,
y
=
4
t
−
3
y=4t−3
and
z
=
2
t
2
−
6
t

(1) obtain the solution for the initial value problem dy/dx+(cotx)y=xcscx,y(pi/2)=1

(2)solve the differential equation dy/dx=x(1+y^2)

(3) solve the differential equation dy/dx+(cotx)y=xcscx

Q. show that u(x, y)=xf(2x+y) is a general solution of x∂u/∂x-2x ∂u/∂y=u

Q. show that u(x, t)=e-8tsin2x is a solution to the initial boundary value problem
∂u/∂t=2(∂^2 u)/〖∂x〗^2
(B.c,s) u(0,t)=0, u(π, t)=0 t>0
(I.C) u(x,0)=sin2x

Q. form the partial differential equation by eliminating the arbitrary function ᵩ
from the relation
ᵩ(x+y+u, x2+y2+u2)=0

Q. form the partial differential equation by eliminating the arbitrary function from the relation
u=f(x-3y)+g(2x+y)