Question

Find all solutions to the following systems. Express answers as ordered pairs. x^2+y^2=7x+24 ,2x=y^2

Answer #1

1a) Find all the integer solutions of each of the following
linear Diophantine equations:
(i) 2x + y = 2,
(ii) 3x - 4y = 0,
and
(iii) 15x + 18 y =17.
1b) Find all solutions in positive integers of each of the
following linear Diophantine equations:
(i) 2x + y = 2,
(ii) 3x - 4y = 0,
and
(iii) 7x + 15 y = 51.

Are the following vector space and why?
1.The set V of all ordered pairs (x, y) with the addition of
R2, but scalar multiplication a(x, y) = (x, y) for all a
in R.
2. The set V of all 2 × 2 matrices whose entries sum to 0;
operations of M22.

Describe all pairs (x , y) of real numbers x and y that satisfy
the following equation: x^2 + 2x + 1 = y^2 − 6y + 9

Find the absolute minimum of f(x,y)=x^2−y^2−x on the region
R={(x,y)|3≤x≤5,2≤y≤4}. Express the answer as an ordered triple.

Find all solutions of the equation and express them in the
form
a + bi.
(Enter your answers as a comma-separated list. Simplify your
answer completely.)
2x2 − 2x + 1 = 0
x =
pt. 2
Find all solutions of the equation and express them in the
form
a + bi.
(Enter your answers as a comma-separated list. Simplify your
answer completely.)
16x2 + 3 = 8x
x =
pt.3
A polynomial P is given.
P(x) = x4 +...

Find (f −1 (a))' :
(a) f(x) = 2x 3 + 3x 2 + 7x + 4, a = 4
(b) f(x) = 2x + cos(x), a = 1

f(x)=3x^4-7x^2+2x+1
Find the tangent line at x=2

Find all solutions to the differential equations.
(a) x^2 yy' = (y^2 − 1)^(3/2)
(b) y' = 6xe^(x−y)
(c) y' = (2x − 1)(y + 1)
(d) (y^2 − 1) dy/dx = 4xy^2
Leave your answer as an implicit solution

Use the Euclidean algorithm to find all integer solutions to the
following diophantine equation:
2x + 6y - 9z = 13
Find all positive integer solutions to the following diophantine
equation:
2x + 6y + 5z = 24

part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...

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