Questions
Differential equation
Solve the differential equation with details explaination :
x²y" + 6xy' - 24y=x^9
In: Advanced Math
Kernal ( Homomorphisms)
Prove that φ : Z ⊕ Z → Z by φ(a, b) = a − b is a homomorphism. Determine the kernel.
In: Advanced Math
Homomorphisms
How many (group) homomorphisms are there from Z20 onto (surjective to) Z8. How many are there to Z8?
In: Advanced Math
Gaussian Elimination
Solve using Gaussian elimination with partial pivoting and 4 digit arithematic
In: Advanced Math
Maclaurin Series
Find the Maclaurin Series of the following functions:
(a) f(x)= Ln(3+x)
(b) f(x)= cos(3x)
(c) f(x) = x^(2)(e^(-x))
In: Advanced Math
Mathematical modeling
A population of squirrels living in a forest with a carrying capacity of 2600.(assume logistics growth with constant k=0.9yr)
(a)find a formula for the squirrels population p(t) assuming an initial population of 650 squirrels.
(b)how long will it take for the squirrels population to double?
In: Advanced Math
Mathematical modeling
A population of squirrels living in a forest with a carrying capacity of 2600.(assume logistics growth with constant k=0.9yr)
(a)find a formula for the squirrels population p(t) assuming an initial population of 650 squirrels.
(b)how long will it take for the squirrels population to double?
In: Advanced Math
Methods 1
Find two linearly independent solution of
y"+7xy=0. of the form
y1=1+a3x^3+a6x^6+....
y2=x+b4x^4+b7x^7+....
Enter the first few co-efficients
a3=
a6=
b4=
b7=
In: Advanced Math
Optimization Problem
We want to construct a box whose base length is three times the base width. The material used to build the top and bottom cost $10/ft2 and the material to build the sides cost $6/ft2 . If the box must have volume 50 ft3 , what is the minimum cost of the box?
In: Advanced Math
Prove the formulas given in this table for the derivatives of the functions cosh, tanh, csch, sech, and coth.
Prove the formulas given in this table for the derivatives of the functions cosh, tanh, csch, sech, and coth. Which of the following are proven correctly? (Select all that apply.)
\(\square \frac{d}{d x}(\operatorname{coth} x)=\frac{d}{d x}\left(\frac{\sinh x}{\cosh x}\right)=\frac{\cosh x \cosh x-\sinh x \sinh x}{\cosh ^{2} x}=\frac{\cosh ^{2} x-\sinh ^{2} x}{\cosh ^{2} x}=-\frac{1}{\cosh ^{2} x}=-\operatorname{csch}^{2} x\) \(\square \frac{d}{d x}(\operatorname{csch} x)=\frac{d}{d x}\left(\frac{1}{\sinh x}\right)=-\frac{\cosh x}{\sinh ^{2} x}=-\frac{1}{\sinh x} \cdot \frac{\cosh x}{\sinh x}=-\operatorname{csch} x \operatorname{coth} x\)
\(\square \frac{d}{d x}(\cosh x)=\frac{d}{d x}\left[\frac{1}{2}\left(e^{x}-e^{-x}\right)\right]=\frac{1}{2}\left(e^{x}+e^{-x}\right)=\sinh x\)
\(\square \frac{d}{d x}(\operatorname{csch} x)=\frac{d}{d x}\left(\frac{1}{\sinh x}\right)=-\frac{\cosh ^{2} x}{\sinh ^{2} x}=-\frac{1}{\sinh x} \cdot \frac{\cosh ^{2} x}{\sinh x}=-\operatorname{csch} x \operatorname{coth} x\)
\(\square \frac{d}{d x}(\operatorname{sech} x)=\frac{d}{d x}\left(\frac{1}{\cosh x}\right)=-\frac{\sinh x}{\cosh ^{2} x}=-\frac{1}{\cosh x} \cdot \frac{\sinh x}{\cosh x}=-\operatorname{sech} x \tanh x\)
In: Advanced Math
Find dy/dx and d2 y/dx2 . For which values of t is the curve concave upward? 13. x = et , y = te-t
Find dy/dx and d2 y/dx2 . For which values of t is the curve concave upward?
13. x = et , y = te-t
In: Advanced Math
Find the equation of the plane through the point (1,1,1) which is perpendicular to the line of intersection of the two planes x−y−3z=−1 and x−3y+z= 2.
Find the equation of the plane through the point (1,1,1) which is perpendicular to the line of intersection of the two planes x−y−3z=−1 and x−3y+z= 2.
In: Advanced Math
Solve the 4 degree polynomial equation.
Solve the 4 degree polynomial equation \( x^4 − 2x^3 + 4x^2+ 6x − 21 = 0 \), given that the sum of two its roots is zero.
In: Advanced Math