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
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. 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
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.
In: Advanced Math
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