Let D be the region bounded below by the plane z=0, above by the sphere x2+y2+z2=196, and on the sides by the cylinder x2+y2=49. Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration. a) dzdrdθ
b) drdzdθ
c) dθdzdr

Hannah is 3 years older than twice her brother joey’s age. joey is 2 years old. how old is hannah? show all of your work! the number of students is five more than seven times the number of teachers. there are 10 teachers. how many students are there? be sure to show all of your work!

For [tex]f(x) = 4x + 1[/tex] and (x) = [tex]g(x)= x^{2} -5,[/tex] find [tex](\frac{g}{f}) (x)[/tex]a. [tex]\frac{x^{2} - 5 }{4x +1 },x[/tex] ≠ [tex]-\frac{1}{4}[/tex]b. x[tex]\frac{4 x +1 }{x^{2} - 5}, x[/tex] ≠ ± [tex]\sqrt[]{5}[/tex]c. [tex]\frac{4x +1}{x^{2} -5}[/tex]d.[tex]\frac{x^{2} -5 }{4x + 1}[/tex]

F(x) = x^2+x-2/x^2-3x-4 what is the domain and range, x-and y-intercepts, horizontal asymptotes, and vertical asymptotes?