sparks

I don't remember how to do this kind of problem.

I would appreciate a detailed explanation.

Here are a few examples:

The center of a circle defined by x^2+y^2-2x-4y+1=0 is ___?

The radius of a circle defined by x^2+y^2-8x+4y+11=0 is ___?

There is a helix with vector-valued function r(t)=2costi+2sintj+tk

I have found arc length to be:sqrt5t in terms of s as parameter.

also I have found the following parametric equations:

x(s)=2cos(s/sqrt5)

y(s)=2sin(s/sqrt5)

z(s)=s/sqrt5

How can I verify that ||r'(s)||=1?

Thank You

A baseball is hit 3 ft. about the ground at 100 ft./sec. and at and angle of 45 degrees with respect to the ground.

I have found:

vector-valued function is

r(t)=(50tsqrt2)i+[3+(50tsqrt2)-16t^2]j

and maximum height= 81 ft

how do I find the range?

and if possible can you help set up the integral for the arc length?

Thank You

A baseball is hit 3 ft. about the ground at 100 ft./sec. and at and angle of 45 degrees with respect to the ground.

I have found:

vector-valued function is

r(t)=(50tsqrt2)i+[3+(50tsqrt2)-16t^2]j

and maximum height= 81 ft

how do I find the range?

and if possible can you help set up the integral for the arc length?

Thank You

(Qualitative observations, please)

AgNO3 + NaCl

AgNO3 + Na2CO3

AgNO3 + MgSO4

AgNO3 + NH4Cl

AgNO3 + H2O

NaOH + all right side

HCl + all right side