Question

http://prntscr.com/12x4ps HELP with app of derivatives.

Answer 1

first thing is slope of tangent line is dy/dx
slope is given as -1/2

use implicit differentiation to find dy/dx
\[\rightarrow \frac{dy}{dx} = (1+\frac{dy}{dx})[-\sin (x+y)]\]
\[\rightarrow \frac{dy}{dx} +\frac{dy}{dx} \sin (x+y) = -\sin (x+y)\]
\[\frac{dy}{dx} = \frac{-\sin(x+y)}{1+\sin(x+y)}\]
set equal to -1/2 to solve for sin(x+y)

Answer 2

done.. i get x+y=pi/2.. what next?

Answer 3

hmm original function could be written as:
\[ x = \cos^{-1} (y) - y\]
apply this to relation required for slope
\[(\cos^{-1} (y) -y) +y = \pi/2\]
\[\cos^{-1} y = \pi/2\]
y=0
thus x = pi/2
this is point where line is tangent to curve

Answer 4

plug in to solve for k

Answer 5

hmm.. thank you.

Answer 6

http://prntscr.com/12x8hy
can you help me with this one too @dumbcow ?

Answer 7

Statement 1 should be wrong no?

Answer 8

i think its true ... rearrange circle equation into standard form
\[(x-3)^{2} + (y+1)^{2} = 10\]
that puts center at (3,-1)
this point is on the line, so line could be diameter

Answer 9

No it says "the only circle with radius ... and diameter ... can be ... "
there can be infinite circles with centre on that line and given radius?

Answer 10

any other circle would have either a different radius or diff center though

Answer 11

but the centre can still lie on that line and with the same radius?

Answer 12

oh i see

Answer 13

so statement 1 false?

Answer 14

guess so

Answer 15

hmm. thank you.

Answer 16

statement II is true since the diameter always perpendicular to tangent line

Answer 17

yup.. got that..
are you good at chemistry?

Answer 18

not really....used to know stuff but been awhile

Answer 19

http://i.imgur.com/8xeuB8I.png
just in case you know. by delta(not) does it mean CFSE?

Answer 20

no idea...is that organic chem

Answer 21

no problem. inorganic..

Answer 22

you might try the chemistry forem

Answer 23

yeah. i'll post it there.