Hello:
Use implicit differentiation : <span>y sin 12x = x cos 2y
y' sin12x+12ycos12x =cos2y -2x y'sin2y
when : x = </span>π/2 and y =π/4<span>
</span>y' sin12(π/2) +12(π/4)cos12(π/2) =cos2(π/4) -2(π/2) y'sin2(<span>π/4)
</span>y' sin(π/6) +(π/3)cos(π/6) =cos(π/2) - π y'sin(π/2)
y' (1/2) +(π/3)(√3/2) = - π
y' (1/2) =-(π/3)(√3/2) - π
y' = -π (1+√3)/3
an equation of the tangent line is : y- π/4 = ( -π (1+√3)/3)(x-<span>π/2)</span>
Answer:
a) two
b) S = {Orange, Purple}
c) 50%
d) 50%
Step-by-step explanation:
a)
When a marble is drawn from the jar, there are <u>two</u> possible outcomes. Either the marble will be orange or it will be purple.
b)
A sample space is a set of all possible outcomes of an event. Thus, the sample space in this case will be:
<u>Sample Space = {Orange, Purple}</u>
c)
The probability of an event is given as the number of favorable outcomes divided by the number of total outcomes.
Therefore,
Probability of selecting orange marble = P(Orange) = 1/2
<u>P(Orange) = 0.5 = 50%</u>
d)
Probability of selecting purple marble = P(Orange) = 1/2
<u>P(purple) = 0.5 = 50%</u>
Plug in the values of xy/z
(-2*-3)/4
=6/4
=3/2
Sorry, I can't do a graph on here for you.
I don't know which quadrent the rectangle started in because there is no image, but it should be easy for you to apply the steps. You know that it is being reflected over the x-axis, this means that x will stay the same, and y will be negative. The x axis is the horizontal one, so if you look at where it is, you can either visualize, or use tracing paper to determine where it will end up.
