Answer: sqrt(2)/2 which is choice D
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Explanation
(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).
The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle
180-135 = 45
Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2
sine is positive in quadrant 2
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Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2
Recall that y = sin(theta).
Z=118 as vertically opposite angles are the same
x= (8x-50)
Missing information:
How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point

Answer:

Step-by-step explanation:
Given




Express the given point P as a unit tangent vector:

Next, find the gradient of P and T using: 
Where

So: the gradient becomes:

![\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j]](https://tex.z-dn.net/?f=%5Ctriangle%20T%20%3D%20%5B%28sin%20%5Csqrt%203%29i%20%2B%20%28cos%20%5Csqrt%203%29j%5D%20%2A%20%20%5B%5Cfrac%7B%5Csqrt%203%7D%7B2%7Di%20-%20%5Cfrac%7B1%7D%7B2%7Dj%5D)
By vector multiplication, we have:




Hence, the rate is:
Answer:
7/18
Step-by-step explanation:
²
=((2*7)+4)/7
2*7=14
14+4=18
18/7⇒7/18
Answer:
0 < t < 
After 1.67 days the stocks would be sold out.
Step-by-step explanation:
The price of a certain computer stock after t days is modeled by
p(t) = 100 + 20t - 6t²
Now we will take the derivative of the given function and equate it to zero to find the critical points,
p'(t) = 20 - 12t = 0
t = 
t =
days
Therefore, there are two intervals in which the given function is defined
(0,
) and (
, ∞)
For the interval (0,
),
p'(1) = 20 - 12(1) = 20
For the interval (
, ∞),
p'(2) = 20 - 12(2) = -4
Positive value of p'(t) in the interval (0,
) indicates that the function is increasing.
0 < t < 
Since at the point t = 1.67 days curve is showing the maximum, so the stocks should be sold after 1.67 days.