Answer: Ф = 20
Step-by-step explanation:
sin2Ф = cos (Ф+ 30 )
if sinα = cosβ , then α and β are complementary ,that is they add up to be 
.
Therefore : 2Ф + Ф + 30 = 90
3Ф + 30 = 90
3Ф = 90 - 30
3Ф = 60
Ф = 20
Answer:
b and c
Step-by-step explanation:
The derivative of an exponential function is
Moreover, in this case we must apply the chain rule because the exponent is -x:
12A+8W > 343 represents the number of minutes the robot filters air A and water W to filter more than 343 liters of air and water.
If the robot filters air for 20 minutes and water for 15 minutes, plugging A as 20 and W as 15, let us check if the equation is true or not.
Checking left side:
12A + 8W = 12(20) +8(15)
240+ 120 = 360
Checking right side: 343
12A+8W > 343
360>343
True.
So the robot meets the first expectation.
Let us check for second equation:
3A+4W < 49
Left side : 3A +4W = 3(20) +4(15) = 60 +60 =120
Right side is 49
comparing left and right side:
3A+4W < 49
120<49
False.
So the robot does not meet the second expectation.
We need to find m and b to find in the equation of a line:
y = mx + b
↑ <span>↑
slope y-intercept
To find m, the slope, we need to find the rise over the run of the line. You pick two points and use the y values finding the difference of them and do the same for the x values and put them on the bottom. Let's use the points (0, -2) and (4, 0):
</span>↑ ↑<span>
(x₁, y₁) (x₂, y₂)
m = (y</span>₂ - y₁)/(x₂ - x₁)
m = (-2 - 0)/(0 - 4)
m = (-2)/(-4)
m = 1/2
The slope is positive since the line is going upward from left to right.
Now we need b, the y intercept, where the line intersects with the y axis, simply by looking at the graph. b is -2.
Thus, the answer is C. y = 1/2x - 2.
