susan took two tests.the probability of her passing both tests is 0.6.the probability of her passing the first test is 0.8.what
1 answer:
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The ramp,the rise and the base, when illustrated, will form a right triangle. The hypotenuse is the ramp which measures 200 ft long. The rise is the vertical height which measures 37 feet. As you can see in the picture, the arc drawn below the ramp to the horizontal line directing to the freeways is the unknown angle that we have to find.
First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:
cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°
Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,
β = 90° + 79.34°
β = 169.34°
First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:
cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°
Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,
β = 90° + 79.34°
β = 169.34°
Answer:
The antenna should be place 0.75 inches above the vertex.
Step-by-step explanation:
We have the equation of the parabola:
(x-4)²=3(y-3)
The general equation of the parabola is:
(x-x₀)²=4p(y-y₀)
where:
(x₀,y₀) is the vertex of the parabola
p is the focus of the parabola
Hence,
The vertex of the parabola is (4,3)
The focus of the parabola is given by:
Then, we have to shift the antenna towards the focus point. The focus point would be:
(x₀,y₀+p)=(4,3+0.75)= (4,3.75)
The directrix of the parabola is:
y=y₀-p
y=3-.75=2.25
A graph of the parabola is attached, with its focus point (4.3.75) and its directrix (y = 2.25)
