if i is a variable
if i is the imaginary unit defined by i²=-1
Answer:
the ratio of the distance in inches travelled by the tip of the hour hand to the distance in inches travelled by the tip of the minute hand is <em>0.125</em>.
Step-by-step explanation:
The given information is:
- length of the hour hand, l = 6 inches
- length of the minute hand, b = 8 inches
Therefore, since the tip of the minute moves from 12 to 3, it moved a distance of:
s₁ = r θ
s₁ = (8)(π/2)
s₁ = 4π inches
The hour hand moves 30 degrees / 60 = 1/2 degree in a minute.
Therefore, in 30 minutes the hour hand moves a distance of:
s₂ = r θ
s₂ = 6(30×1/2×π/180)
s₂ = π/2 inches
Therefore, the ratio of the distance in inches travelled by the tip of the hour hand to the distance in inches travelled by the tip of the minute hand is:
s₂ / s₁ = (π/2) / 4π
<em>s₂ / s₁ = 0.125</em>
Answer:
<em> f ( x ) = - 2x^2 + 3x + 1</em>
Step-by-step explanation:
If f ( x ) extends to → − ∞, as x→ − ∞ , provided f(x) → − ∞, as x → +∞, we can rewrite this representation as such;
− ∞ < x < ∞, while y > − ∞
Now the simplest representation of this parabola is f ( x ) = - x^2, provided it is a down - facing parabola;
If we are considering a down - facing parabola, the degree of this trinomial we should create should be even, the LCM being negative. Knowing that we can consider this equation;
<em>Solution; f ( x ) = - 2x^2 + 3x + 1</em>, where the degree is 2, the LCM ⇒ - 2
Let's supposes the number of cups sold is <em>c</em>.
We can use an equation to solve this problem. Since both people are down some money, we will write the number they spent on supplies as negative, and use their rates as the unit rates for each side of the equation.
-35 + 1.50c = -20 + 1c
.05c = 15
c = 30
Thus, they will have to sell 30 cups.
