Answer:
- Maria–Ava: 15.7 feet
- Lucas–Maria: 10.1 feet
- angle at Maria: 50°
Step-by-step explanation:
The cosine and tangent functions are useful here. The relevant relations are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
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The distance from Maria to Ava (ma) is the hypotenuse of the triangle, so we have ...
cos(40°) = 12/ma
ma = 12/cos(40°) ≈ 12/0.76604 ≈ 15.7 . . . feet
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The distance from Lucas to Maria (ml) is the side opposite the given angle, so we have ...
tan(40°) = ml/12
ml = 12·tan(40°) ≈ 12·0.83910 ≈ 10.1 . . . feet
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The angle formed at Maria's position is the complement of the other acute angle in the right triangle:
M = 90° -40° = 50°
In summary, ...
- Maria–Ava: 15.7 feet
- Lucas–Maria: 10.1 feet
- angle at Maria: 50°
Answer:
288π or 904.78
Step-by-step explanation:
We know that the diameter of this beach ball is 12 inches and we want to determine how much air it can hold using the formula for the volume of a sphere which is 
× π × r³ where 'r' is the radius. In the question we are given the diameter not the radius but we can half the diameter to find the radius so 12 ÷ 2 = 6. The radius of the beach ball is 6 inches so let's work out how much air it can hold.
Volume = × π × r³
→ Let's substitute in the values
Volume = × π × 6³
→ Simplify
Volume = × π × 216
→ Simplify further
Volume = 288π or 904.78
(4x2 + 2y)(3x+y^2)
= 12x^3 + 4x^2y^2 + 6xy + 2y^3
coefficient of xy is ----> 6
A) Demand function
price (x) demand (D(x))
4 540
3.50 810
D - 540 810 - 540
----------- = -----------------
x - 4 3.50 - 4
D - 540
----------- = - 540
x - 4
D - 540 = - 540(x - 4)
D = -540x + 2160 + 540
D = 2700 - 540x
D(x) = 2700 - 540x
Revenue function, R(x)
R(x) = price * demand = x * D(x)
R(x) = x* (2700 - 540x) = 2700x - 540x^2
b) Profit, P(x)
profit = revenue - cost
P(x) = R(x) - 30
P(x) = [2700x - 540x^2] - 30
P(x) = 2700x - 540x^2 - 30
Largest possible profit => vertex of the parabola
vertex of 2700x - 540x^2 - 30
When you calculate the vertex you find x = 5 /2
=> P(x) = 3345
Answer: you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.
