Answer:
A) The fish was out of water for 0.6875 seconds.
B) Maximum height = 5.672
Step-by-step explanation:
Height is modeled by;
y = -16t² + 11t
A) To find total time of the fish out of water, we need to find the x - intercept. That is the points where y = 0
So, 0 = -16t² + 11t
So the roots of this equation are;
t = 0 or 0.6875
Thus,the fish was out of water for 0.6875 seconds.
B) y = -16t² + 11t
The x coordinate of the vertex is at - b/2a
For y = -16t² + 11t
a = -16, b = 11, c = 0
So, -b/2a = -11/(2*-16) = 11/32
The maximum height will be at the y-coordinate of the vertex.
Thus, we need to find f(11/32)
f(11/32) = -16(11/32)² + 11(11/32) = 1.890625 + 3.78125 = 5.671875 ≈ 5.672

let the equation be





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Simple interest formula
Interest = Pit = $50
P=principal (initial investment)
i=annual interest rate = 0.04
t=time in years = 6 months = 0.5 years
Substitute values,
$50 = P*0.04*0.5
Solve for P
P=$50/(0.04*0.5)=$2500
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
__
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
__
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°