A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x2 + 3x. A beam of light modeled by the eq
uation -2x + 5.5y = 19.5 passes through the fountain to create a rainbow effect. If the beam cuts the water spray at points A and B, such that point B is at a higher level than point A, what distance from the ground level is point A?
1 answer:
See the attached figure.
Water model ⇒⇒⇒ y = -0.3 x² + 3x ( blue graph )
Light model ⇒⇒⇒ -2x + 5.5 y = 19.5 ( red graph )
The intersection between the two models A and B
A = ( 1.657 , 4.148 )
B = ( 7.13 , 6.138 )
<span>B is at a higher level than point A
</span>
<span>The distance from the ground level to point A = y-coordinate of point A
= 4.148
</span>
Water model ⇒⇒⇒ y = -0.3 x² + 3x ( blue graph )
Light model ⇒⇒⇒ -2x + 5.5 y = 19.5 ( red graph )
The intersection between the two models A and B
A = ( 1.657 , 4.148 )
B = ( 7.13 , 6.138 )
<span>B is at a higher level than point A
</span>
<span>The distance from the ground level to point A = y-coordinate of point A
= 4.148
</span>
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Answer:
y = 20
Step-by-step explanation:
Use the points to find the values of a and b
Using (0, 20 ) , then
20 = a [
= 1 ] , then
20 = a
y = 20
Using (3, 1280 ) , then
1280 = 20 b³ ( divide both sides by 20 )
64 = b³ ( take the cube root of both sides )
= b , that is
4 = b
Then exponential function is
y = 20.