SOLUTION: Indiana Jones is in search of the "pot of gold" at the end of the rainbow. After careful analysis, he has found that the rainbow can be modeled by the quadratic equation; h(x)=

Question 726708: Indiana Jones is in search of the "pot of gold" at the end of the rainbow. After careful analysis, he has found that the rainbow can be modeled by the quadratic equation;
h(x)= 0.73x - 0.12x^2 - 0.73
where h = height and x = horizontal distance in kilometers.
(a)What assumptions can be made?
(b)Find the total distance between the ends of the rainbow.
(c) Indiana knows that if clouds were to obstruct his view, he will be unable to follow the rainbow's path. What is the lowest that the clouds can be to not obstruct Indiana's quest.
This was from a revision sheet for an exam I have coming up, this exam is on Monday, if you could answer this question ASAP, it would be greatly appreciated. Thank you so much, :)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
After careful analysis, he has found that the rainbow can be modeled by the quadratic equation;
h(x)= 0.73x - 0.12x^2 - 0.73
normally written
h(x) = -.12x^2 + .73x - .73
where h = height and x = horizontal distance in kilometers.
(a)What assumptions can be made?
That it is a parabola, opening downward.
:
(b)Find the total distance between the ends of the rainbow.
That would be the distance between the x intercepts, solve the equation using the quadratic formula

where: a=-.12; b=.73; c=.-73

Two solutions

x =
x = +1.26
and

x =
x = +4.82
The distance between the ends of the rainbow
4.82 - 1.26 = 3.56 km
:
(c) Indiana knows that if clouds were to obstruct his view, he will be unable to follow the rainbow's path.
What is the lowest that the clouds can be to not obstruct Indiana's quest.
That would be the maximum of the parabola, find the axis of symmetry
x =
x = 3.04 ~ 3 should be close enough
Substitute 3 for x in the original equation to find the max height
h(x) = -.12(3^2) + .73(3) - .73
h(x) = .38 km or about 380 meters max height of the rainbow
:
I am sure of the method but you should check the math here.
:
Looks like this

RELATED QUESTIONS
A naturalist estimated the total number of rainbow trout in a certain lake using the... (answered by ankor@dixie-net.com)

The Set of Colors of the rainbow? (answered by Fombitz)

Mr. jones is visiting his son at college. After driving 180 miles he has completed 5/8 of (answered by solver91311)

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first... (answered by stanbon)

Marina has a gold bracelet that weighs 90 grams. 45% of the bracelet is pure gold. How... (answered by ikdeep)

24-carat gold is pure gold. 18 carat gold is 3/4 gold. 20- carat gold is 5/8 gold. the (answered by noahhamstra,abdullahkhawer)

I tried this one for at least 45 minutes, and really need help, please. Mr. Elliot is... (answered by stanbon)

Alex has a total of 50 g of gold to make a necklace. He has two different types of gold. (answered by Alan3354)

In his demonstration on the art of tea making, John first poured some tea from a pot into (answered by Theo)