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a frog is sitting on a stump 24 ft above the ground. it hops off the stump and lands on the ground 8 ft away.

a frog is sitting on a stump 24 ft above the ground. it hops off the stump and lands on the ground 8 ft away. during its leap, its height h is given by the equation h=-0.5x^2+x+24 where x is the distance from the base to the stump, and h is height in ft. how far was the frog from the base of the stump when it was 21.12 ft above the ground?
Simplify the answer. type an integer or a decimal. round to nearest tenth if needed.
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2 Answers

21.12 represents the height (h) of the frog
 
Using the formula h=-0.5x2+x+24, we use 21.12 for h
 
21.12 = -0.5x2+x+24
 
0=-0.5x2+x+2.88
 
I'd suggest the quadratic equation
 
x= -b± √(b2-4ac)
           2a
 
a=-0.5
b=1
c=2.88
 
x= -1 ± √(12-4(-0.5)(2.88))
                   2(-0.5)
 
Simplifying
 
x= -1 ± √(6.76)      =      1 ± 2.6
            -1
 
So, the solution is x=3.6  OR -1.6   BUT!!:
 
since x represents the distance from the base to the stump, the distance is NOT negative.
So, our answer is:
 
x = 3.6 ft
 
 
 
It is as follows: h will be 21.12 and the equation that gives the height at any moment is h = -0.5X^2 + X +24
Checking this equation for x = 0 and x = 8 the equation is true.
so plugging the 21.12 into the equation we have: 21.12 = -0.5 X^2 + X +24,  the equation is now:
-0.5 X^2 + X + 2.88 = 0
solving this quadratic equation, we obtain:
X=-b +-((b^2 - 4*a*c)^0.5)/2*a Being b = 1; c = 2.88; a= -0.5
X1=3.6
X2= - 1.6
the answer is 3.6 feet from the base because the negative value in not logic.