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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.

### 2 Answers by Expert Tutors

Pete R. | Experienced Math TutorExperienced Math Tutor
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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

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.

x = 3.6 ft

Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
5.0 5.0 (1 lesson ratings) (1)
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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.