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DiKsa [7]
3 years ago
10

A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the

function shown below. After how many seconds will the grasshopper land on the ground? Round to the nearest tenth.
h(t) = -t^2 + 4/3t + 1/4

A. -0.2 seconds
B. 0.5 seconds
C. 1.5 seconds
D. 0.7 seconds
Mathematics
1 answer:
Monica [59]3 years ago
0 0

The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function , which is

h(t) =-t^2+\frac{4}{3}t+ \frac{1}{4}

When the grasshopper land on the ground,

h(t)=0

that is,

-t^2+\frac{4}{3}t+ \frac{1}{4}=0

Multiplying whole equation by 12 to get rid of denominators 3 and 4

-12t^2+16t +3=0

(3-2t)(6t+1)=0 \\ 3-2t=0 , 6t+1=0 \\ t= \frac{3}{2} , \frac{-1}{6}

And time cant be negative, so the correct option is

t = \frac{3}{2}=1.5 seconds

Correct option is C .

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