answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kondor19780726
1 month 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:
zzz [12.3K]1 month ago
0 0

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

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

When the grasshopper reaches the ground,

h(t)=0

that is,

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

Multiplying the entire equation by 12 to eliminate the denominators of 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}

Moreover, time cannot be negative, therefore the accurate answer is

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

The correct option is C.

You might be interested in
I=$720, P=$1000, r=9%<br> Find the amount of the time.
Leona [12618]
I = PRT....seeking T...rearrange......I / PR = T

I / PR = T
I = 720
P = 1000
R = 9% = 0.09
substituting values
720 / (1000)(0.09) = T
720 / 90 = T
8 = T <===
4 0
1 month ago
Read 2 more answers
To reduce wear and tear on the family vehicle, you decide to rent a car. Happy Harry’s Rentals has a $500 fee for any rental up
Inessa [12570]
Assuming a maximum rental duration of 8 days, if we apply this to the equation, Happy Harry's Rentals costs $500, while Smilin' Sam's charges $600. Therefore, for the 7th and 8th days, Happy Harry's Rentals is a better option, while Smilin' Sam's is preferable for the first six days.
8 0
1 month ago
In the Ma-and-Pa grocery store, shelf-space is limited and must be used effectively to increase profit. Two-cereal items, Grano
Inessa [12570]
No. Allocate 2/3 of the space to Grano and 1/3 to Wheatie. This results in approximately 57% for Wheatie and 43% for Grano—meaning 60(.57)=34.2 ft² for Wheatie and 60(.43)=25.8 ft² for Grano. Therefore, there would be about 85.5 boxes of Wheatie and 129 boxes of Grano, leading to a total profit of 129(1)+85(1.35)=$243.75. The best choice would be to place 200 boxes of Grano and 50 boxes of Wheaties on the shelf. Allocating 40 ft² to Granos (200(.2)) and 20 ft² to Wheaties (50(.4)) means that 40/60=2/3=66.6% of the space would be for Granos, and 20/60=1/3=33.3% would be for Wheaties. The total profit would be 200(1)+50(1.35)=$267.5.
5 0
1 month ago
A man purchased 6 fruits at Rs 10 How many fruits will he sell at Rs 9 so that he may make an overall profit of 8%
Svet_ta [12734]

Response:

Detailed breakdown:

P(x)=S(x)-C(x)

0.8=9-C(x)

C(x)=9 -0.08

C(x)=8.92

3 0
20 days ago
Forensic scientists use the equation h=2.6f+47.2 to estimate the height h of a woman given the length in centimeters of her femu
zzz [12365]

Answer:

waaa

Detailed explanation:

6 0
28 days ago
Other questions:
  • An object is traveling at a steady speed of 8 2/3 miles per hour. How long will it take the object to travel to 5 1/5 miles
    6·2 answers
  • Which function has an inverse that is also a function?
    12·2 answers
  • A mattress store sold 1,330 mattresses in one year. If 30% of the mattresses sold were king size mattresses, how many king size
    8·2 answers
  • Peter mixes 4 1/2 cups of orange juice, 2 1/4 of ginger ale and 6 1/3 cups of strawberry lemonade to make some punch. What is th
    6·1 answer
  • The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in theratio is 10, what is the Second numb
    7·2 answers
  • The average diameter of sand dollars on a certain island is 5.00 centimeters with a standard deviation of 0.90 centimeters. If 1
    5·1 answer
  • A teacher wants to see if a new unit on taking square roots is helping students learn. She has five randomly selected students t
    5·2 answers
  • Not including tax, a total of 19 pens and markers cost $11.50. The pens cost $0.25 each, and the markers cost $0.75 each. Which
    5·1 answer
  • Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let
    6·1 answer
  • jack and kevin play in a basketball game if thr ratio of point scsred by jack to points scored by kevin is 4 to 3 which of the f
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!