A rock is tossed vertically from a height of 2m with an initial velocity of 20 ms-1. The height of the rock, h, after t seconds can be modeled by the polynomial function :h(t)=−4.9t2+20t+2, t≥0. Calculate how many seconds, rounded to three significant figures, it takes for the rock to hit the ground.
Answer:
The rock takes 4.18 seconds to hit the ground
Step-by-step explanation:
Function Model
The height of a rock h, after t seconds, can be modeled by the polynomial function:
[tex]h(t)=-4.9t^2+20t+2, t\geq 0[/tex]
When the rock hits the ground, the height is 0, thus we need to find the value of t such as:
[tex]-4.9t^2+20t+2=0[/tex]
A quadratic equation can be expressed as:
[tex]at^2+bt+c=0[/tex]
where a,b, and c are constants.
Solving with the quadratic formula:
[tex]\displaystyle t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The values for the given equation are:
a=-4.9, b=20, c=2
Applying the formula:
[tex]\displaystyle t=\frac{-20\pm \sqrt{20^2-4(-4.9)(2)}}{2(-4.9)}[/tex]
[tex]\displaystyle t=\frac{-20\pm \sqrt{400+39.2}}{-9.8}[/tex]
[tex]\displaystyle t=\frac{-20\pm 20.957}{-9.8}[/tex]
There are two possible solutions:
[tex]\displaystyle t=\frac{-20- 20.957}{-9.8}=4.18[/tex]
[tex]\displaystyle t=\frac{-20+ 20.957}{-9.8}=-0.1[/tex]
Since t > 0, the only solution is t=4.19 seconds
The rock takes 4.18 seconds to hit the ground
what is negative 1 and 4/5 as a decimal
Answer:
1.08
Step-by-step explanation:
Answer:
9/5 or -1.8 or -1 4/5
Step-by-step explanation:
anty: Word problems LLV
Questions
answered
You have prizes to reveall Go to your game board. X
Oakland is hosting a city-wide arts festival at which vendors can pay to have a small booth or
a large booth. The fee for a small booth is $31, whereas the fee for a large booth is $87. The
city hopes to receive at least $2,300 in fees.
Select the inequality in standard form that describes this situation. Use the given numbers
and the following variables.
10
Time
elapsed
x = the number of small booths
26
00 12
HRIN
y = the number of large booths
SmartScore
out of 100
31 + x + 87 + y 2 2,300
50
87x + 31y 2 2,300
31x + 87y 2 2,300
87 + x + 31 + y 2 2,300
Sign out
Answer:
Step-by-step explanation:
Coco butter
10.
There are estimated 255 births every minute of every day. How many babies are born in the
world each hour?
255
6,120
12,250
15,300
Answer:
15,300
Step-by-step explanation:
multiply the estimated total number of births (255)
times 60 because there is 60 minutes in an hour
255*60= 15,300
Answer:
15,300
Step-by-step explanation:
1 hour: 60 minutes
60 x 255 = 15,300
The least common multiple of two numbers is 60, and one of the numbers is 7 less than the other number. What are the numbers? Complete the explanation. The two numbers are . 60 is a multiple of each of its factors. The factors with a difference of 7 are , and their LCM is 60.
17.546 rounded to the nearest hundred
Answer:
17.55
Step-by-step explanation:
tenths are 1 to the right of the decimal hundredths are 2 places right of the decimal and thousands are 3 times right of the decimal
17.546 rounded to the hundredths is 2 times to the right and there is a 5 that rounds it up to 17.55
Answer:
17.55
Step-by-step explanation:
Hundredth .05-0.09 is 0.1 but 0.04 and lower is 0
PLZ HELP ME! What is this! I need help! y = -3x/5 + 2
Answer:
That is the slope intercept form
Step-by-step explanation:
The double number line shows that 4 bottled of water cost 20 dollars at a music
There are about 4,000,000 students attending school, kindergarten through Grade 12, in New York. The average number of students attending a middle school in New York is 8 x 10^2. Approximately how many times greater is the overall number of K–12 students compared to the average number of middle school students?
Question 1 options:
A. 200,000,000 times greater
B. 2,000,000 times greater
C. 50,000,000 times greater
D. 5,000 times greater
Answer:
C
Step-by-step explanation:
big number
Answer:
D
Step by step explanation:
08*10^2=800
4,000,000/800=5,000
Joshua's cousin pledged $12 for a charity walk. If Joshua walked 3 miles, how much did his cousin pay per mile?
Answer:
$4
Step-by-step explanation:
A parking garage charges a 3.50$ base fee plus an hourly rate of 7.00$. If you have at most 21.50$ to pay for parking, how long can you park?
Answer:
You get a total of two hours of parking.
Step-by-step explanation:
First, you subtract the base fee of $3.50, which gives you $18.00. Then you subtract as many sevens there are in 18, which is two. And then your answer is shown, as two. Hope this helps!
Evaluate the expression, -1 x (-0.1 x -5 + 0.5)
Answer:
-1
Step-by-step explanation:
-1 x (-0.1 x -5 + 0.5)
= -1 x 1
= -1
A rectangular table top needs to be divided into six equal sections. Suppose that you are only able to determine the halfway mark between any interval. Explain how you would use these benchmarks to estimate 1/6 of the length of the table top.
Answer:
yes
Step-by-step explanation:
what is 1/2- 1 and 1/5
Answer:
-0.7 is the answer to your question
Answer:
Answer:
-0.7 is the answer to your question
Step-by-step explanation:
What expression is equivalent to: 100
Answer:
10 x 10, 2 x 50
Step-by-step explanation:
12. ROS
CALCULATE THE ARC
LENGTH. ROUND TO THE
NEAREST TENTH.
180
63 11
IQ
S
Answer:
576.97
Squared
A music player app has 2 gigabytes of storage and can hold about 500 songs. A similar, but larger app has 80
gigabytes of storage. About how many songs can the larger app hold?
Answer:
40,000 songs, I think
Step-by-step explanation:
Please help!!!
I will give brilliance!!
Answer:
15
Step-by-step explanation:
sqrt 230 = 15.165...
What is the slope on this graph PLEASE HELP FAST!!!
Answer:
slope = 6
Step-by-step explanation:
slope = rise/run
rise = 12 run = 2
You might need
4.
3
2
1
-4 -3
-2
-1
1
2
CAS
3
4
-1-
1
-2
-3
-4+
What is the slope of the line?
Answer:
1
Step-by-step explanation:
Find the slope passes through (-5,2) and (3,3)
what is the answer of 3x-5>1/2x+8x?
Answer:
x < -10/11
Step-by-step explanation:
Which relation is a function?
Answer: B
Step-by-step explanation:
what -45 divided by 75
Answer:
-0.6
Step-by-step explanation:
The answer is negative because -45 was a negative number.
I didn't explain that very well :|
Hope I helped :)
Can I get Brainliest anyway, even though I did a terrible job explaining? .-.
w over 5 = 3
w = ?
needs sum help
Answer:
w=15
Step-by-step explanation:
Solve for w by simplifying both sides of the equation, then isolating the variable.
What is an equation of the line that passes through the points (-2,-5) and (4,7)
Answer:
y=2x-1
Step-by-step explanation:
the other person is wrong
If b = 3, then b ^-2 is equivalent to ... please help fast lol I’m in a test
Answer:1/9
Step-by-step explanation:
A student evaluated −4 + (−9 1/2) and got an answer of 5 1/2. What might the student have done wrong?
Answer:
Never converted -9 1/2 into an improper fractionAdded the two numbers together instead of subtractedI hope this helps!
can someone help out with this please? (i just put a random answer) but can someone help me out with the actual answer and explain how it’s the answer?
Answer:
distribute on each side is correct :)
Can someone help explain this To me? I need help
Answer:
x=18
Step-by-step explanation:
XZ/RT=XY/RS
60/40=(5x-3)/(3x+2)
1.5=(5x-3)/(3x+2)
1.5(3x+2)=5x-3
4.5x+3=5x-3
9=0.5x
18=x