A model rocket is launched directly upward at a speed of 20 meters per second from the ground. The function f(t)=−4.9t2+20t, models the relationship between the height of the rocket and the time after launch, t, in seconds. When, in seconds after launch, will the rocket reach its highest point? Round to two decimal places.
Answer:
The rocket will reach its highest point about 2.04 seconds.
Step-by-step explanation:
The function:
[tex]f(t)=-4.9t^2+20t[/tex]
Models the relationship between the height of the rocket and the time after launch t in seconds.
Since this is a quadratic function, the rocket will reach its highest point at its vertex. The vertex of a quadratic is given by:
[tex]\displaystyle \Big(-\frac{b}{2a}, f\Big(-\frac{b}{2a}\Big)\Big)[/tex]
In this case, a = -4.9, b = 20, and c = 0. Thus:
[tex]\displaystyle t=\frac{-(20)}{2(-4.9)}=\frac{10}{4.9}\approx 2.04[/tex]
The rocket reaches its maximum height after 10/4.9 or about 2.04 seconds.
Further Notes:
Then the maximum height of the rocket will be f(10/4.9):
[tex]\displaystyle f\Big(\frac{10}{4.9}\Big)=-4.9\Big(\frac{10}{4.9}\Big)^2+20\Big(\frac{10}{4.9}\Big)\approx20.41\text{ feet}[/tex]
If f(x)=3x^2+x-2, then f(-2)=
Answer:
f(- 2) = 8
Step-by-step explanation:
To evaluate f(- 2) , substitute x = - 2 into f(x) , that is
f(- 2) = 3(- 2)² + (- 2) - 2 = 3(4) - 2 - 2 = 12 - 4 = 8
HELP PLSS I BEG plss
Answer:
Answer for 3:
its 6/2 and 3/1 because 6/2 simplified is 3 and 3/1 is 3
Step-by-step explanation:
Answer for 4
box one 1/4
box 2 4/10
box 3 3/4
23. Find the perimeter and area of the rectangle below. 10x^2 7xy^2
Answer:
Area= 70x^3y^2
Perimeter = 20x^2 + 14 xy^2
Step-by-step explanation:
Area is just multiplying the length and width, I multiplied the constants first which gets us 70 then multiplied the variables, they combine however only the x's can be multiplied to each other which results in 70x^3y^2 . The perimeter you just multiply the length by two and the width by two, they are separate because the variables when added to each other do not combine.
Which three dimensional figures could be used
Answer:
A cube, rectangular prism, sphere, cone and cylinder are the basic 3-dimensional shapes we see around us.
Joe has $70 in a savings account. The interest rate is 10% per year and is not compounded,
How much interest will he earn in 4 years?
Use the formula i = prt, where / is the interest earned, p is the principal (starting amount),
is the interest rate expressed as a decimal, and t is the time in years.
Answer:
$28
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 10%/100 = 0.1 per year,
then, solving our equation
I = 70 × 0.1 × 4 = 28
I = $ 28.00
The simple interest accumulated
on a principal of $ 70.00
at a rate of 10% per year
for 4 years is $ 28.00.
Choose all that correctly solve for the variable x
[tex]\frac{5}{2} x[/tex] = [tex]\frac{15}{2}[/tex]
x = 3
------------------------------------------------------------------------------
x + [tex]\frac{7}{2} = 7\\x
= \frac{7}{2}[/tex]
---------------------------------------------------------------------------------
x + 3 = [tex]\frac{21}{5}\\x
= \frac{5}{6}[/tex]
----------------------------------------------------------------------------
5x = \frac{11}{2}
x = |frac{10}{11}
The entire graph of the function f is shown in the figure below.
Write the domain and range of f as intervals or unions of intervals.
Question
A bag contains 3 pink gumballs, 4 red gumballs, and 2 green gumballs. Find the probability that you do not draw all green
gumballs if there are 3 drawings that occur and the gumballs are replaced after each draw. Round your answer to two
decimal places.
Provide your answer below
Answer:
.47
Step-by-step explanation:
9 gumballs in all
7 of them are not green
'ng' = not green
P(ng,ng,ng) = 7/9 x 7/9 x 7/9 = .47
The probability will be 0.87.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that,
Number of Pink gumballs = 3,
Number of Red gumballs = 4,
Number of Green gumballs = 2,
Now,
Total number of gumballs = 3 + 4 + 2 = 9,
Thus, total number of ways of selecting 3 gumball
= 9 x 9 x 9
= 729
Number of Green gumballs = 2
Number of gumballs other than green = 9 - 2 = 7
So, Number of ways to draw 3 gumballs other than green is;
= 7 x 7 x 7
= 243
And, Number of ways to draw one green and two other gumballs in 3 draw = 2 x 7 x 7 + 7 x 2 x 7 + 7 x 7 x 2
= 294
( Since the green gumballs can be drawn in 1st, 2nd, and 3rd draw.)
Thus, The probability of not drawing all 2 green gumballs is;
= 343 + 294 /729
= 637/729
= 0.87
So, The probability will be 0.87.
Learn more about the probability visit:
https://brainly.com/question/25870256
#SPJ6
15 POINTS!!!!
7 ÷ 0.1 = 7 ÷ 1/10
7 is 1/10 of____.
Help Please
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
I believe this question should be one solution
Step-by-step explanation:
Hope this Helped
x+3= -10 what is x in the equation
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answer:No
Step-by-step explanation:
what is the answer of 5ax +8ax+6ax=?
All have ax included so add the numbers together.
5ax + 8ax + 6ax = 19ax
Find the sum of the first 10 terms of the following series to the nearest Integra 3, 5, 25/3,...
Answer:
S(10)=3*(1-(5/3)^10)/(1-5/3)
Step-by-step explanation:
It is Geometric series with r:
r=5/3=(25/3)/5=5/3
a=3
Sum of G.S. in formula:
S(n)=a(1-r^n)/(1-r)
S(10)=3*(1-(5/3)^10)/(1-5/3)
=246.5725...
18. If 4 - 5x = -3, then what is 10x - 8
Answer:
6
Step-by-step explanation:
[tex]4 - 5x = - 3 \\ \\ - 5x = - 3 - 4 \\ \\ - 5x = - 7 \\ \\ x = \frac{ - 7}{ - 5} \\ \\ x = \frac{7}{5} \\ \\ 10x - 8 \\ \\ = 10 \times \frac{7}{5} - 8 \\ \\ = 2 \times 7 - 8 \\ \\ = 14 - 8 \\ \\ = 6[/tex]
5 divided by 62.55 pleaseeee answer asap
The answer is 12.444
Answer:
the answer is on top me
Step-by-step explanation: lol
HEEEELPPPPPPPPP Which properties describe the graph of (x + 5)2 + (y – 10)2 < 169?
Answer:
circle with center at (–5, 10), shading inside the circle
Step-by-step explanation:
edge2021
Answer:
A. circle with center at (–5, 10), shading inside the circle
5 in = ___________ ft
Answer:
0.416667 foot
Step-by-step explanation:
Answer: 0.41666667
Step-by-step explanation:
From the internet
How do savings account differ from checking accounts
- they’re not offered at banks
- they typically pay interest
- the funds are easier to get
-you have to keep the money in for a long
Answer:
Savings accounts typically pay interest.
Step-by-step explanation:
there is a sales tax of $22 on an item that costs$272 before tax. the sales tax on the second item is $19.25 how much does the second item cost before tax
Answer:$240.62
Step-by-step explanation:
You divide 22/272 to get .08 then you divide 19.25 by .08 to get 240.62.
What is the constant of variation of c=2.15g
Thx to all that help
Answer:
Since the equation can be written in the form y=kx, y varies directly with x and k. The constant of variation, k, is 2.15
Can a triangle have three acute angles? Justify your answer
Solve the equation.
q − 11 = 16
Answer:
q = 27
Step-by-step explanation:
Answer: 27
Step-by-step explanation: 16+11=27
8. Carisa is four inches taller than her friend Lily.
Answer:
cool
Step-by-step explanation:
3. Factor the following trinomial. x^2 - 15x + 56.
Step 1: The trinomial factors as x2 + bx+ c = (x + p)(x + 9), where p+ q = b and p. q = c. Fill in the
following table with all of the possible values of p and q, using the fact that their product is the
constant term, c = 56. (4 points)
Answer:
(-7, -8)
Step-by-step explanation:
Yes, this is the same answer as the other person, but I just included the other factors, a picture of my table, and the answer to part two is "The pair (-7, -8) equal the coefficient of the x-term in the trinomial."
Have a great day, I hope this helps you or anyone else who might've needed this!
water flows into a tank through a cylindrical pipe with a radius of 10cm at a rate of 30cm/sec. how long will it take to fill the water tank? give answer in hours and minutes.
volume of tank is 157.5m
Answer:
volume of tank is 157.5m
Step-by-step explanation:
that's too high
Does someone know the answer I NEED IT NOW
Answer:
2nd option ,
A is correct, B is incorrect, C is correct
I suck at geometry can someone help??
Answer:
Last option is the correct answer
Step-by-step explanation:
None of these choices are correct.
Correct order would be,
Since,
58° < 59° < 63°
Therefore,
AC < CB < AB
AC, CB, AB (this is the correct order of the sides from shortest to longest.)
The length of Andy's bed is 123 what is the length in feet