Answer:
I hope this helps.
Step-by-step explanation:
h(t) = -16t2 + 108t + 28
(a)
Maximum height occurs at the vertex of the height-vs.-time parabola, which is at
t = -108/[2(-16)] sec = ? sec
Evaluate h(t) at this value of t to get hmax.
(b)
Set h(t) = 0 and solve the quadratic equation for t. You will get a positive and a negative solution. Discard the negative solution, since time starts at t = 0.
The quadratic function, h = -16t + 136t + 72, gives us:
a) The maximum height of the ball is 360 feet.
b) The time taken by the ball to hit the ground is 9 seconds.
What is a quadratic function?A quadratic function is a function over a quadratic expression, that is, over an expression having degree 2.
How to solve the question?In the question, we are informed that a person standing close to the edge of a 72-foot building throws a ball vertically upward. The quadratic function h = -16t² + 136t + 72 models the ball's height above the ground, h in feet, t seconds after it was thrown.
We solve the following:-
a) What is the maximum height of the ball?
The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.
Differentiating both sides. we get:
[tex]\frac{\delta h}{\delta t} = -32t + 136[/tex] .
To get point of inflection, we equate this to 0, to get:
[tex]\frac{\delta h}{\delta t} = -32t + 136 = 0[/tex],
or, -32t + 136 = 0,
or, t = 136/32 = 4.5.
To check whether the value of h is maximum/minimum at t = 4.5, we differentiate [tex]\frac{\delta h}{\delta t} = -32t + 136[/tex] again, to get:
[tex]\frac{\delta^{2} h}{\delta t^{2} } = -32[/tex] , which is < 0, which that implies, h is maximum at t = 4.5.
Now, we calculate the maximum height, by putting in t = 4.5, in the equation, to get:
h = -16(4.5)² + 136(4.5) + 72,
or, h = -16(20.25) + 612 + 72,
or, h = -324 + 684 = 360.
Therefore, The maximum height of the ball is 360 feet.
b) How many seconds does it take until the ball hits the ground?
The time taken can be calculated by putting the value of h = 0, and solving the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.
Therefore, it can be written as:
0 = -16t² + 136t + 72.
or, 16t² - 136t - 72 = 0.
Solving this using the quadratic equation, we get:
[tex]t = \frac{-(-136)\pm \sqrt{(-136)^{2} - 4(16)(-72)}}{2(16)}[/tex] ,
or, [tex]t = \frac{136\pm \sqrt{18496 + 4608}}{32}[/tex] ,
or, [tex]t = \frac{136\pm \sqrt{23104}}{32}[/tex] ,
or, [tex]t = \frac{136\pm 52}{32}[/tex]
Therefore, either t = (136+152)/32 = 9,
or, t (136 - 152)/32 = -0.5.
Since t represents time, we won't take the negative value, and hence t = 9.
Therefore, The time taken by the ball to hit the ground is 9 seconds.
Learn more about quadratic equations at
https://brainly.com/question/15340389
#SPJ2
need help asap please
Answer:
[tex]\displaystyle no[/tex]
Step-by-step explanation:
The triangle on the right is shorter than the triangle on the left, plus you an clearly see that we do not have enough information as proof that we cannot use this theorem.
I am joyous to assist you at any time.
share 660kg in ratio of 5:7
5x+7x=660;
12x=660;
x=660:12;
x=55 (kg).
Then 5x=5×55=275 kg and 7x=7×55= 385 kg.
The required ratio is therefore
660= 275:385.
15-24 divide3 •2+13= Simplify the expression
Answer:
7
Step-by-step explanation:
Given: 15 - 24 divide 3 . 2 + 13 =
The expression can be solved step-wisely so as to determine the appropriate answer.
So that,
15 - 24 = -9
-9 ÷ 3 = -3
-3 . 2 = -6
-6 + 13 = 7
The required answer to the expression is 7.
Thus,
15 - 24 divide 3 . 2 + 13 = 7
Graph the line that passes through the points (-6,5) and (-9,9) and determine
the equation of the line.
Which could be the name of a plane?
A. JK
B. M (kinda cursive)
C. h
D. GH
Answer:
gh i think im not sure but that might be right i hope
Answer:
jk
Step-by-step explanation:
para jungkook de jk lang
Find the missing angle.
Answer:
75
Step-by-step explanation:
All the angles would add up to 360
145+55+35+55=285
Then:
360-285=75
>ZUW=75
Find the unit rate.
Please help ty! :)
Answer:
0.008333 Servings per Calorie
Step-by-step explanation:
Guess the rule and add the next number in the sequence.
6, 8, 12, 18, 26,
Answer:
The rule: Adds twice as much as the previous number added
Next number: 38
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
The rule is every time you add 2 so 6 plus 2 equals 8 them you would do 8+4=12. your counting by 2 as u go up the line.
Please help! I'll mark brainliest!! :)
Answer:
Area = 201 1/4 yard^2
Or in decimal form: 201.25 yard^2
Step-by-step explanation:
First convert the mixed numbers into improper fractions or even decimal form so it is easier to operate with them:
Base = 11 1/2 yards = 23/2 yards = 11.5 yards
Height = 17 1/2 yards = 35/2 yards = 17.5 yards
Use the formula for the area of a parallelogram:
Area = Base x Height
which in our case give:
Area = 23/2 x 35/2 = 805/4 yard^2 = 201 1/4 yard^2
Or in decimal form: 201.25 yard^2
A survey was given to 323 people asking whether people like dogs and/or cats.
181 said they like dogs
137 said they like cats
80 said they don't like cats or dogs.
How many said they liked both cats and dogs?
Answer:
57
Step-by-step explanation:
when you divide both of the answers you get 57 and I'm 98 percent positive it's correct
Answer:
97?
Step-by-step explanation:
323 people
323-80= 234
234-137
97?
again if im wrong im truly sorry
Can u guys help me plz quick (write a expression for the table plz)
Answer: Where is the table?
Step-by-step explanation:
78 miles in 3 days, how many in 5 days
Answer:
390 but i might be wrong
Step-by-step explanation:
Answer:
130
Step-by-step explanation:
26 miles per day 5 days is 130 miles
Please and thanks DUE IN 5min
Answer:
3 and 1/4
Step-by-step explanation:
Eric´s mother drives to work in 20 min when driving at her usual speed. When traffic is bad, she drives 10 miles per hour slower, and the trip takes 10 minutes longer. What is Eric´s mother´s usual speed?
Answer:
30
Step-by-step explanation:
I could be wrong
The usual speed of Eric's mother is 4 miles per hour .
Eric´s mother drives to work in 20 min when driving at her usual speed.
Let the usual speed of Eric's mother be "u" miles per hour (mph)
When the traffic is bad she drives 10 miles per hour slower.
The speed of Eric's mother when the traffic is bad = u-10 mph
The time taken by Eric's mother when the traffic is bad = 30 min
[tex]\rm Displacement = \dfrac{Velocity }{Time }[/tex]
The considering the displacement in both the cases is same hence we can
say that
[tex]\rm \dfrac{u}{20/60} = \dfrac{-(u-10)}{30/60} \\\rm 3u = -2u +20 \\5u = 20 \\u = 4[/tex]
So the usual speed of Eric's mother is 4 miles per hour .
For more information please refer to the link given below
https://brainly.com/question/23294846
8(5 + 4n) + 11 = -5(3 - 7n)
Isolate the variable by dividing each side by factors that don't contain the variable.
n = 22
Answer:
n=22
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
8(5+4n)+11=−5(3−7n)
(8)(5)+(8)(4n)+11=(−5)(3)+(−5)(−7n)(Distribute)
40+32n+11=−15+35n
(32n)+(40+11)=35n−15(Combine Like Terms)
32n+51=35n−15
32n+51=35n−15
Step 2: Subtract 35n from both sides.
32n+51−35n=35n−15−35n
−3n+51=−15
Step 3: Subtract 51 from both sides.
−3n+51−51=−15−51
−3n=−66
Step 4: Divide both sides by -3.
−3n /−3 = −66 /−3
n=22
A Netflix subscription is on sale for $41.94 for six months. What is the cost per month
Answer:
$6.99
Step-by-step explanation:
Divide the total cost by the number of months
4
Step-by-step explanation:
plz help will make brainliest!!!
Answer:
I think it is B.
Rana and Josie are cooking food for a party they need to cut up the food so people can share
Answer:
You didn't put a file or a question in ya question..
Step-by-step explanation:
Answer:
Hey there is nothing to solve here
Step-by-step explanation:
Please make something so we can solve it.
Which is the graph of f(x) = x2 - 2x + 3?
Answer:
the one in the bottom is the graph in pretty sure
Answer:A
Step-by-step explanation:
Edge 2021
How do you live a normal average life?
Answer:
by being normal UvU
Step-by-step explanation:
Common sense
"Normal isn't a thing because you are living your own life, it's your choice to make" -MikuHatsunepink
I know this is old, but someone's answer was deleted so I put this here
PLEASE HELP, Will give brainliest if u help and 38 points.
You are deciding between two laptops to purchase. The first laptop has an initial value
of $2000 but loses 14% of its value every year. The second laptop has an initial value
of $1200 but loses 11% of its value every year.
a. Write functions that represent the values (in dollars) of the laptops after t years.
Then graph the functions in the same coordinate plane.
b. Find the approximate monthly percent decrease in value for each laptop.
C. Which laptop should you buy if you plan on selling the laptop in 5 years? Explain
your reasoning
Step-by-step explanation:
a)
The first laptop
Initial value- $2000Value loss - 14% every yearFunction for value- V(t) = 2000*0.86^tThe second laptop
Initial value- $1200Value loss - 11% every yearFunction- V(t) = 1200*0.89^tb)
Monthly percent decrease
The first laptop:
14%/12 = 1.16%The second laptop:
11%/12 = 0.92%c)
The second laptop will lose less value in 5 years hence is better choice
See the graph attached
help plzzzzzzz
15 points for that
Answer:
You just find the volume of the cup and subtract the volume of the froth (whatever that is).
V(cup) = pi * r^2 * h
...........= pi * 4.3^2 * 11.2
...........= 650.586cm^3
V(froth) = pi*r^2*h
............= pi*4.3^2*0.4
.............=23.232cm^3
V(hot chocolate) = V(cup) - V(froth)
.........................= 650.586 - 23.232
.........................= 627cm^3
18 percent of what number is 74
Answer:
411.1111111
Step-by-step explanation:
18% of x = 74
Convert 18% into a decimal.
0.18 • x = 74
Isolate x by dividing by 0.18.
x = 411.1111111
Check answer.
0.18 • 411.1111111 = 74
74 = 74
Simplify the following expression (2x^2y^5)^3
Answer:
The correct answer is,
[tex] {8x}^{6y {}^{5} } [/tex]
If y=1.8x, then k is equal to...
Is there no solution?
Answer:
There no solution, because there have no k in this equation.
(a) 3 -10
(b) 5 - (-2)
(c) -5 +12
(d) -18 + -15
(a)-7
(b)17
(c)7
(d)-33
please help me i seriously have no idea what im doing
Answer:
When time watching TV increases the grade decreases
Step-by-step explanation:
U just gotta look at the graph and find the relationship
I hope that this helps you out...
Please help it's due by 11 59 i will make as brainliest, thanks, and 5.0 for those who give actual and proper answers
Orange colors - Why are the locations of the police station and fire department congruent?
blue colors - Why are the locations of the restaurant and bank congruent?
Answer:
Step-by-step explanation:
Congruent are angles that are in identical angles. For example the orange colors are congruent because both of the angles are across each other, and because of them being crossed they are both the same degrees making the congruent, same with the blue but instead of being across eachother they are in the angle to the left of the parallel lines that are the same degrees as well.
Rewrite as a simplified fraction. 0.51 = ?
the one is repeating btw
Answer:
17/33
Step-by-step explanation:
100 x = 51.51
100 x − x = 51.51 − 0.51
99 x = 51
divide both sides by 99 to get x as a fraction.
x=51/99
=17/33
Answer:
23/45
Step-by-step explanation:
This is directly from Khan academy itself as I got this question too.
(The red marker is the incorrect answer I put in before.)
Find the inequality by the graph
Answer:
y > 1/3 x -3
Step-by-step explanation:
slope = 1/3
y intercept = -3
equation: y > 1/3 x -3