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
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Please help ASAP !!
Answer: surface area is 215.27; volume is 297.1
Step-by-step explanation:
you have to find the radius first, c = 2(pi (3.14))r, the formula for surface area is 4(pi(3.14)r^2, the formula for volume is 4/3(3.14(pi))r^3
The shadow of a 60 foot pole is a 100 feet long. What is the angle of evaluation from the end of the shadow to the top of the pole?
Answer:
θ = 36.86°
Step-by-step explanation:
Given that,
The shadow of a 60 foot pole is a 100 feet long.
We need to find the angle of elevation from the end of the shadow to the top of the pole.
Height, h = 60 foot
Hypotenuse, H = 100 feet
Using trigonometry to find it.
[tex]\sin\theta=\dfrac{\text{Height}}{\text{Hypotenuse}}\\\\\sin\theta=\dfrac{60}{100}\\\\\theta=\sin^{-1}(\dfrac{60}{100})\\\\\theta=36.86^{\circ}[/tex]
So, the angle of elevation is 36.86 degrees.
Given f(x) = x^3 + kx + 2, and x + 1 is a factor of f(x), then what is the value of
k?
Answer:
k = 1
Step-by-step explanation:
Given that,
[tex]f(x) = x^3 +kx + 2[/tex]
If (x+1) is a factor of (x), we need to find the value of k.
Using remainder theorem to find it.
Put (x+1) = 0
x = -1
Put x = -1 in equation below.
[tex]x^3 + kx + 2=0\\\\(-1)^3+k(-1)+2=0\\\\-1-k+2=0\\\\1-k=0\\\\k=1[/tex]
So, the value of k is 1.
Subtract $987.59 from $1,581.06.
The difference is?
A. $593.47
B. $603.47
C. $693.47
D. $694.47
Answer
A=1,597.06
Step-by-step explanation:
Given ΔPQR and ΔSTU, what is m∠Q?
Given that ΔPQR and ΔSTU are similar triangles, m∠Q = 64°.
Similar TrianglesThe ratios of the corresponding sides of similar triangles are always equal to each other, that is, the corresponding sides are proportional.Also, corresponding angles of two similar triangles are congruent.Thus:
ΔPQR and ΔSTU are similar because:
PQ/ST = PR/SU = QR/TU = 3.5
Therefore,
m∠Q = 180 - 70 - 46
m∠Q = 64°
Thus, given that ΔPQR and ΔSTU are similar triangles, m∠Q = 64°.
Learn more about similar triangles on:
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The manager of a theater wants to know whether the majority of its patrons were adults or children. one day 5100 tickets were sold in the receipts totaled $22,210. The adult admission is $5.50, and the children’s admission is $3.50. How many adult patrons were there?
Answer:
x= 2,180
x= number of adult tickets sold
Step-by-step explanation:
First, we need to establish the system of equations:
x= number of adult tickets sold
y= number of children tickets sold
5.5x + 3.5y = 22,210
x + y = 5,100
Now, we isolate one variable in a formula and substitute its value in the other:
x= 5,100 - y
5.5*(5,100 - y) + 3.5y= 22,210
28,050 - 5.5y +3.5y = 22,210
2y= 5,840
y= 2,920
x= 5,100 - 2,920
x= 2,180
EMERGENCY IF you dont know the answer do not answer IT
Answer:
[tex]x^2+11x+24[/tex]
Step-by-step explanation:
The area of a rectangle is given by [tex]l\cdot w[/tex]. Plugging in our given values, we get:
[tex]A=(x+3)(x+8)=x^2+8x+3x+24=\fbox{$x^2+11x+24$}[/tex].
This is a polynomial in standard form [tex]\checkmark[/tex]
Answer:
x^2 + 11x + 24
Step-by-step explanation:
x times x is x^2
x times 8 is 8x
x times 3 is 3 x
8 times 3 is 24
add it all together and its x^2 + 11x + 24
a florist can creat 16 bouquets of flowers during an 8-hour workday. how many bouguets can the florist creat per hour what is the unit rate
Answer:2 per hour
Step-by-step explanation:16 divided by 8 equals 2 making it 2 per hour
Answer:
A florist can create 2 bouquets of flowers per hour
Step-by-step explanation:
16/8 = 2
I will give brainiest to whoever answers correctly !!
Answer:
26275
Step-by-step explanation:
if simple interest its just .017*25000 which is 1 year then multiply by 3 and add to 25000
If 2x+y=10 and y=3x find the value of both x and y
32 POINTS! *URGENT*
When Pizza Paradise first opened their business in 2010, they decided on a price for their large cheese pizza. After their first full year in business, they decided they would increase the price at a constant rate each year for four years. The new price in 2011, after their first increase, was $7.75. The price in 2014 was $10.00.
What is the slope!
Answer:
The price in 2010 was $7. every year the price went up $0.75 slope should be 0.75x
Step-by-step explanation:
Answer:
lol i had the same question
Step-by-step explanation:
The artist realizes she has 49 ounces left . How many ounces of blue does she need to add
2 ounces of blue paint to every 7 ounces of yellow
Answer:
hwope this helps ＼(=^‥^)/’`
Step-by-step explanation:
Find the sum of the expressions .
8+x-13+n(3-x) =
Answer: =−nx+3n+x−5
Step-by-step explanation:
what is the value of x when x:3=2.13
Answer:
The other dude was wrong :( the answer is 6.39
Step-by-step explanation:
I took the test on K12
Work out the area of the triangle.
Answer:
A = 12.92
Step-by-step explanation:
Base x Height x 1/2
3.4 x 7.6 = 25.84
26.52 x 1/2 = 12.92
Hope this helps :)
slope is 2 and contains the point (5,-7)
write the equation of a line
Answer:
y = 2x - 17
Step-by-step explanation:
y = mx + b
m = 2
y = 2x + b
Plug in (5, -7) for x & y.
-7 = 2(5) + b
-7 = 10 + b
Subtract 10 from both sides.
-17 = b
y = 2x - 17
Check work.
-7 = 2(5) - 17
-7 = 10 - 17
- 7 = -7
Your answer is correct.
Subtract. Simplify (or reduce) your answer, if necessary.
2 1/5 - 5/6 =
Answer:
2 1/5 - 5/6 = 41/30
Step-by-step explanation:
Turn the denominator to be the same because if the denominator is not the same so you can't subtract neither can you add.
Next find the least common multiple of both denominator (5, and 6) and ask yourself what time the denominator would give you the least common multiply you got.
1/5 x 6/6 = 6/30 and 5/6 x 5/5 = 25/30
Your expression now would be 2 6/30 - 25/30
You can't subtract 6 from 25 so you have to turn the proper fraction into a improper fraction
2 6/30 = 2 x 30 + 6 = 66/30. 25/30 = 0 x 0 + 25 = 25/30.
Your new expression would be:
66/30 - 25/30
Now you can subtract 66 - 25 and you get 41
Therefore the correct answer is 41/30 you can not simplify the answer because the numerator is a odd number and the denominator is a even number.
30% of what number is 150? A. 500 B. 50 C. 45 D. 200
Answer:
500
Step-by-step explanation:
.
Answer:
A. 500
Step-by-step explanation:
We know that it can't be B. or C. since it has to be greater than 150, so (I know this isn't the way to do it) bet is you try multiplying your leftover answers you have by .3 you would see that 200 times .3 is 60, so that isn't it but 500 times .3 is 150!
I hope this helps and you have a great day! :)
4x+8≥5(3-x)
solve with steps pleaseee!
Answer:
[tex]x >\ or\ =\ \frac{7}{9}[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\4x+8>\ or =\ 5(3-x)\\Hence,\\We\ can\ treat\ inequality\ in\ the\ same\ way\ we\ do\ for\ solving\ equalities.\\Hence,\\4x+8>\ or\ =\ 5(3-x)\\By\ simplifying\ the\ RHS,\\4x+8 >\ or\ =\ 15-5x\\Hence,\\Adding\ (+5x)\ to\ the\ LHS\ and\ RHS,\\4x+8+(5x) >\ or\ =\ 15-5x+(5x)\\Simplifying,\\5x+4x+8 >\ or\ =\ 15+(5x-5x)\\9x+8 >\ or\ =\ 15\\Adding\ (-8)\ to\ both\ LHS\ and\ RHS,\\9x+8+(-8) >\ or\ =\ 15+(-8)\\Simplifying,\\9x+(8-8) >\ or\ =\ 7\\[/tex]
[tex]9x >\ or\ =7\\x >\ or\ =\ \frac{7}{9}[/tex]
Step-by-step explanation:
4x+8≥5(3-x)
4x+8≥15-5x
adding 5x on each term
4x+5x+8≥15-5x+5x
9x+8≥15
subtract each term by 8
9x+8-8≥15-8
9x≥7
dividing each term by 9
9x/9=7/9
x≥7/9
is your answer
A diagram of a new competition swimming pool is shown. If the width of the
pool is 25 meters, find the length of the actual pool. (Round to the nearest
tenth)
47m at least I think it is
f(x) = -x^2
Find f(3)
Answer:
9
Step-by-step explanation:
f(x) = -x^2
f(3) = -3^2
f(3) = 9
which statement is true about the function f(x) = -√-x?
does anyone understand this i never get it
Answer: 18
Step-by-step explanation:
6 ÷ 2 = 3
162 ÷ 54 = 3
The constant ratio is 3
6 × 3 = 18
Hope I helped!
35 degrees divided by 20
Answer:
1.75 degrees
Step-by-step explanation:
Someone answer this for me. I will give u branily whoever right.
Step-by-step explanation:
21x+72+105+78=360
21x=105
x=5
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
(1.5,1)
Step-by-step explanation:
The formula for the volume of a sphere is given below and the relationship between the radius r and the diameter d is r=d/2. Find the EXACT volume of the sphere in terms of the diameter d. Be sure to fully simplify the expression
Answer:
for the volume of the sphere its answer is 4πr³/3 which when converted to diameter will be 2(4πr³/3) as r=diameter/2 so diameter =2r
Answer:
4πr³/3
Step-by-step explanation:
When converted to diameter will be 2(4πr³/3) as r=diameter/2 so diameter =2r
what is the product of 4.35 and 0.95
What is the measurement of the indicated central angle. 6 pi. R=15
Answer:
r=12
Step-by-step explanation:
r=12
circumference of arc = theta/360*2πr=3π given
Pi cancels
theta/360*2*12=3
theta*6/90=3
theta*3/45=3
3 cancels,45 to the other side
theta=45 degrees
This should do it :)
Write an equation for the line that passes through (−10,3) and whose slope is undefined. Give an answer in standard form.
Answer:
y=-10x+3
Step-by-step explanation:
The slope is -10
