A water balloon is tossed vertically from a window at an initial height (s-sub zero) of 37 feet and with an initial velocity(v-subzero) of 41 feet per second. Answer the following using the fact that h(t)=-16T^2+v-sub zer0t+s sub zero. a) Determine a formula, h)t), for the function that models the height of the water balloon at time t . b)Plot the function in Desmos in an appropriate window. Use the graph to estimate the time the water balloon lands c)Use algebra to find the exact time the water balloon lands. Show your work. No decimals in your answer. d)Determine the exact time the water balloon reaches its highest point and its height at that time. e)4 pts] Compute the average rate of change of on the intervals . Include units on your answers and write a sentence to explain the meaning of the values you found. Arc{1.5,2}____________________________. Explanation: Arc{2,2.5}____________________________. Explanation: årc{2.5,3}____________________________. Explanation:
Answers
Answer:
a) h(t) = -16t^2 +41t +37
b) see attached (3.270 seconds)
c) (41+√4049)/32 seconds
d) 1.28125 seconds; 63.265625 feet
e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47
Step-by-step explanation:
a) The formula and initial values are given. Putting those values into the formula, we get ...
h(t) = -16t^2 +41t +37
__
b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.
__
c) Using the quadratic formula, we can find the landing time as ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]
The exact landing time is (41+√4049)/32 seconds.
__
d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.
The value of the function at that point is ...
h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64
The maximum height is 4049/64 = 63.265625 feet.
__
e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...
h'(t) = -32t +41 . . . in feet per second
Then the average rates of change are ...
arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s
arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s
arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s
These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.
Answer:
(a) h(t) = -16t² + 41t + 37
(b) About 3.3 s
[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]
(d) -15 ft/s; -31 ft/s; -47 ft/s
Step-by-step explanation:
(a) The function
h(t) = -16t² + v₀t + s₀
v₀ = 41 ft·s⁻¹
s₀ = 37 ft
The function is
h(t) = -16t² + 41t + 37
(b) The graph
See Fig. 1.
It looks like the water balloon lands after about 3.3 s.
(c) Time of landing
h = -16t² + 41t + 37
a = -16; b = 41; c = 37
We can use the quadratic formula to solve the equation:
[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]
(i) Evaluate the discriminant D
D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368 = 4049
(ii) Solve for t
[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]
[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]
(d) Time and maximum height
(i) Time
The axis of symmetry (time of maximum height) is at t = -b/(2a)
[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]
(ii) Maximum height
The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37 = 63.27 ft
(e) Average rate of change
(i) Arc{1.5,2}
h(1.5) = 62.5
h(2) = 55
m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s
The water balloon has started to fall after it has reached peak height, so it is not going very fast
(ii) Arc{2,2.5}
h(2.5) =39.5
m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s
The balloon is in mid-fall, so gravity has caused it to speed up.
(iii) Arc{2.5,3}
h(3) = 16
m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s
The balloon is about to hit the ground, so it is falling at almost its maximum velocity.
Fig. 2 shows the height of the balloon at the above times.
Related Questions
HELPPPPPPPPPPP PLZZZZZZZZZZZZZZZZZZZZ!!!!!!!!!!!!
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Answer:
58
Step-by-step explanation:
First, find the interior angle adjacent to the angle GFD.
180 - (34+24) = 180 - 58 = 122
Now, the exterior angle = 180 - 122 = 58
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Answer:
draw a table and calculate the x axis and find the x intercept
Step-by-step explanation:
Answer:
The correct answer is ..
(-1,-2)
Step-by-step explanation:
First, you reflect over the x-axis and get (1,-2) then reflect over the y- axis and the point will be on (-1,-2)
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Answer:
The triangles are similar by the AA similarity postulate
Step-by-step explanation:
The only thing we know is that the three angles are the same
70+30 +80 = 180 so the missing angle in each triangle is 80 in the first and 70 in the second
The triangles are similar by the AA similarity postulate
please explain while solving
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Answer:
48Step-by-step explanation:
In the picture above
I hope it helps :)
Evaluate the following expression
Answers
Answer:
Hope this is correct
Step-by-step explanation:
HAVE A GOOD DAY!
10 ft
8 ft
Find the perimeter of this figure to the
nearest hundredth. Use 3.14
Answers
Answer:
48.56 ft
Step-by-step explanation:
==>Given:
A rectangular figure joined with a half circle with the following dimensions:
Length of rectangle (l) = 10ft
Width of rectangle (w) = 8ft
Diameter of the half circle (d) = the width of the rectangle = 8ft
π = 3.14
==>Required:
Perimeter of the figure = perimeter of a rectangle + permimeter of the half circle
==>Solution:
Perimeter of rectangle = 2(l + w)
Perimeter of half circle = ½ of circumference of a circle = ½πd
Perimeter of the figure = 2(10 + 8) + (½*3.14*8)
= 2(18) + (3.14*4)
= 36 + 12.56
Perimeter = 48.56 ft (to the nearest hundredth)
Answer:56.56
Step-by-step explanation:
For the perimeter of a rectangle
P = 2 × (a + b)
P = 2 × (8 + 10)
P = 2 × 18
P = 36
For the perimeter of a semicircle
P = (pi × r) + (2 × r)
Diameter = 8
Radius = 8/2
Radius = 4
P = (3.14 × 4) + (2 × 4)
P = 12.56 + 8
P= 20.56
Perimeter of this figure
P = r + c
P = 36 + 20.56
P = 56.56
This is my last one please help you need to explain it just tell me the right answer thank you
Answers
Answer:
i might be 25
Step-by-step explanation:
if f(x)= x/2-3 and g(x)=4x^2+x-4 find (f+g) (x)
Answers
Answer:
(f+g) (x)=4x^2+3x/2-7
Step-by-step explanation:
f(x)= x/2-3 and g(x)=4x^2+x-4
(f+g) (x)=?
(f+g) (x)=f(x)+g(x)
(f+g) (x)=x/2-3+4x^2+x-4
combining like terms
(f+g) (x)=4x^2+x/2+x-3-4
(f+g) (x)=4x^2+3x/2-7
hope it helps. Brainliest please
square root of 0.925 by long division method
Answers
0.96176920308
Hope it Helps you :)liz buys 17 identical tickets for £208.25 estimate the cost of one ticket
Answers
Answer:
£12.25
Step-by-step explanation:
Using unit rate:
[tex]\frac{\text{Price}}{\text{Tickets}}=\frac{208.25}{17}=\frac{208.25/17}{17/17}=\frac{\boxed{12.25}}{1}[/tex]
£12.25 should be the correct answer.
Help a chick out only if u know what u doing
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Answer:
for 12:00 1 for 1:00 2
Step-by-step explanation:
this is a pattern where each number multiplies itself by 2 making 12:00 and 1:00 pm 1 and 2
edit: is it right? if it is, may I have brainliest?
Using the quadratic formula, which of the following are the zeros of the quadratic equation below
Answers
Answer:
the answer for this question is D
Answer:
Correct answer is actually B
Step-by-step explanation:
I used someone’s answer with their work shown for my test
A school allots £1500 to spend on a trip to the theatre. Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off A train ticket for the day will cost £15 each. If 2 teachers and the maximum number of students attend, how much money will the school have left over?
Answers
Answer:
Step-by-step explanation:
School allots £1500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off
therefore 4/5*35 = 28 for the tickets
:
A train ticket for the day will cost £15 each.
therefore total cost for each: 28 + 15 = 43 pounds each
:
If 2 teachers and the maximum number of students attend, how much money will the school have left over?
:
let s = no. of students
43(s+2) =< 1500
43s + 86 =< 1500
43s =< 1500 - 86
43s =< 1414
s =< 1414/43
s =< 32.88, 32 students max
:
find how much left over. plus 2 teachers = 34 people
1500 - 43(34) =
1500 - 1462 = 38 pounds left over
A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like algebra, 53 like geometry, and 6 do not like either subject.
Answers
Answer:
D. a = 29, b = 16, c = 24, d = 30, e = 22
Step-by-step explanation:
got it right on edge
The number of students who like both algebra and geometry is 27.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
The number of students who like both algebra and geometry is the intersection of A and G, denoted as A ∩ G.
The number of students who like algebra only is the difference between A and A ∩ G, denoted as A - A ∩ G.
The number of students who like geometry only is the difference between G and A ∩ G, denoted as G - A ∩ G.
The number of students who do not like either subject is the complement of the union of A and G with respect to U, denoted as U - (A ∪ G).
We are given that:
A = 45
G = 53
U = 75
U - (A ∪ G) = 6
Now,
U - (A ∪ G) = 6
75 - (45 + 53 - A ∩ G) = 6
27 = A ∩ G
Therefore,
The number of students who like both algebra and geometry is 27.
Learn more about the Venn diagram here:
https://brainly.com/question/1605100
#SPJ5
The complete question.
A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like algebra, 53 like geometry, and 6 do not like either subject.
Find the number of students who like both algebra and geometry.
Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle
Answers
Answer:
30° each
Step-by-step explanation:
Complementary angles are those that add up to 90° so if they are all equal then it's
90/3=30°
Answer: 30° each
Complementary angles are those that add up to 90° just to remind you!!
When [(a2bc4)(ab3c2)]2(b2c5)3 is simplified, the exponent of b is Answer
all the numbers are roots and powers
Answers
Answer:
14
Step-by-step explanation:
We want to simplify [tex][(a^2bc^4)(ab^3c^2)]^2 (b^2c^5)^3[/tex] so as to find the exponent of b.
Let us expand all brackets:
[tex][(a^2bc^4)(ab^3c^2)]^2 (b^2c^5)^3\\\\= [a^3b^4c^6]^2 (b^{2*3}c^{5*3})\\\\= [a^6b^8c^{12}] (b^{6}c^{15})\\\\= a^6b^{8+6}c^{12 + 15}\\\\= a^6b^{14}c^{27}[/tex]
The exponent of b is 14.
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Answer:
sup!
the answer is
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Step-by-step explanation:
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Yolo has 2 pieces of string. One is 32 inches long, the other is 48 inches long. She wants to make as many necklaces as she can, all of the same length. What is the longest necklace that can be made?
Answers
The Greatest Common Factor of 32 and 48 is 16.
The longest necklace she can make is of 16 inches length.
given angle2 and angle 4 are vertical angels. prove angle 2 cong angle 4
Answers
Answer:
Use the Vertical Angles Theorem
Step-by-step explanation:
The vertical angles theorem states that angles vertical/opposite to each other are congruent. Use the vertical angles theorem in your proof.
Answer:
See below.
Step-by-step explanation:
Please please help guys
Answers
Answer:
234.85
Step-by-step explanation:
This was easy!!!
(The gardener comes 4 times a month... so divide 85.40 by 4 and you will get 21.35. Each time he comes, he gets 21.35 and by the end of the month, he has 85.40. It says he already came 11 times. So 4 + 4 = 8 + another 4 that equals 12. He came only two months and a few weeks. This means multiply 85.40 by 2 so you would get 170.8. It said he came 11 times so substract 11 from 8 and you would get 3. So multiply 21.35 by 3 and get a total of 64.05. Add 170.8 and 64.05 to get 234.85!!! The answer is 234.85 or C!!!!
Answer: C. $234.85
Explanation: $85.40 (how much Katrina pays each time the gardener comes) * 4 (the number of times the gardener comes each month) = $234.85 (how much the gardener made)
Harun and Anis have m boys and n girls. How many children do they have?
Answers
Explanation: They have an unknown amount of children.
Applying the recursive rule aₙ; a ₙ ₋ ₁ + 3, write the first seven (7) terms of the sequence when a = 10.
Answers
Answer:
First seven terms apart from 10 are
13, 16, 19, 22, 25, 28, 31
Step-by-step explanation:
Given recursive rule aₙ = a ₙ ₋ ₁ + 3
a1 = 10
[tex]x_{1} = 10\\x_{2} = x_{2-1} + 3= x_{1} + 3 = 10 + 3 = 13\\x_{3} = x_{3-1} + 3= x_{2} + 3 = 13 + 3 = 16\\x_{4} = x_{4-1} + 3= x_{3} + 3 = 16 + 3 = 19\\x_{5} = x_{5-1} + 3= x_{4} + 3 = 19 + 3 = 22\\x_{6} = x_{6-1} + 3= x_{5} + 3 = 22 + 3 = 25\\\x_{7} = x_{7-1} + 3= x_{6} + 3 = 25 + 3 = 28\\x_{8} = x_{8-1} + 3= x_{7} + 3 = 28 + 3 = 31[/tex]
Thus, first seven terms apart from 10 are
13, 16, 19, 22, 25, 28, 31
Rectangle ABCD has vertices A(–6, –2), B(–3, –2), C(–3. –6), and D(–6, –6). The rectangle is translated so that the coordinates of the image are A’(–10, 1), B’(–7,1), C’(–7, –3), and D’(–10, –3). Which rule was used to translate the image? T–4, 3(x, y) T–4, 1(x, y) T4, –1(x, y) T4, –3(x, y)'
Answers
Answer:
T₋₄, ₃ (x, y)
Step-by-step explanation:
The coordinates of rectangle ABCD are;
A = (-6, -2)
B = (-3, -2)
C = (-3, -6)
D = (-6, -6)
The coordinates of the image are;
A' = (-10, 1)
B' = (-7, 1)
C' = (-7, -3)
D' = (-10, -3)
We note that for A and A', x - x' = -6 + 10 = 4 and y - y' = -2 - 1 = -3
For B and B', x - x' = -3 + 7 = 4 and y - y' = -2 - 1 = -3
For C and C', x - x' = -3 + 7 = 4 and y - y' = -6 + 3 = -3
For D and D', x - x' = -6 + 10 = 4 and y - y' = -6 + 3 = -3
Therefore, the transformation rule used to translate the image of rectangle ABCD is T₋₄, ₃ (x, y)
Answer:
T₋₄, ₃ (x, y)
Step-by-step explanation:
Please Hurry!!!! A Newly-planted tree needs to be staked with three wires. Each wire is attached to the trunk 3 ft above the ground, and then anchored to the ground 4ft from the base of the tree. How much wire is needed for the trees
Answers
Answer:
5 ft, I think
Find the area of this irregular figure. All angles are right angles. 128 in2 296 in2 256 in2 80 in2
Answers
Answer:
256in²
Step-by-step explanation:
Just add the area the two Rectangals = A=128*2 = 256in² or calclute the whole and deduct the 2 missing sqares 16
384-128=256in²
One fourth of a number is added to one fifth of the same number. If the result is 18, find the number
Answers
Answer:
[tex]40[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the number.
[tex]\frac{1}{4} x+\frac{1}{5} x=18[/tex]
[tex]\frac{9}{20} x=18[/tex]
[tex]x=18 \times \frac{20}{9}[/tex]
[tex]x=40[/tex]
If one fourth of a number is added to one fifth of the same number, and the result is 18, then the number = 40
Let the given number be represented by x
One-fourth of the number = x/4
One-fifth of the same number = x/5
One-fourth of the number is added to one fifth of the same number =
x/4 + x/5
The result is 18
This can be represented mathematically as:
x/4 + x/5 = 18
Simplifying the equation above
(5x + 4x)/20 = 18
Cross multiply
5x + 4x = 18(20)
9x = 360
x = 360/9
x = 40
The number = 40
Learn more on word problem here: https://brainly.com/question/21405634
What is the slope of the line on the graph below 1/5 1/3 3 or 5
Answers
Answer:
1/3
Step-by-step explanation:
We are given to find the slope of the line shown on the graph.
We note that
the line on the graph passes through the points (3, -4) and (6, -3).
The slope of a straight line passing through the points (a, b) and (c, d) is given by
m=\dfrac{d-b}{c-a}.m=
c−a
d−b
.
Therefore, the slope of the given line is
\begin{lgathered}m=\dfrac{-3-(-4)}{6-3}\\\\\\\Rightarrow m=\dfrac{-3+4}{3}\\\\\\\Rightarrow m=\dfrac{1}{3}.\end{lgathered}
m=
6−3
−3−(−4)
⇒m=
3
−3+4
⇒m=
3
1
.
Thus, the required slope of the line is \dfrac{1}{3}.
3
1
.
Option (B) is CORRECT.
What is the length, in units, of segment CD?
Answers
Answer:
The answet is C.
Step-by-step explanation:
First, you have to find the angle of ACB using Sine Rule, sinθ = opposite/hypotenuse :
[tex] \sin(θ ) = \frac{oppo.}{hypo.} [/tex]
[tex]let \: oppo. = 4 \\ let \: hypo. = 5[/tex]
[tex] \sin(θ) = \frac{4}{5} [/tex]
[tex]θ = {\sin( \frac{4}{5} ) }^{ - 1} [/tex]
[tex]θ = 53.1 \: (1d.p)[/tex]
Given that line AB is parallel to line CD so ∠C = 90°. Next, you have to find the angle of ACD :
[tex]ACD = 90 - 53.1 = 36.9[/tex]
Lastly, you can find the length of CD using Cosine rule, cosθ = adjacent/hypotenuse :
[tex] \cos(θ) = \frac{adj.}{hypo.} [/tex]
[tex]let \: θ = 36.9 \\ let \: adj. = 5 \\ let \: hypo. = CD[/tex]
[tex] \cos(36.9 ) = \frac{5}{CD} [/tex]
[tex]CD \cos(36.9) = 5[/tex]
[tex]CD = \frac{5}{ \cos(36.9) } [/tex]
[tex]CD = 6.25 units\: (3s.f)[/tex]
Edmund makes a cube using eight small cubes. Samuel uses cubes of the same size as the small cubes to make a cuboid twice as long, three times as wide and four times as high as Edmund's cube. How many more cubes does Samuel use than Edmund?
Answers
Answer:
Step-by-step explanation:
The number of small cubes that Edmund used is 8. Let us assume that the volume of each small cube is 1m³. This means that the volume of the cube made is 8m³. Since volume of cube = s³, then s = 3√8 = 2m
Each side of the cube made is 2m
Samuel uses cubes of the same size as the small cubes to make a cuboid twice as long, three times as wide and four times as high as Edmund's cube. It means that the sides of the cuboid are
Length = 2 × 2 = 4m
Width = 3 × 2 = 6m
Height = 4 × 2 = 8m
Volume = length × width × height
Volume = 4 × 6 × 8 = 192 m³
Number of small cubes used is 192/1 {= 192
The number of cubes that Samuel used more that Edmund is 192 - 8 = 184 small cubes
which rule would best describes this pattern 8,4,10,6,12,8,14
Answers
Answer:
Subtract 4 and then add 6.
Step-by-step explanation:
8-4=4
4+6=10
10-4=6
6+6=12
12-4=8
8+6=14
The rule for this pattern can be subtracting 4, and then adding 6.