Isaiah decides to launch a model rocket to demonstrate parabolic motion. Given x stands for time and y stands for height in feet, find the equation for his rocket if it launches at 5 seconds, lands at 11 seconds, and is at 80 feet after 10 seconds. Explain in one sentence how you created your equation.
The parabolic motion is an illustration of a quadratic function
The equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
How to model the function?Given that:
x stands for time and y stands for height in feet
So, we have the following coordinate points
(x,y) = (5,0), (11,0) and (10,80)
A parabolic motion is represented as:
y =ax^2 + bx + c
At (5,0), we have:
25a + 5b + c = 0
c= -25a - 5b
At (11,0), we have:
121a + 11b + c = 0
Substitute c= -25a - 5b
121a + 11b -25a - 5b = 0
Simpify
96a + 6b = 0
At (10,80), we have:
100a + 10b + c = 80
Substitute c= -25a - 5b
100a + 10b - 25a -5b = 80
75a -5b = 80
Divide through by 5
15a -b = 16
Make b the subject
b = 15a + 16
Substitute b = 15a + 16 in 96a + 6b = 0
96a + 6(15a + 16) = 0
Expand
96a + 90a + 96 = 0
This gives
186a = -96
Solve for a
a = -16/31
Recall that:
b = 15a + 16
So, we have:
b = -15 * 16/31 + 16
b =-240/31 + 16
Take LCM
b =(-240 + 31 * 16)/31
[tex]b =256/31
Also, we have:
c= -25a - 5b
This gives
c= 25*16/31 - 5 * 256/31
Take LCM
c= -880/31
Recall that:
y =ax^2 + bx + c
This gives
y = -16/31x^2 + 256/31x - 880/31
Hence, the equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
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A fuel tank is in the shape of a right circular cylinder. The radius of the base and height of the tank are
10
feet and
25
feet, respectively. Due to safety measures, the tank can be filled to only
80
%
of its capacity.
If
100
cubic feet of fuel are equal to
2. 78
gallons, what is the maximum number of whole gallons of fuel the tank can contain due to safety measures?
The maximum number of whole gallons of fuel the tank can contain due to safety measures is 174.584 gallons
Volume of a cylinderv = πr²hr = radius
h = height
Therefore,
r = 10 ft
h = 25 ft
The tank can only be 80% filled due to safety measures. Therefore,
v = 3.14 × 10² × 25
v = 3.14 × 100 × 25
v = 3.14 × 2500
v = 7850 ft³
80% capacity of 7850 ft³ is as follows:
80 / 100 × 7850 = 628000 / 100 = 6280 ft³
100 ft³ = 2.78 gallons
6280 ft³ = ?
cross multiply
maximum number of whole gallons = 6280 × 2.78 / 100 = 17458.4 / 100 = 174.584 gallons
Therefore, the maximum number of whole gallons of fuel the tank can contain due to safety measures is 174.584 gallons
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someone pleaseee helppppp
The current temperature is 48°F. It is expected to drop 1.5°F each hour.
Which equation can be used to find in how many hours, h, the temperature will be 36°F?
A) 36 + 48h = 1.5
B) 48 – 1.5h = 36
C) 48 + 1.5h = 36
D) 36 - 1.5h = 48
Answer:
B
Step-by-step explanation:
what are the x- intercepts of the graph that represents y=(x+1)(x+5)
Answer:
x= -1 and x= -5
Explanation
y=(x+1)(x+5)
set both equations equal to 0
x+1=0 and x+5=0
subtract each constant from the appropriate side
x= -1 x=-5
7^-6/7^-2 rewrite it using a singular positive exponent
Answer:
1/7^4
Step-by-step explanation:
negative exponents flip to opposite side of the fraction and add to like-base terms.
The concession stand has 18 gallons of punch. If there are a total of 240 students who want to purchase 1 cup of punch each, will there be enough punch for everyone?
Answer:
Yes.
Step-by-step explanation:
18 gal = 288 cups.
(1 gal = 16 cups)
If 240 students purchase 1 cup each, there will be 48 cups left over.
So,yes, there will be enough punch for everyone.
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Thanks!
PLEASE PLEASE PLEASE HELP ME YALL‼️‼️‼️‼️‼️
There are four boys in a class of ten students. Four students are to be randomly selected
(without replacement) to help in the lunch line. Determine the probability that all four
students are boys.
Answer:
Hi .. im happy to help
answer is 0.033
Step-by-step explanation:
P = C(4,4)÷C(10,4)
P = 1 ÷ 30
[tex]p = \frac{1 }{30} [/tex]
p = 0.033
what is 6(x+?)= 6x + 30
??????????
Answer:
Let y = '?'
6(x + y) = 6x + 30
6x +6y = 6x + 30
6x + 6y - 6x = 6x + 30 - 6x
6y = 30
6y / 6 = 30 / 6
y = 5
find the hcf by prime factorization method of 18 and 24
Answer:
6
Step-by-step explanation:
Prime factorization of 18 = 2 × 3 × 3
Prime factorization of 24 = 2 × 2 × 2 × 3
Common factors of 18 and 24 = 2 × 3 = 6
HCF (18,24) = 6
For a sphere with a radius of 8 cm, find the volume of the sphere. Write each answer as an exact value or as a number rounded to the nearest tenth.
Answer:
V≈2144.66cm³
Step-by-step explanation:
Help pleazeeeeee! I need this as soon as possible
A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the lengths of the prisms vary. It cost $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
The maximum length of the prism is highest length of the hexagonal prism
The maximum length of each prism is 8.0 cm
How to determine the maximum length of each prism?The surface area of the hexagonal prism is calculated using:
A = 6al + 3[tex]\sqrt[/tex]3 a^2
Where:
a represents the edge length; a = 4 cm
l represents the length (or height) of the prism
The surface area costs $0.04 per square centimeter.
So, we have:
C = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
The maximum cost is $11.
So, the equation becomes
11 = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
Substitute 4 for a
11 = 0.04 * [6 * 4l + 3[tex]\sqrt[/tex]3 * 4^2]
Evaluate the products and exponents
11 = 0.04 * [24l + 48[tex]\sqrt[/tex]3]
Divide both sides by 0.04
275 = 24l + 48[tex]\sqrt[/tex]3
Subtract 48[tex]\sqrt[/tex]3 from both sides
24l = 275 - 48[tex]\sqrt[/tex]3
Evaluate the difference
24l = 191.9
Divide both sides by 24
l = 8.0
Hence, the maximum length of each prism is 8.0 cm
Read more about surface areas at:
https://brainly.com/question/6613758
Answer:
275, 7.99
Step-by-step explanation:
i got it right
and please get me too branliest
Please answer this order of operations question
-8 - (-2 + 7)2
Answer:
-18
Step-by-step explanation:
= -8 - (-2 +7) x 2
= -8 - 5 x 2
= -8 - 10
= -18
A triangular bandana has an area of 38 square inches. The height of the triangle is 9
inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.
Answer:
Base=8.4 inches
Step-by-step explanation:
Area of triangular bandana is 38sq inches
Height of triangle is 9 inches
Area of ∆ =½×b×h
38=½×b×9
38×2=b×9
76/9=b
b=8.4 inches
Given that x is an acute angle and cos x=2√5÷5,find without using mathematical tables or a calculator , tan(90-x)°.
Answer: 2
Step-by-step explanation:
Need help with b please and thank you (lots of points)
Answer:
17.34 years
Step-by-step explanation:
The equation you wrote in the first part of the problem can be solved for the value of t that makes the population be 5000.
[tex]P(t)=\dfrac{10000}{1+11.5e^{-0.1408614477t}}[/tex]
Setting this equal to 5000 and multiplying by the denominator, we have ...
[tex]5000=\dfrac{10000}{1+11.5e^{-0.1408614477t}}\\\\5000+57500e^{-0.1408614477t}=10000\\\\e^{-0.1408614477t}=\dfrac{5000}{57500}\qquad\text{subtract 5000, divide by 57500}\\\\-0.1408614477t = \ln{\dfrac{1}{11.5}}=-\ln(11.5)\qquad\text{take logs}\\\\t=\dfrac{\ln(11.5)}{0.1408614477}\approx17.3386[/tex]
For the population to reach 5000, it will take about 17.34 years.
_____
Additional comment
The value -0.14086... is the natural log of the ratio 1818/2093. This means the "exact answer" is ln(11.5)/(ln(2093) -ln(1818)), an irrational number.
A graphing calculator can answer the question easily.
If there are fifty dimes in a roll of coins, then it is equal to________dollars
Answer:
$5
10 Dimes = $1 so If we have 50 dimes that = 5$
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GUYS PLS HELP
What kind of
drawing is this
figure?
A. A triangle
B. A perspective drawing
C. A cylinder
D. A net
B: A perspective drawing
Answer:
B. perspective drawing.
Step-by-step explanation: perspective drawings can be inspirational drawing and can be imagined and created to be like anything and can be anything.
please help me answer this?
Answer:
$102
Step-by-step explanation:
The pay for the day of work is the total of morning hours worked and afternoon hours worked. In each case, the hours worked is the difference between the "Out" time and the "In" time.
morning hours = 12:15 -8:15 = 4:00
afternoon hours = 17:30 -13:00 = 4:30
total hours worked = morning hours + afternoon hours
total hours worked = 4:00 +4:30 = 8:30
This notation tells you (hours):(minutes). You know that 30 minutes is 1/2 hour, so the total time worked is 8 1/2 hours.
The pay is the product of the hours worked and the pay per hour:
pay = (8 1/2 hours) × ($12 /hour) = $102
Please help I will give brainliest.
Answer:
The first two
Step-by-step explanation:
graph the parabola to see
solve pls brainliest
Answer:
Simplify the radical by breaking the radicand up into a product of known factors.
Exact Form:
3
√
75
5
Decimal Form:
0.84343266
…
Answer:
[tex]\frac{27}{125}[/tex]
Step-by-step explanation:
[tex](\frac{3}{5})^{3}[/tex] is [tex]\frac{3^{3}}{5^{3}}[/tex]
[tex]3^{3} = 27[/tex] and [tex]5^{3} = 125[/tex]
[tex]\frac{27}{125}[/tex]
Cole is buying a new rain barrel to help with watering his garden. The rain barrel is shaped like a right circular cylinder. What is the volume of the rain barrel if it is 26 inches tall and has a diameter of 22 inches? Use straight pi equals 3.14.
A right circular cylinder diameter 22 inches and a height of 26 inches.
V equals_(blank)_ inches cubed
Round to the nearest hundredth if necessary. Type your numerical answer (without units) below.
Answer:
[tex]V = 9878.44 in^3[/tex]
Step-by-step explanation:
The volume of a cylinder, is essentially base multiplied by height. Think of it like this, you are taking a flat 2D circle and extending it in 3rd dimension by a length 'h'.
[tex]V = base * h[/tex]
The base here is the circle area, and the height is the amount you extended that 2d circle in the 3rd dimension.
The area of a circle is [tex]\pi r^2[/tex]. If we put that into our equation we get the volume of a cylinder.
[tex]V = \pi r^2 *h[/tex]
Now applying that to the question; Firstly, we are given the diameter, which is 22 inches. We need radius, to actually put it in the equation. The diameter is essentially 2 multiplied by the radius. That means to get the radius we divide the diameter by 2, giving us 11 inches. Next we are given how tall it is, 26 inches; that is the height.
[tex]r = 11in\\h = 26in[/tex]
Plug these values into the equation.
[tex]V = 3.14(11in)^2 * 26in[/tex]
Calculate this, and you get [tex]V = 9878.44 in^3[/tex]
LAY
STOP
Solve using the Zero Product Property.
15. The height of a football after it has been kicked from the top of a hill can be modeled
by the equation h= 2(-2-4t) (2t - 5), where h is the height of the football in feet
and tiltihe time in seconds. How long is the football in the air?
A
A. t=2.5 seconds
B.
B. t=-0.5 seconds
с
C. t=1.5 seconds
Answer:
A
Step-by-step explanation:
how long is the ball in the air ?
that is the same as asking : after how many seconds will the ball hit the ground (= reach the height of 0) ?
so, that means we need to find the zero solution of h(t).
at what t is h(t) = 0 ?
when at least one of the factors is 0 :
2(-2 - 4t)(2t - 5)
we have 3 factors
2 : can never be 0.
(-2 -4t) : can only be 0 for negative t, which does not make sense in our scenario (we cannot go back in time, only forward).
(2t - 5) : is 0 when 2t = 5 or t = 2.5
so, A is the right answer.
FYI : the starting height (on the hill) is given by t = 0 :
2(-2 - 0)(0 - 5) = 2×-2×-5 = 20 ft
There are 250 wolves in a national park. the wolf population is increasing at a rate of 16% per year. write an exponential model to represent the situation. use the model from problem 1 to determine how long it will take the wolf population in the national park to reach 1000. round the answer to the nearest hundredth.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill[/tex]
[tex]A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}[/tex]
Find the values of x and y. State which theorem(s) you used.
Answer:
3x+45=180
3x=180-45
x=135/3
x=45
(y-4)=45
y=45+4
y=49
Answer:
x=45° and y=49° (180°in a straight line, co-interior angles add up to 180°)
Step-by-step explanation:
There are 180° in a straight line so 180°-45=135, 135=3x
135 divided by 3= 45, so x=45°, then because co-interior angles always add up to 180°, 45+ the missing angle=180, 180-45=135, so the angle next to angle (y-4) is 135°.
Then, solving the equation u have 135+(y-4)=180 because there are 180° in a straight line.
The equation ends up as y=49°
A toy car launches off a ramp with a height of 6 feet with an upward velocity of 10 feet per second. The function h = -16t^2 +10t +6 gives the height in feet of the car after t seconds. After how many seconds does the car land on the ground?
On factoring, the value of t is 1. This shows that the car will land on the ground after 1 sec.
Solving quadratic functionsQuadratic functions are functions having a leading degree of 2.
Given the function height in feet of the car after t seconds expressed as
h = -16t^2 +10t +6
The height of the car on the ground is zero, hence:
16t^2 -10t -6 = 0
8t^2 - 5t - 3 = 0
Factorize the quadratic function
8t^2 - 5t - 3 = 0
On factoring, the value of t is 1. This shows that the car will land on the ground after 1 sec.
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Find of 14. 3/7
A. 3
B. 5
C. 6
D. 2
Answer:
C. 6.
Step-by-step explanation:
3/7 of 14
= 3*14/7= 42/7
= 6.
Find the slope of the line.
PLS HELP I AM SO BEHIND
Answer:
-1
Step-by-step explanation:
Follow the example below and Good Luck!!!
Answer:
-6/5
Step-by-step explanation:
The slope of the line is the ratio of "rise" to "run". That is, it is the ratio of the vertical change between two points to the horizontal change between those points.
__
Here, two points are marked, (-1, 2) and (4, -4). Either by counting grid squares or by subtracting coordinates, we find the vertical change (rise) from the first point to the second to be (-4 -2) = -6 units. The horizontal change (run) from the first point to the second is (4 -(-1)) = 5.
The slope is the ratio of these values:
slope = rise/run = -6/5
Find the equation of the exponential function represented by the table below,
X.Y
0 4
1 8
2 16
3 32
Answer:
Graph the exponential function.
[tex]y=-3(8)^{x}[/tex]
Step-by-step explanation:
to make a sketch of this graph. We're gonna make a table of values. I think that's probably our best route. So we'll do a couple negative values, but I'm gonna actually start at 08 to 0. Power zero. And I'm sorry. 80 parts one and one times negative. Three is negative. Three eight to the first. Power is eight and eight times negative. Three is negative. 24 8 X squared is 64 64 times negative. Three is on negative. 192. Okay, I think that's plenty. E to the negative. First power is 18 and 1/8 times negative. Three is negative. 3/8 and eight to the negative. To power is 1 64th times negative. Three is negative. 3 60 force. Okay, I think we can see where that's going. Is getting really close to zero. So as faras my graph here, I'm gonna focus on the fourth quadrant, I think. All right. So we got our X and y axis here. We're starting at 01 and to and we'll also do negative one. And negative two aren't horizontally, vertically. I do. I want to scale this whole the way to 1 92 I guess I will. Um, so whatever it is scaled by, maybe twenties. Yeah, let's do that. 20 40 60 8120 40 60 8200. So there's negative. 200? Um, negative. 1 80 Negative 1 60? Nope. That's not right. Because I scaled by twenties didn't. So this is actually negative. 1 60 This one's negative. 1 20 This one's negative. 80. And this is negative. 40. There we go. All right now a plot. These points to negative 1 92 is practically to 200 one. Negative. 24 is all the way over here. Zero negative three is practically on the X axis The way I have this, and same with those fractional values. They're practically on the X axis. So let's start almost parallel to the X axis because it's never actually touch step than its we don't ever. Slowly and then it starts going down rapidly, decreasing in value to the point where it's almost vertical, but it never will get vertical, so there's a decent sketch of y equals negative three times eight to the power of acts