Assignment Goal:
Describe the motion of a rocket using a quadratic model.
Instructions:
Respond to each of the questions. Your solutions must document all of your work.
Scenario: A toy rocket is launched straight upward from a pad 10 ft above ground level with an initial velocity of 80 ft/sec.
Use the general formula for the vertical position (height) of an object moving under the influence of gravity s=-1/2 gt^2+ v_0 t+ s_0 where s0 is initial vertical position, v0 is initial velocity, and s is vertical position of the object.
1. Define a model (equation) to express the vertical position (height) of the rocket s (in meters) above ground level t seconds after launch. Let g = 32 ft/sec2.
Answer:
Your question is a little unclear if it wants meters or feet because it has everything listed in nicely feet then you say "(in meters)" at the bottom.
If it wants feet, the answer is
[tex]s=-16t^2+80t+10[/tex]
If it wants meters, the answer is
[tex]s=-4.8768t^2+24.384t+3.048[/tex]
Step-by-step explanation:
To solve, use the quadratic equation.
[tex]y=ax^2+bx+c[/tex]
It wants the x-axis to represent time (t) and the y-axis to represent position (s)
[tex]s=at^2+bt+c[/tex]
It gives us a formula that tells us what a, b, and c equal.
[tex]s=(-1/2)gt^2+v_0t+s_0[/tex] where g is gravity, v_0 is the initial velocity, and s_0 is the initial starting position.
From here, it is just a plug and chug to get the final answer.
[tex]s=(-1/2)(32)t^2+80t+10\\s=-16t^2+80t+10[/tex]
If it wants everything in meters, just convert feet to meters at every step. You can search to find that 1 meter=3.28084 feet.
For what positive number is the cube of the number greater than twice it’s square
Answer:
You want to solve the equation
x2=2x3 ,
which is equivalent to
x2(1−2x)=0 .
The product of two factors is zero if and only if one of the factors is zero. Thus, this implies that either x2=0 or that 1−2x=0 .
In the former case we have x=0 , which isn’t a positive number. In the latter case you have x=1/2 , which is the solution that we want.
Step-by-step explanation:
help 1234567891011121314151617181920
AYUDA!!!!!!! Pls help me answer
You don't mention what's the question
what would be the volume of the cone that has the same measurement as the cylinder above in the pic
do the working also
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Volume of cone will be ~
[tex]\fbox \colorbox{black}{ \colorbox{white}{volume} \: \: \: \: \: \colorbox{white}{=} \: \: \: + \colorbox{white}{462 \: cm³ }}[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's find the volume of cone with ~
radius (r) = 7 cmheight (h) = 9 cmAnd as we know, volume of cone is equal to ~
[tex] \dfrac{1}{3}\pi {r}^{2} h[/tex]now, let's plug in the values and find the volume ~
[tex] \dfrac{1}{ \cancel{3} }\times \dfrac{22}{\cancel{7}} \times \cancel{7 }\times 7 \times \cancel{9}[/tex][tex]1 \times 22 \times 7 \times 3[/tex][tex]462 \: \: {cm}^{3} [/tex]Volume of cone is 462 cm³ = 462 ml
What is the value of g(1)? What is the value of g(-12)? For which of the following x-values is g(x)=-6
The numeric values of the function are given as follows:
g(1) = 4.g(-12) = -10.g(x) = -6 for -8 ≤ x < -1.g(1)When x = 1, the function has a closed value on the graph at y = 4, hence:
g(1) = 4.
g(-12)When x = -1,2 the function is passing through y = -10, hence the numeric value is given as follows:
g(-12) = -10.
g(x) = -6The function is passing through the horizontal line y = -6 when -8 ≤ x < -1, hence:
g(x) = -6 for -8 ≤ x < -1.
Learn more about the numeric values of a function at https://brainly.com/question/28296698
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what is the intercepts of the line?
x-intercept and y-intercept
4x-1=3y+5
Answer: X (3/2,0) Y (0,-2)
Step-by-step explanation:
3a) A box contains trays of melons, There are 15 melons in a tray. There are 3 trays in a box. A supermarket sells 40 boxes of melons. How many melons does the supermarket sell?
Answer:
1,800
Step-by-step explanation:
15 x 3 x 40 = 1,800
( A box)
The price of an item has been reduced by 85%. The original price was $37.
Answer: Multiply the original price by the decimal form of the percent and subtract that from the original price.
37*0.85=31.45
37-31.45=5.55
Answer: New price is $5.55
Please solve for a: b = 2 - (1/a)
[tex]b = 2 - \dfrac 1a\\\\\implies ab = 2a -1\\\\\implies 2a -ab = 1\\\\\implies a(2-b) =1\\\\\implies a = \dfrac 1{2-b}[/tex]
$250, 3.4%, 3 years what would my interest be?
Is x = 1 a function?
Answer:
Yes
Step-by-step explanation:
It is a constant linear function, which is in fact a function.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Find the product. Simplify your answer.
(4z+4)(z+4)
just letting you know that the variable is x on here thats just what happened it is the right answer though
slope of thissss
please help
-0.66
Step-by-step explanation:
can u mark me a brainliest
Help please please need quick
Abigail earned $10.26 for babysitting her cousin for 3 hours. How much did she earn in each hour?
Divide total earned by number of hours:
10.26/3 = $3.42
She earned $3.42 per hour
no link fast but righ and if you get the answer right can you help me with other question
Answer:
12 inches
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h where r is the radius and h is the height
113.04 = 1/3*3.14 ( 3)^2 h
113.04 = 9.42 h
Divide each side by 9.42
113.04/9.42 = h
12 = h
12 inches
Answer:
Height = 12 in
Step-by-step explanation:
Volume Cone = 1/3(πr²h)
113.04 = 1/3(3.14)(3²)(h) [tex]\longmapsto[/tex] Note that the 1/3 and 9 simplify
113.04 = 3.14(h)(3)
37.68 = 3.14(h)
h = 12
-Chetan K
Solve the right triangle. a = 2.2 m, B = 37.7°, C = 90° 4) A) A = 52.3°, b = 0.6 m, c = 2.3 m B) A = 52.3°, b = 1.7 m, c = 2.8 m C) A = 52.3°, b = 3.2 m, c = 3.9 m D) A = 52.3°, b = 3.2 m, c = 2.8 m
Answer:
B) A = 52.3°, b = 1.7 m, c = 2.8 m
Step-by-step explanation:
We know that it is a right angle triangle because C = 90°
because of that we can do 180 - 90 + 37.7
which is a=52.3
Because it is a right angle triangle, we can use sin, cos,tan
I will use sin to find the side of c
2.2 is a
sin 52.3 = 2.2/x
x= 2.2/ sin 52.3
x=2.78
You could do cos or tan but the pythagorean theorem for me is much faster
so it looks like this, a^2+b^2 =c^2
in this case we have both a and c we want b
so we rearrange
c^2-a^2=b^2
2.78^2-2.2^2= b^2
[tex]\sqrt{2.89}[/tex]=b
1.7=b
therefore it would be this option B) A = 52.3°, b = 1.7 m, c = 2.8 m
Write a recursive formula for a_n the n^th term of the sequence 36, 6, 1, ....
a_1=
a_n=
Answer:
you plus them together then you get 42 out of your number you close during / N which is 3 to get your final answer thank
Apply the distribute property, substitute the given numerical value given:
9(-3r -11), r=10
Answer:
-369
Step-by-step explanation:
Replace r with 10.
9(-3(10)-10))
9(-30-11)
9*-30+9*-11
-270+ -99
-369
Hope this helped. :)
Juan wants to buy a video game for $63. He saves $12 every Friday. Part A. Create an equation to represent Juan's total savings, y, in dollars, after x Fridays. y
Answer:
Answer in explanation.
Step-by-step explanation:
An equation to represent Juan's total savings y, in dollars, after x Fridays will be;
⇒ y = 12x
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Juan wants to buy a video game for $63.
And, He saves $12 every Friday.
Now,
Let total dollars after x Friday = y
And, He saves $12 every Friday.
So, We can formulate;
⇒ Total money (y) = 12x
⇒ y = 12x
Thus, An equation to represent Juan's total savings y, in dollars, after x Fridays will be;
⇒ y = 12x
Learn more about the mathematical expression visit:
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This circle is centered at the point (3,2) and the length of its radius is 5 what is the equation of the circle
Answer:(x-3)² + (y-2)² = 25
Step-by-step explanation:
A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².
So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.
Answer:
(x - 3)² + (y - 2)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Here (h, k ) = (3, 2 ) and r = 5 , then
(x - 3)² + (y - 2)² = 5² , that is
(x - 3)² + (y - 2)² = 25 ← equation of circle
The diagram below shows two parallel lines, m and n, cut by a transversal, k. Angles A, B, and C are shown in the diagram
A student writes a proof to show that the corresponding angles, A and B, are congruent. The student's proof is shown below
A. Both reason 2 and Reason 3 are correct as shown in the table
B. Reason 2 is correct, but Reason 3 should "Alternate interior angles are congruent"
C. Reason 2 should be "Alternate interior angles are congruent," but Reason 3 is correct
D. Both Reason 2 and Reason 3 should be "Alternate interior angles are congruent"
(look at picture to understand better)
9514 1404 393
Answer:
B
Step-by-step explanation:
Angles A and C are vertical angles; angles B and C are alternate interior angles. Only line 3 of the proof is in error.
The applicable description is found in choice B.
The cost of a ride in a taxi is $2.50 for the first half-mile plus a constant amount per half-mile after that. The sequence below shows the pattern of numbers that appear on the driver's screen.
2.50, 2.75, 3.00. 3.25, 3.50, 3.75
Part A: Write a recursive function that can be used to determine f(x), the cost in dollars, for a ride in the taxi of, x, half-miles.
Answer: 2.50 + 0.35(15.75-1)*4 = $23.15 is the answer
Step-by-step explanation: Hope this helps!
A bag contains 11 apples and 6 oranges. If you select 6 pieces of fruit without looking, how many ways can you select exactly 5 apples
Answer:
you have a 11/17 percent chance of getting an apple
Step-by-step explanation:
if there are 11 apples and 6 oranges. 11 out of 17 times you will get an apple
The graph of f(x) = x2 has been shifted into the form f(x) = (x - h)2 + k:
5
365
What is the value of k? (1 point)
0 1
0-1
O-2
O 2
An estimate for - 72
-8.1
-8.5
-9.1
-9.5
[tex]solution[/tex]
[tex] \sqrt{72} [/tex]
Factor the expression
[tex] \sqrt{6 }^{2} \times 2[/tex]
Use the properties of radicals
[tex] \sqrt{6 {}^{2} } \sqrt{2} [/tex]
simplify the root
[tex]answer[/tex]
[tex]6 \sqrt{2} [/tex]
Answer:
the answer is -8.5
you should use m.a.t.h.w.a.y it is very helpful with math and brainly would not let me say the name the correct way so I had to put periods but anyways have a good day or night
︎
please help me completing square
x^²+2x-24=0
Answer:
Step-by-step explanation:
x² + 2x -24 = 0
delta = 2² - 4*1*(-24)
delta = 4 + 96
delta = 100
x' = (-2 + [tex]\sqrt{100}[/tex]) / 2*1
x' = (-2 + 10) / 2
x' = 8 / 2
x' = 4
x" = (-2 -10) / 2
x" = -12 / 2
x" = -6
-3y<-14 i dont get the dam question
Answer:
Step-by-step explanation:
-3y<-14
divide both sides by -3
y<4.67
i’m not exactly sure what the question is asking or what you’re trying to find, but this is what i could figure out.
Answer:
y>14/3
I'll provide the step by step solution too.
=3y÷(-3)>-14÷(-3)
y>-14÷(-3)
y>14÷3
turn it into a fraction
y>14/3
hence your given answer above
anyone good at maths?
1 ) 4 × 11 = 44 yd
____________________
2) 4 × 2 = 8 ft
____________________
3) 4 × 4 = 16 in
____________________
4) 4 × 6 = 24 ft
____________________
5) 4 × 18 = 72 in
____________________
6) 4 × 5 = 20 yd
____________________
7) 4 × 9 = 36 in
____________________
8) 4 × 13 = 52 yd
____________________
9) 4 × 10 = 40 ft
Answer:
I am good, but not for peremiter
Step-by-step explanation: