Interpret the key features of the graph in the given context, and answer the following questions.
Part A
What is the vertex of the function? How do you interpret it in the given situation?
Part B
What is the x-intercept of the function? How do you interpret it in the given situation?
Part C
What is the y-intercept of the function? How do you interpret it in the given situation?
Part D
What is the domain of the function in the given situation? Explain your answer.
Part E
Calculate the average rate of change over the intervals [0, 20] and [60, 80]. What does the average rate on these intervals tell you about the balloon’s journey?
Answers
Answer:
Part A
The vertex of the graph lies at (40,18). This is the maximum value on the graph. This means the balloon reached a maximum altitude of 1,800 meters about 40 minutes after its launch.
Part B
One of the x-intercepts of the function lies somewhere between x = 82 and x = 83. This is this point where the balloon is at zero altitude, or sea level. So, the balloon stays in the air for a little over 82 minutes. There is another x-intercept to the left of the origin. But a negative time value doesn’t make sense. So, we won’t considerate it for this scenario.
Part C
The -y-intercept of the function lies at (0,2). This is the starting point of the balloon’s journey. The point the balloon launched from was 200 meters above sea level.
Part D
We can’t interpret negative time values in this situation. So, the domain of the function is restricted to positive values of x. A negative y-value indicates an altitude below sea level. While some locations have negative altitudes, we can consider only positive values for this scenario. So, we should only consider positive values of y. So the domain of the function is restricted to only those values of x that produce positive values of y. Since we can’t see the x-intercept clearly from the graph, we’ll consider the domain of the function to be [0, 82].
Part E
Average rate of change on [0, 20] = f(20)-f(0) / 20-0
= 14-2 / 20
= 12 / 20
=0.6
Average rate of change on [60, 80] = f(80)-f(60) / 80-60
= 2-14 / 20
= -12 / 20
= -0.6
In this case, the rate of change represents the change in the balloon’s altitude within a time interval. The average rate of change on [0, 20] is positive. This indicates that the balloon is ascending, or climbing, during the first 20 minutes of its journey.
The average rate of change on [60, 80] is negative. This indicates that the balloon is descending between 60 and 80 minutes. Although negative, the rate of change in the second interval has the same absolute value as the rate of change for the first interval. So, during the last 20 minutes the balloon is descending at the same rate it was ascending during the first 20 minutes.
Related Questions
Bad Bunny o Darell??
Freę points
Answers
Answer:
ok
Step-by-step explanation:
Which function has real zeros at x = 3 and x =
7
Answers
Answer:
x^2-10x+21
Step-by-step explanation:
(x-3)(x-7)=
x^2-7x-3x-21=
x^2+10x+21
Find an angle α that is coterminal with an angle measuring −460∘, where 0∘≤α<360∘. Do not include the degree symbol in your answer. For example, if your answer is 20∘, you would enter 20.
Answers
Answer:
The coterminal angle is 260°
Step-by-step explanation:
Suppose that we have an angle A.
All the coterminal angles to A are written as:
B = A + n*360°
Where n is any whole number.
Notice that if n = 0, we get:
B = A + 0*360° = A
So A is coterminal with itself, which is trivial.
Now we want to find a conterminal angle to -460° such that it is in the range:
0° < α < 360°
So we just need to find a value of n such that:
α = -460° + n*360°
is on the given range.
We can assume that n = 2 will work, let's check:
α = -460° + 2*360° = 260°
α = 260°
And this angle is in the given range:
0° < 260° < 360°
what is the standard form of 3+5x-4x^2
and what is the standard form of 8x+x+5+x^3
Answers
Answer:
1. -4x^2 + 5x + 3
2. x^3 + 9x + 5
Step-by-step explanation:
hope this helps
PLEASE HELP!!! 25 POINTS & WILL MARK BRAINLIEST
Answers
Answer:
It is answer A without a doubt
Step-by-step explanation:
There are 2 yellow, 3 green, 1 orange, and 4 red cards in a stack of cards turned facedown. Once a card is selected, it is not replaced.
Answers
Answer:
1/45
Step-by-step explanation:
Here is the complete question
here are 2 yellow, 3 green, 1 orange, and 4 red cards in a stack of cards turned facedown. Once a card is selected, it is not replaced. Find each probability.
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one ids attached to the event. If it doesn't a value of zero is attached to the event.
1. P(two yellow cards)
there are a total of 10 cards and 2 yellows cards. If 1 yellow card is picked, it would remain 1 yellow card and 9 cards
P(two yellow cards) = 2/10 x 1/9 = 1/45
Amanda has already run 14 miles on her own, and she expects to run 5 miles during each track practice. How many tracks would it take for Amanda to run 29 miles? heeeeeeeelllllppppp mmmmmeeeee!
Answers
Answer:
It will take Amanda 3 track practices to run 29 miles.
Step-by-step explanation:
29-14=15
15/3=5
or
14+5x=29
subtract 14 from both sides
5x=15
divide both sides by 3
x=3
Hope this helps. Brainliest will be appreciated.
Need help fast will give brainliest! Please help me solves this equation!
Answers
Answer:
x = 15, y = 75
Step-by-step explanation:
hope it helps
. Simplify: (2 x 2 + 6-10 ÷
2)
Answers
Answer: 5
Step-by-step explanation:
You see 2x2 = 4 right and since this is operation 2 / 10 = 5 and 6-5 = 1 so add 1 and that gives you 5
2x2 = 4 / 10/2 = 5 / 6-5 = 1 +4 = 5
Answer:
= 4x + -4
Step-by-step explanation:
Let's simplify:
[tex]2x(2) + 6 -10 \\ = 4x + 6 - 10[/tex]
Combine Like Terms:
[tex]=4x+6+−10
\\ =(4x)+(6+−10) \\ =4x+−4[/tex]
A jar contains 12 oatmeal cookies, 13 sugar cookies and 5 chocolate chip cookies. The percent of cookies that are oatmeal is_?
Answers
Answer:
40%
Step-by-step explanation:
12+13+5 = 30
oatmeal = 12/30 which is 4/10 or 40%
The equation of two circles are known, circle A’s equation is (x-3)^2+(y+4)^2=9 and circle B’s equation is (x+4)^2+(y+12)^2=8.
What is the radius of circle A and the radius of circle B.
Answers
Answer:
Step-by-step explanation:
The circles are written in standard form. The standard form squares the radius on the right hand side.
Circle A
radius = sqrt(9)
radius = 3
Circle B
radius = sqrt(8)
radius = sqrt(2 * 2 * 2)
radius = 2 sqrt(2)
If it cost 16.50 for 6 shirts how much would it cost for just one shirt?
Answers
Answer:
Each shirt would cost $2.75
Step-by-step explanation:
please help meee!!!lol
Answers
Answer:
X represents the number of product so 3 cause you have 2 pastas and 1 cheese. The length represents the total cost. I think 3 would represent cost? I'm not totally sure on that one. Hope this helps!
Step-by-step explanation:
PLEASE HELP MEEE
select all that apply
A. integer
B. whole
C. irrational
D. real
E. rational
no links please
Answers
Answer:
Step-by-step explanation:
A:Cna be a fraction
B:Not a fraction
D: Just because (it is on a number line, I guess)
E:can be a fraction
2
6
+
2
Area
HELP PLEASE
Answers
Answer:
X= 40
Step-by-step explanation:
if you compare the shapes, the X square is half of 6. so i added 6 and 3, then 2 and 3, then multiplied it, and the answer is 40.
PLEASEE HELPPP!!!! Bots will be taken down.
Answers
Answer:
um what grade
Step-by-step explanation:
is like 8th grade math or 7th grade math
Answer:
What do we do?
Step-by-step explanation:
I don’t know what we do
help me pleaseee QUICK I WILL GIVE SOMEONE BRAINLY
Answers
Answer:
B. 5626.9
Step-by-step explanation:
• volume of cylinder= pi(r)2h
• plug in the values into the equation
• pi(8)2(28)
pi=3.14 so 3.14(8)2(28)
• multiply all the values
• you get 5629. 73
• b is the closest the that answer since it says approximate
What do you used to find perimeter
Answers
Answer:
Perimeter = 2 ( l + w )
if u r given for rectangle thats the formula
Step-by-step explanation:
To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width).
Given that m is parallel to n, what must be true of the two lines? Check all that apply.
Answers
Answer:
I don't have the options but I know parallel lines will never touch, they have the same slope, and the distance between the lines never changes
i really need help with this!!! thank you i appreciate it
the volume of the square pyramid is ___ cubic meters
Answers
20X30=6000
Answer:
6000 m^3
Step-by-step explanation:
The basic formula for the area of a pyramid is 1/3 * b * h
where b is the base and h is the height.
The base is a square, so, we can find the area by squaring the side:
30^2 = 900.
Now, we can plug the values we have into the formula from above:
1/3 * 900 * 20
6000 m^3
Please explain how to do #3
Answers
Please help mee!!! Will give brainliest!
Answers
Answer:
B.11+7=18
Step-by-step explanation:
its B because since its 7 days AFTER it means your going to have to add the 11 days plus this 7 days. Which would give you 18 days left till Susie's concert.
Which scatter plot could have
A trend line with the equation below?
Y=x+4
Answers
Answer:
you're correct the second one
Step-by-step explanation:
Which can be represented by the expression 17 – 2x? A. 17 less than twice a number B. the difference between 17 and twice a number C. a number x squared, subtracted from 17 D. 17 less than a number x squared
Answers
Answer:
b it has a difference when subtracting
Answer:
The answer is B.
Step-by-step explanation:
When you subtract you get a difference.
help me please. i need this now
Answers
Step by step exploration
A tepee is designed to have a diameter of 10 feet and the volume of 419 ft.³ at what height the support poles crossed with some of the tepee correctly?
Answers
Answer:
The required height is equal to 5.33 feet.
Step-by-step explanation:
Given that,
Diameter, d = 10 feet
Volume, V = 419 ft.³
We need to find the height the support poles crossed with some of the tepee correctly. Let the height is h.
The tepee is in the form of a cylinder. The volume of a cylinder is given by :
[tex]V=\pi r^2 h\\\\h=\dfrac{V}{\pi r^2}\\\\h=\dfrac{419}{3.14\times 5^2}\\\\h=5.33\ ft[/tex]
So, the required height is equal to 5.33 feet.
e)1- Tan A/1 + Tan A=1-Sin 2A/Cos 2A
Answers
Step-by-step explanation:
Answer :
11. Max is designing a hot tub for a local spa.
He wants the hot tub to have a diameter of 89 inches, What is
the approximate area required for the installation of the hot tub?
(Use 3.14 for pi.)
NO PDF PLZ
Answers
Answer:
Area required for circular hot tube = 6,218 inch² (Approx.)
Step-by-step explanation:
Given:
Diameter of circular hot tube = 89 inches
Value of π = 3.14
Find:
Area required for circular hot tube
Computation:
Radius of hot tube = Diameter / 2
Radius of hot tube = 89 / 2 inches
Area required for circular hot tube = Area of circle
Area of circle = πr²
Area required for circular hot tube = πr²
Area required for circular hot tube = (3.14)(89/2)²
Area required for circular hot tube = (3.14)(7921 / 4)
Area required for circular hot tube = (3.14)(1,980.25)
Area required for circular hot tube = 6,217.985
Area required for circular hot tube = 6,218 inch² (Approx.)
Is (1, 4) a solution to this system of equations? 8x + 3y = 20 x + 4y = 17
Answers
Answer:
Yes.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Systems of EquationsStep-by-step explanation:
Step 1: Define
Identify
8x + 3y = 20
x + 4y = 17
(1, 4)
Step 2: Check
Plug and verify the coordinates is a solution.
Substitute in point [1st Equation]: 8(1) + 3(4) = 20Multiply: 8 + 12 = 20Add: 20 = 20 [tex]\checkmark[/tex]Substitute in point [2nd Equation]: 1 + 4(4) = 17Multiply: 1 + 16 = 17Add: 17 = 17 [tex]\checkmark[/tex]∴ Since both equations work out, (1, 4) is a solution to the systems of equations.
Round 32629 to 1 significant figure