The height of an acrobat who jumps from a trampoline to a large mat on the ground can be modeled by f(x)=-8x^2+16x+10, where x is the time in seconds after the acrobat jumps.
How high is the trampoline off the ground?
Find the maximum height of the acrobat and the time it takes to reach this height.
Answers
The trampoline is 10 units off the ground.
The maximum height of the acrobat is 18 units, and it takes 1 second to reach this height.
We have,
To find the height of the trampoline off the ground, we need to determine the value of f(x) when x is equal to zero.
This is because at the moment the acrobat jumps (x=0), the height of the acrobat is the height of the trampoline.
Given the function f(x) = -8x² + 16x + 10, we substitute x=0 into the function:
f(0) = -8(0)² + 16(0) + 10
f(0) = 0 + 0 + 10
f(0) = 10
Now,
To find the maximum height of the acrobat and the time it takes to reach this height, we can observe that the function f(x) is in the form of a quadratic equation in the form of ax² + bx + c, where a = -8, b = 16, and c = 10.
The maximum height of the acrobat occurs at the vertex of the quadratic function.
The x-coordinate of the vertex is given by:
x = -b / (2a)
Substituting the values, we have:
x = -16 / (2 * -8)
x = -16 / -16
x = 1
The time it takes to reach the maximum height is 1 second.
To find the maximum height, substitute the value of x back into the function:
f(1) = -8(1)² + 16(1) + 10
f(1) = -8 + 16 + 10
f(1) = 18
Therefore,
The trampoline is 10 units off the ground.
The maximum height of the acrobat is 18 units, and it takes 1 second to reach this height.
Learn more about functions here:
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Related Questions
Could anyone help me with this problem? Will mark brainiest! Please show all the work!
Semir, Sarah, and SungSo decided to raise money for a local homeless shelter by working in a local deli. The deli agreed to donate to the shelter a portion of the profits from each meal the three sold. Semir sold 3 times as many meals as Sarah. SungSo sold 2 more meals than Sarah.
a. Write an expression for the number of meals that each sold.
b. If Sarah sold 24 meals, how many meals did Semir and SungSo each sell?
c. How many meals did the three sell in all? Explain how to use the commutative property and the associative property of addition to make finding the sum easier.
Answers
Answer:
(A) 24+72+48
(B) Sarah sold 24 meals and Samir sold 72 and SungSo sold 48.
(C) 144 is how many they sold in all.
Step-by-step explanation:
Samir sells 3 times as much as Sarah, so he sells 72. SungSo sells twice as much as Sarah so he sells 48. Sarah sells 24.
Using the Addition Standard Algorithm I calculated that they sold 144 deli meals.
h=r/3
o=h+2
b.) Semir sold 72 because 24x3=72
Sungso sold 26 because 24+2=26
c.) in total they sold 24+72+26 we can just add the two of them with fitting second digits that being 24+26 because it will equal 50 which is an easy number to work with then we can just do 50+72 which is 122
Referring to the Fig. in Question #7, think about spinning this spinner, which is
divided into 8 equal segments. Give the probability in simplest form.
P(even) =
Answers
Answer: 1/4
Step-by-step explanation: because there is only 4 on there so it would be 1/4
Answer:
P(even)=5/8
Step-by-step explanation:
count the amount of even numbers so there is 3 2s and 2 4s so 5 even numbers
count the amount of odd numbers so there is 2 1s and a 3 so 3 odd numbers
add the total amount of numbers so 8 and as there is 5 even the answer is 5/8
Ashira has $1,000 in her savings account. The interest rate is 2.5%. How much interest will Ashira earn when her money has been in the bank for 3 years?
Answers
Answer:
$75
Step-by-step explanation:
Have a Fabulous Monday! ✨
Answer:
$75
Hope This Helps!
what is 500+600
i apologize for any post I've made today that was my sister
Answers
Answer: 1100
Step-by-step explanation:
Ms. Maher ran 7.400 meters. How many kilometers is that? Who ever get it right first gets brainlest
Answers
Idgehevehdgdencevww
i need help ! please asap!!!!
Answers
Answer:
C & F
Step-by-step explanation:
29 - 13 is 16 and 46 - 21 is 25. Everything else is wrong because the differences are not the correct answers except for C and F. Sorry if this sounds kinda confusing
This is probably wrong so...
Find the number that makes the ratio equivalent to 2:25.
__:50
Answers
To get 25 into 50, you multiply by 2. So, 2:25 is the same as 4:50.
I need help please i need correct answer
Answers
Answer:
-8x^3(3x^2+2)
Step-by-step explanation:
If y varies directly with x, and y = 2 when x = −4, what is the value of y when x = 20 ?
Answers
Answer:
y=kx
2=k.-4
k=-1/2
then
y=-1/2×20
y=-10
Answer:
y = - 10
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 2 when x = - 4, that is
2 = - 4k ( divide both sides by - 4 )
\(\frac{2}{-4}\) = k, that is
k = - \(\frac{1}{2}\)
y = - \(\frac{1}{2}\) x ← equation of variation
When x = 20, then
y = - \(\frac{1}{2}\) × 20 = - 10
what is the height of a rectangular prism that has a volume of 28- meters cubed, a length of 8 meters and a width of 7 meters,
Answers
Can you help me with this?
Answers
✨✨✨✨✨
because 2 people spent less than 120 out of 3 total people.
answer:2/3
i need help asap pleasee!
Answers
Answer:
\( {7}^{?} 8\)
yannnnnnnnnnnn na
Mackey invested some money in an account paying 6% interest for one year. She invested $1000 more than this amount in an account paying 8.5%. How much did she invest in total if the total interest earned in the year was $737.50?
Answers
Step-by-step explanation:
Let's assume the amount Mackey initially invested in the 6% account is x dollars.
According to the given information, Mackey invested $1000 more than x in the 8.5% account, which means she invested (x + $1000) dollars in that account.
The total interest earned from the 6% account would be 0.06x dollars, and the total interest earned from the 8.5% account would be 0.085(x + $1000) dollars.
The total interest earned in the year is given as $737.50, so we can set up the equation:
0.06x + 0.085(x + $1000) = $737.50
Simplifying the equation:
0.06x + 0.085x + 0.085($1000) = $737.50
Combining like terms:
0.145x + $85 = $737.50
Subtracting $85 from both sides:
0.145x = $737.50 - $85
0.145x = $652.50
Dividing both sides by 0.145:
x = $652.50 / 0.145
x ≈ $4500
Therefore, Mackey initially invested approximately $4500 in the 6% account, and she invested $1000 more, which means she invested a total of $5500.
$4500
$4500
$4500
$4500
2. The number of people in a
town n years after the initial
count can be modeled by
the equation p(n)=25,000(0.8)n
where P is the population
and n is the number of years.
b. Is this town growing or
shrinking in population?
By what percentage?
a. What was the population
at the initial count?
c. Write an expression to
predict what the population
will be in 5 years
Answers
Answer:
Step-by-step explanation:
25,000*0.8*n
25,000* 0.8= 20,000n
Therefore if the value of n is any number below 1 (including) then the population will decrease
If the value of n is any number above 1 (not including 1 specifically above 1.25 to show increase because 1.25* 20,000= 25,000) then it will show an increase with 1 it will just be 20,000 that being less then 25,000.
Answer:
-Population at the initial count: 25,000
-Is it increasing or decreasing: It depends on the value of n (explained above)
-By what percent: 80%
-Expression for 5 years: 25,000*0.8*5
- 25,000*0.8*5= 100,000 people
find three consecutive integers for which 3 times the sum of the first and third integers is -342? show step by step
Answers
Answer:
The integers are -58, -57, -56.
Step-by-step explanation:
The difference between two consecutive integers is 1.
If you let the smallest of the three consecutive integers equal x, then the next greater one is x + 1, and the greatest of the three is x + 2.
Integers: x, x + 1, x + 2
The sum of the first and third is: x + x + 2
3 times the sum of the first and third is: 3(x + x + 2)
That product equals -342.
3(x + x + 2) = -342
3(2x + 2) = -342
Divide both sides by 3.
2x + 2 = -114
Subtract 2 from both sides.
2x = -116
Divide both sides by 2.
x = -58
x + 1 = -57
x + 2 = -56
The integers are -58, -57, -56.
not my answer...found it from somewhere else... but hope this helps
it was v helpful
Don put $3,000 in a savings account with an interest rate of 3% for three years. If the interest is compounded annually, how much money will he have at the end of the three years?
A. $3,278.18
B. $3,378.18
C. $6,591.00
D. $3,182.70
Answers
Answer:
B
Step-by-step explanation:
I do not know how to explain it but I know it is B
Explanation
So you would use the formula A=p(1+r/n)^(n)(t)
n=1
(since it’s annually and it’s compounded once a year)
P=3000 the principle
rate=0.03
time=3
(3000)(1+0.03/1)^(1)(3)= which would equal 3278.18
Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?
here are the answers given
\/
f(x) = −one eighth (x − 2)2 − 2
f(x) = one sixteenth (x − 2)2 + 2
f(x) = one eighth (x − 2)2 − 2
f(x) = −one sixteenth (x + 2)2 − 2
Answers
Answer:
f(x)=1/16(x-2)^2+2
Step-by-step explanation:
The Equation can be written like this:
f(x) = 1/(4p)(x -h)^2 +(k-p)
where (h, k) is the focus, and p is half the distance between focus and directrix. Here, (h, k) = (2, 6) and p=(6-(-2))/2 = 4. So the equation is ...
f(x) = 1/16(x -2)^2 +2
whats the constants of 4+7n-8+6m+9
Please hurry this is due soon!!!
Answers
Answer:
6m+7n+5
Step-by-step explanation:
there you go 4+7n-8+6m+9 =6m+7n+5
PLS help with this question
Answers
Answer:
translate it
Step-by-step explanation:
translate it in translater
9. Expand using identites.
1) (3/2 m - 5n) (3/2 m + 5n)
Answers
Answer:
(3/2 m)^2 -(5n)^2^
Step-by-step explanation:
Answer: 9m^2 / 4 - 25n^2
Step-by-step explanation:
Use the identity: (a-b)(a+b)=a^2 - b^2
substitute values of a and b, where a=3/2m and b=5n.
The following simplifies to (3/2m)^2 - (5n)^2.
The cost of renting an inflatable bounce house for 2 hours is $53.50. At this rate, what is the cost of renting the bounce house for 5 hours?
Answers
Answer:80.25
Step-by-step explanation:
I need help, please quickly
Answers
Answer: The ratio is 18:3
Step-by-step explanation:
Answer: 6 to 1
Step-by-step explanation:
A ratio refers to a fraction. In this case the question asks how many players to coaches there are.
The word "to" means that is where the fraction bar goes.
Players/Coaches
There are 18 players and 3 coaches.
18/3
18 can be divided by 3, 6 times so the fraction can be simplified to
6/1 meaning there are 6 players for every coach.
Which rational expression has a value of 1 when x =-1?
Answers
The rational expression that has a value of 1 when x =-1 would be; D 2x²/ (x + 3).
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.
We need to determine the expression that has a value of 1 when x =-1
Let's consider the rational expression of the option D;
2x²/ (x + 3)
Now substitute the value x = -1 in the given expression
2x²/ (x + 3)
2(-1)²/ (-1 + 3)
= 2/ 2
= 1
Hence, the required rational expression is D 2x²/ (x + 3).
To know more about an expression follow;
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Consider the functions below -
Answers
Answer:
y-intercept
Step-by-step explanation:
In all cases, when x = 0, f(0) = a or b or c.
Answer: y-intercept
Mr. Smith's class has collected 112 cans in a food drive. They plan to sort the cans into x bags, with an equal number of cans in each bag . Write an expression to show how many cans there will be in each bag .
Answers
Answer:
14 cans in each bag
Step-by-step explanation:
112 divided by 8 = 14
A class trip is going on a trip to a museum. It costs $820 to rent a bus. Each ticket to the museum costs $11. Evaluate the cost of this trip for 39 people *
please help me
Answers
Answer:
I got to the answer 1,249 correct me if I'm wrong
Answer:
1,249
Step-by-step explanation:
if I'm wrong correct me but I think it should be right because you multiply 11 and 39 and get 429 then add 820 to it and it should be 1249
pls explain how this works
Answers
Step-by-step explanation:
The domain is the all the possible inputs of the function.
We need to find the span of the function on the horizontal axis.
Here the function start at -8 and ends at 8.
So the domain is [-8,8].
We use brackets because -8 and 8 is defined over the domain.
The range is all the possible outputs.
We need to find the span of the function in the vertical axis
The function lowest point is -4 and the highest point is 7.
So the range is [-4,7].
To find whether this graph is a function, draw multiple vertical lines. If the lines intersect the curve more than once, then this curve is not a function
Here this curve is a function because all the lines only intersect the curve once.
So the answer is yes.
which pair of numbers has a lcm of 12
1 and 6
2 and 3
2 and 6
3 and 4
Answers
Answer:
3 and 4
and
2 and 6
Step-by-step explanation:
3×4=12
2×6=12
Answer:
3 and 4
2 and 6
Step-by-step explanation:
Chart and Graph Questions (image inserted)
Answers
X is the horizontal line and y is the vertical one- so (1,3) you would move one horizontally (right) and 3 vertically (up)
Answer:
X is the horizontal line and y is the vertical one- so (1,3) you would move one horizontally (right) and 3 vertically (up)
What is 12 5/25 as a mixed number in simplest form?
Enter your answer in the box.
Answers
Answer:
12 1/5
Step-by-step explanation:
Answer:
in an improper fraction, it is 305/25
in a simple form, it is 12 and 1/5
Step-by-step explanation: