A baseball is thrown in a parabolic arc. It's position above the ground at a given point in time can be represented by the quadratic function LaTeX: p\left(t\right)=\frac{1}{2}gt^2+v_0t+p_0p ( t ) = 1 2 g t 2 + v 0 t + p 0, where LaTeX: t\ge0t ≥ 0, LaTeX: gg is -32 ft/sec/sec, LaTeX: v_0v 0 is initial velocity, and LaTeX: p_0p 0 is its initial position above the ground. If the ball was thrown straight up at 16 ft/sec when it was 5 ft above the ground, how high did it go?
Answers
Answer:
The baseball reached 9 feet high above the ground
Step-by-step explanation:
The given quadratic function representing the position of the baseball above ground is p(t) = 1/2·g·t² + v₀·t + p₀
Where;
t ≥ 0
g = -32 ft./sec²
v₀ = The initial velocity
p₀ = The initial position
Given that when the ball is thrown, we have;
The initial, straight up, velocity, v₀ = 16 ft./sec
The initial position, p₀ = 5 ft.
Substituting the above values in the quadratic function representing the position of the baseball above ground, we have;
p(t) = 1/2·(-32)·t² + 16·t + 5 = 16·t - 16·t² + 5
At the maximum point, the rate of change of the height with time = 0, therefore;
dp(t)/dt = 0 = d(16·t - 16·t² + 5)/dt = 16 - 32·t
16 - 32·t = 0
16 = 32·t
t = 16/32 = 0.5 seconds
Therefore, the time takes to reach the maximum height = 0.5 seconds
The height (maximum) reached in 0.5 seconds is given as follows;
h(t) = 16·t - 16·t² + 5, from which we have;
h(0.5) = 16 × 0.5 - 16 × (0.5)² + 5 = 9
Therefore, the height baseball reached = 9 ft. above ground
Related Questions
Ben can type 2/5 of a page of an essay in 1/2 minute. How much time would
take him to type one full page of the essay?
Answers
Answer:
ok so first i want to figure out what 2/5 converted to percent is......
you can find it out on a calculator or on paper by dividing 2 / 5 = 0.4
so this is 40% and if it takes him half a minute to do this, it takes him about 30 seconds to finish 40% of the essay and there is a full 60% still waiting to be done, so lets see,
40% + 40% = 80%
so that is about 1 full minute to write 80% we are still left with 20% so let's see how much time does it take to write 20% of the essay, in 40% it takes 30 seconds and in 80% it takes 60 seconds. So since 20% is half of 40% then we must divide the time in half so 30 / 2 = 15
So if we add all these numbers up it equals 1:15 minutes to write an essay
I hope this helps and please mark brainliest if i got it right!
The time taken by Ben to write a full page will be 1:15 minutes.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
you can find it out on a calculator or on paper by dividing 2 / 5 = 0.4
So this is 40% and if it takes him half a minute to do this, it takes him about 30 seconds to finish 40% of the essay and there is a full 60% still waiting to be done, so let's see,
40% + 40% = 80%
so that is about 1 full minute to write 80% we are still left with 20% so let's see how much time it takes to write 20% of the essay, in 40% it takes 30 seconds and in 80% it takes 60 seconds. So since 20% is half of 40% then we must divide the time in half so 30 / 2 = 15
Therefore, the time takes Ben to write a full page will be 1:15 minutes.
To know more about an expression follow
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An electrician is hired to install a ceiling fan. She estimates that the installation will take no more than 45 minutes if the house is up to building code. If the house is not up to building code, she estimates that the installation will take longer than 120 minutes. Which graph represents the number of minutes it could take her to install the fan?
Answers
Answer:
The third image
Step-by-step explanation:
Your mom
Answer:
option C
Step-by-step explanation:
I got the right answer c;
The tape diagram represents the ratio of the time you spend tutoring to the time your friend spends tutoring. You tutor for 3 hours. How many hours does your friend spend tutoring?
Answers
Answer:
By a quick online search, i found two tape diagrams:
13) You: -
Friend: - -
So you have one block, and your friend has two.
We know that you work for 3 hours, this means that your only block must represent 3 hours.
And all the blocks represent the same amount of time, then each one of the two blocks of your friend also represents 3 hours.
Then in total, he tutored for 3 hours + 3 hours = 6 hours.
14) You: -
Friend: - - - - -
In this case, you still have only one block, but now your friend has 5.
Using the same reasoning as above, we can conclude that each block represents 3 hours, and your friend has 5 of them, this means that he tutored for:
5*3 hours = 15 hours
Which is an integer
Answers
Answer:
6.2 is an integer
Step-by-step explanation:
Answer
6.2
Step-by-step explanation:
help in algebra 1!! needed asap!! in khan academy btw
Answers
Answer:
10 not in
5 in
0 not in
Step-by-step explanation:
How do I find the correct slope on a graph?
Answers
Answer:
To find the slope of a line from a graph, first choose 2 points along the line and write down the X and Y coordinates for each. Next, find the rise by taking the difference between the 2 Y coordinates. If the line slopes up as it moves to the right, the rise will be positive. If it slopes down, the rise will be negative.
Step-by-step explanation:
I would also use this site called desmos it’s a graphing calculator and it should help if you have multiple choice questions or just need to see a clearer picture
Russia's currency is called the ruble, and is denoted with this symbol: Rub. An electrical contractor has Rub850,360 in his business's bank account.If at the end of the week he deposits Rub119,980 in payments made from clients and then pays out Rub79,205 in wages, how much money will he have left in his account?
Answers
Answer:
He will
have RUB 891,135 present to the same government
Step-by-step explanation:
Here, we want to calculate the amount of money that will be left in the account
To get this, we simply subtract the payments and add up the deposits to the initial
Thus, we have;
850,360 + 119,980 - 79,205 = 891,135
Please help polynomial stuff
Answers
don’t have time for the next one sorry
Which of the following would produce a graph that is the reflection of f(x)= (x−3)2−4 across the x-axis?
Answers
Answer:
c took the quiz on edge 2020
Answer:
[tex]x2 - 6x + 5[/tex]
Step-by-step explanation:
The function f(x) = (x-3)^2 - 4
This can be written as ;
(x-3)(x-3) -4
x(x-3)-3(x-3)-4
[tex]x2 - 3x - 3x + 9 - 4 [/tex]
The animal shelter had a special on adoption rates for their dogs and cats. Each dog adoption fee was $75 and each cat adoption fee was $35. On Christmas Eve, the animal adopted out 8 total animals and brought in $400 in total adoption fees. How many dogs and how many cats were adopted out on Christmas Eve?
dogs:
cats:
Answers
Answer:
3 dogs and 5 cats were adopted out on Christmas eve.
Step-by-step explanation:
Let the number of dogs adopted out on Christmas eve be x and the number of cats be y.
From the question,
On Christmas Eve, the animal adopted out 8 total animals
That is, x + y = 8 ...... (1)
and brought in $400 in total adoption fees.
Also from the question,
Each dog adoption fee was $75 and each cat adoption fee was $35.
∴ On Christmas Eve,
75x + 35y = 400 ...... (2)
Now, to determine how many dogs and how many cats were adopted out on Christmas Eve, we will solve the two equations simultaneously.
From equation (1)
x + y = 8
Make x the subject of the relation.
∴ x = 8 - y ...... (3)
Substitute the value of x into equation (2)
75(8 - y) + 35y = 400
600 - 75y + 35y = 400
600 -40y = 400
600 - 400 = 40y
200 = 40y
∴ 40y = 200
y = 200/40
y = 5
Substitute the value of y into equation (3)
x = 8 - y
x = 8 - 5
x = 3
∴ x = 3 and y = 5
Hence, 3 dogs and 5 cats were adopted out on Christmas eve.
Mauricio can string 8 guitars in 2 hours how many can he string in 15 ?
Answers
Answer:
He strings 52 guitars in 15 hours
please solve for t this is very important
Answers
hope this helps:)
Francis used the distributive property of multiplication to help him solve the equation 6 x 2 = ________. Francis did not get the same answer for each side of the expression. Explain the steps required to correct his mistake. 6 x 2 = (3 x 2) + (4 x 2) 12 = 6 + 8 12 = 14
Answers
Solution :
The distributive property of multiplication :
It is given that we have to find the solution for the below expression using the distributive property of multiplication,
So 6 x 2 = __________
Using distributive property, we can write :
⇒ 6 x 2 = 12
⇒ (3 + 3) x (2 ) = 12
⇒ (3 x 2) + (3 x 2) = 12
⇒ 6 + 6 = 12
⇒ 12 = 12
owo help me plz *smiles* thanks
Answers
Answer:
I belive it is A
Step-by-step explanation:
Answer:
I think it is #1
Step-by-step explanation:
28/45
6th grade math i mark as brainliest
Answers
which statement is true
Answers
Answer:
the answer is B that is
ΔABC is similar to ΔEDC
Step-by-step explanation:
look at the figure abc and edc completely match together as a is a right angle and is at the the first, similarly e is also a right angle and is at the first. also b is at the same place as d i.e. in between the right angle and the last angle.
moreover, c is at the last in abc just like in edc
The solution of 3x - 4 ( x - 2 ) = 0 is ;
Answers
Answer:
8
Step-by-step explanation:
simplify the expression
3x - 4x+8 = 0
put like terms together 3x-4x = -x
-x + 8 = 0
add x on both sides
x = 8
happy holidays :)
please click the heart to give thanks :)
Step-by-step explanation:
STEP 1:
Equation at the end of step 1
(3x - 4)2 = 0
STEP 2:
Solving a Single Variable Equation:
2.1 Solve : (3x-4)2 = 0
(3x-4) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : 3x-4 = 0
Add 4 to both sides of the equation :
3x = 4
Divide both sides of the equation by 3:
x = 4/3 = 1.333
One solution was found :
x = 4/3 = 1.333
7÷7/11=
Please explain for me
Answers
Answer:
11
Step-by-step explanation:
You have to first make the 7 into a fraction (7/1) then keep, change, flip.
You keep the 7/1 as it is, you change the division sign into a multiplication sign, and you flip the 7/11 to 11/7. You then just multiply straight across to get 77/7 which is the same thing as 11/1 which is the same thing as 11!
Final answer:11
Is the following relation a function?
Relation:
Х Y
6 8
5 1
6 6
2 4
The domain:
{2,5,6}
The range:
{1,4,6,8}
Answers
Answer: No
Step-by-step explanation:
The domain consists of the numbers 6, 5, 6, 2
6 is repeated twice
The criteria for a function is that there are no repeating numbers in the domain
This does not follow the criteria, therefore this is not a function
Answer-No
how do you solve
3^3 ÷ 9^1
Answers
Answer:
pemdas
Step-by-step explanation:
3^3 = 27 (3*3*3)
9^1 =9 (9)
27/9= 3
PLEASE HELP ME I DONT UNDERSTAND
Answers
Answer:
i got 8.944272
Step-by-step explanation:
might be wrong because i havent done a probelm like this in a long time
but i used the distance formula between the 2 plotted points.
One batch of walnut muffins uses 1 cups of walnuts. How many cups of walnuts are needed to make 3 batches of muffins?
A.) 3 cups
B.) 57 cups
C.) 5 cups
D.) 4 cups
Answers
Answer:
3 cups
Step-by-step explanation:
If one needs one cup then three needs three cups.
Can you guys help me pls
Answers
Answer:
The answer is 4/6
Step-by-step explanation:
2:3 and 4:6 share the same exact relationship but is expressed using different numbers, for example, 2:3 * 2 = 4:6 and 4:6 / 2 = 2:3
Answer:
4/6
Step-by-step explanation:
2:3 = 2/3
2/3 × 2 or 2/3 + 2/3
is equal to
or equivalent 4/6
hope this helps :)
A number is selected from the set (1, 2, 3, 5, 15, 21, 29, 38,500). If equal elemental probabilities are assigned, what is
the probability that the number chosen is either less than 29 or odd?
Answers
Answer:
7/9 is the answer
Step-by-step explanation:
There are 4,389 dogwood trees in the state park. The park workers are going to plant 342 more trees. How many trees will there be when they are done?
Answers
Answer:
4731
Step-by-step explanation:
4,389+342=4,731
solve this equation 3x + 5 = 7x – 7
Answers
3x + 12 = 7x
Subtract 3x
12 = 4x
Divide by 4
x = 3
Answer:
3
To find:
x
Step-by-step explanation:
3x + 5 = 7x – 7
3x - 7x = -7 - 5
-4x = -12
x = -12/-4
x = 3
hope it helps u!
Help please!!!!!! HELP
Answers
Answer:
number 1
Step-by-step explanation:
15. Write the slope intercept form of the equation of each line given the
slope and y-intercept. Slope = 2 y-intercept = -7
Answers
Answer:
y=2x-7
Step-by-step explanation:
it is in the form y=mx+b where m=2 and b=-7
please answer this question
Answers
Answer:
D. 1,300
Step-by-step explanation:
Type the correct answer in the box. Use numerals Instead of words. Consider the function shown on the graph. у 8 8 02 4 2 2 X -10-8 -6 0 2 N- 6 6 8 10 -2 -4 -6 -8 Complete the statements to make them true,
domain x >
range y >
Answers
Answer:
Domain → [-5, ∞)
Range → [-2, ∞)
Step-by-step explanation:
Domain:
Domain of a function on from its graph is represented by the set of x-values (Input values).
Range:
Range of a function is a set of y-values (output values).
From the graph attached,
Graph starts from x = -5 and tends towards the infinity, so the domain will be,
Domain → [-5, ∞)
Similarly, y-values vary from y = -2 to y = ∞
Therefore, Range → [-2, ∞)
Given the graph of the function:
Domain is: [-5, ∞)
Range is: [-2, ∞)
Domain and Range of a FunctionThe domain of a function are all the values of x that are plotted on the x-axis, while the corresponding y-values are the range of the function.
Thus:
From the given graph representing a function:
Domain of the function is between -5 to infinity.
Range of the function is between -2 to infinity.
Therefore, given the graph of the function:
Domain is: [-5, ∞)
Range is: [-2, ∞)
Learn more abut domain and range of function on:
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