Answer:
110
Step-by-step explanation:
110/5 = 22
22 - 11 = 11
Given the function f(x) =6|x-2|+3, for what values of x is f(x) =39
Answer:
225
Step-by-step explanation:
6x-12+3,f(39)=6(39)-12+3,234-12+3=225
URGENTTT PLEASE!! in middle of test help!
I WILL MARK BRAINIEST! if you answers in under 5mins!
Answer:
equation: 2(2w + 2) = 60
length = 16
width = 14
Step-by-step explanation:
width = w
length = w + 2
perimeter = 2(w + w + 2) = 60
equation: 2(2w + 2) = 60
4w + 4 = 60
4w = 56
w = 14
width = 14
length = w + 2 = 14 + 2 = 16
length = 16
2. (1 pt) For the following polynomial for \( 1+G(s) H(s)=0 \) and using Routh's method for stability, is this close loop system stable? \[ 1+G(s) H(s)=4 s^{5}+2 s^{4}+6 s^{3}+2 s^{2}+s-4 \] No Yes Ca
The closed loop system is stable since all the elements in the first column have the same sign and are positive. Therefore, the correct option is Yes.
Using Routh's method for stability, let us investigate whether this closed loop system is stable or not. Since the polynomial equation provided is:
$$1+G(s)H(s)=4s^5+2s^4+6s^3+2s^2+s-4$$
To examine the stability of the closed loop system using Routh's method, the Routh array must first be computed, which is shown below.
$\text{Routh array}$:
$$\begin{array}{|c|c|c|} \hline s^5 & 4 & 6 \\ s^4 & 2 & 2 \\ s^3 & 1 & -4 \\ s^2 & 2 & 0 \\ s^1 & -2 & 0 \\ s^0 & -4 & 0 \\ \hline \end{array}$$
If all of the elements in the first column are positive, the system is stable.
The closed loop system is stable since all the elements in the first column have the same sign and are positive. Therefore, the correct option is Yes.
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Ex2. Prime Numbers ( 40 points) You will implement in this exercise an ancient Greek algorithm for finding the prime numbers less than a given number. (ask your instructor about the name of the algorithm after class!) Reminder: A prime number is a positive integer greater than 1 that is divisible only by itself and by 1 . Here is how the algorithm works assuming we would like to find the prime numbers ≪=20 : 1. Initially, assume that all the numbers are prime by marking them with 1 (0 means not prime). 2. For each number that is marked as prime, starting at 2, mark all of its multiples as not prime. which marks all the multiples of num in the array (of size n ) as not prime (excluding num). 2. Write a program that prints the prime numbers κ=150 : a) Create and initialize an array for marking the numbers with 0 (not prime) or 1 (prime). b) For every number 2<=i<150, use function cross_multiples_out to mark all of its multiples as not prime. c) Pass through the array and print the numbers marked as prime.
Previous question
The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.
This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.
It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.
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Each minute, a faucet allows 4/7 gallons of water to enter a large tub, and the drain allows 5/7 gallons to leave the tub.
What is the change in the amount of liquid in the tub after 1/4 minute?
Enter your answer as a fraction in lowest terms in the box.
gal.
Answer: -1/28 gallon
Step-by-step explanation:
divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)
Answer: -1/28 gallon
Step-by-step explanation:
Consider the diagram and the paragraph proof below.
Given: Right △ABC as shown where CD is an altitude of the triangle
Prove: a2 + b2 = c2
Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to point D on side A B to form a right angle. The length of C B is a, the length of A C is b, the length of A B is c, the length of A D is e, the length of D B is f, and the length of C D is h.
Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Which is the last sentence of the proof?
Because f + e = 1, a2 + b2 = c2.
Because f + e = c, a2 + b2 = c2.
Because a2 + b2 = c2, f + e = c.
Because a2 + b2 = c2, f + e = 1
The last sentence of the proof states, "By the Pythagorean theorem, since a squared plus b squared equals c squared, the sum of f and e is equal to c."
The proof establishes the proportions and similarities between the triangles in the diagram. It shows that the ratios of corresponding sides in the similar triangles hold true, leading to the proportions a/c = c/a and b/c = c/e. These proportions can be rearranged to obtain a2 = cf and b2 = ce.
The next step in the proof adds b2 to both sides of the equation a2 = cf, resulting in a2 + b2 = cf + b2. Since b2 = ce, we substitute ce into the equation, giving us a2 + b2 = cf + ce.
The final step applies the converse of the distributive property, which states that if a + b = c, then a(b + d) = ab + ad. In this case, we have a2 + b2 = cf + ce, which can be rewritten as a2 + b2 = c(f + e).
Therefore, the last sentence of the proof concludes that because a2 + b2 = c2 (as derived from the previous steps), it follows that f + e = c. This statement completes the proof and establishes the relationship between the lengths of the sides and the altitude in the right triangle. Option C is correct.
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image.......................
Answer:
10.75
Step-by-step explanation:
The cost of an adult ticket is £6 more than that of a child ticket, so will be shown by c+6.
Now, we are told that the cost of four child tickets and two adult tickets is £40.50, so we can put this in an equation and solve for c:
(c+6)+(c+6)+c+c+c+c=40.50
6c+12=40.50
6c=28.50
c=4.75
so, a childs ticket is 4.75
now to find the cost of an adult ticket you add 6,
4.75 + 6
= 10.75
12. use summation (õ) or product (œ) notation to rewrite the following.(a) 2 4 6 8 ··· 2n.(b) 1 5 9 13 ··· 425.(c) 1 12 13 14 ··· 150 .
Hello! I'm happy to help you with your question. Here's the notation for each sequence:
(a) 2 + 4 + 6 + 8 + ... + 2n can be rewritten as:
∑(2i) where i goes from 1 to n.
(b) 1 + 5 + 9 + 13 + ... + 425 can be rewritten as:
∑(4j-3) where j goes from 1 to 106. (Note: 425 is the 106th term in this sequence)
(c) 1 + 12 + 13 + 14 + ... + 150 can be rewritten as:
1 + ∑(k) ,where k goes from 12 to 150
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Let f be a function defined as fx = 2x + log x over the interval [1, 2]. What conclusion can be made about the value of k such that f (p) = 4?
The value of p is 18.
The value of p must be between 1 and 2
No conclusion can be made about because 1 <2<4
No conclusion can be made about p because fx is not continuous over the interval.
Answer:
It's B...
Step-by-step explanation:
"The value of k must be between 1 and 2" on edge 2023... the problem is the exact same, just this problem was variable p and the one on edge was k
The value of p must be between 1 and 2.
What is Continuous Functions?Continuous functions can be simply defined as a function whose graph does not have a break or jump or an abrupt change, it will goes continuously.
In other words, if all the parameters like right hand limit, left hand limit and value of the function at a definite point 'p' exist and are equal to each other, then the function is continuous.
The given function is f(x) = 2x + ㏒ x
The function is continuous at an interval [1, 2].
f(1) = (2 × 1) + (㏒ 1)
= 2 + 0
= 2
f(2) = (2 × 2) + (㏒ 2)
= 4 + 0.301
= 4.301
So if f(p) = 4, then p must be a value in between (1, 2).
Hence if f(p) = 4, for some value of p, then p must be a point between 1 and 2.
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Please help
FIND THE VALUE OF X
10 Explain why it is less appropriate to express the area of the property cultivated by the agricultural cooperative in m²?
It is less appropriate to express the area of the property cultivated by the agricultural cooperative in m² because this unit of measurement is too small for such a large area.
The area of a property cultivated by an agricultural cooperative is typically very large, often spanning several hectares or even square kilometers. Expressing the area in m² would result in a very large number that is difficult to comprehend and work with. It is more appropriate to use a larger unit of measurement, such as hectares or square kilometers, to express the area of the property cultivated by the agricultural cooperative. This allows for a more concise and understandable representation of the area.
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The point-slope form of the equation of the line that passes through (1,-1) and has a slope of 4
Answer:y = 4x - 5
Step-by-step explanation:
point slope form is in the form of y = mx + b. m is the slope so we plug thatin and have the equation y = 4x + b. since we also have a point on the line we can plug those into the equation too. -1 = 4 * 1 + b.
now we simplify that through algebra.
-1 = 4 + b
b= -5
sp we get b and we can say the equation is y = 4x -5
is n^2 x n^2 equal to (n x n) ^2
How many times larger
is 8 x 10^4 than 8 x 10^1
Answer:
8x10^4=80,000
8x10^1=80
79,920 times larger!
Step-by-step explanation:
Hope that helps! :)
The values 8 * 10^4 is 1000 times larger than 8 * 10^1
Scientific notations are expressions written in the form A * 10^n
Given the following scientifc notations:
A = 8 x 10^4
B = 8 x 10^1
In order to know how many times larger is 8 x 10^4 than 8 x 10^1, we will take the ratio of both values as shown;
Ratio =
\(\frac{A}{B} = \frac{8 \times 10^4}{8 \times 10^1}\\ \frac{A}{B} = 1 \times 10^{4-1} \\ \frac{A}{B} = 10^3\\ \frac{A}{B} = 1000\)
This shows that the values 8 * 10^4 are 1000 times larger than 8 * 10^1
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7, 000 000 000 000 000 000
how do you read this
Answer: Seven trillion i think
Step-by-step explanation:
Grapes cost $2.39 per pound. Bananas cost $0.59 per pound. You have $15 to spend on g pounds of grapes and b pounds of bananas.
Answer:
2.39g + 0.59b = 15
Step-by-step explanation:
Algebraic Expressions
Let:
g = pounds of grapes
b = pounds of bananas
Since grapes cost $2.39 per pound, g pounds of grapes cost 2.39g dollars.
Since bananas cost $0.59 per pound, b pounds of bananas cost 0.59b dollars.
The total cost of fruits is:
C = 2.39g + 0.59b
And this cost is equal to $15:
2.39g + 0.59b = 15
This is the equation that relates the costs of the fruits. If another condition was given, then we could find how many pounds of each fruit is to be purchased.
Supervisor: "your salary is $25,000 and you will be receiving a 2.5% pay increase this year. what will your new salary be?"
In case of a 2.5% increase in your pay which is now $25,000, your new salary will be $25,625.
First, you need to determine the percent increase i.e.2.5% of 25,000 (old salary),
2.5% x 25,000 = ?
2.5/100 x 25,000 = 625
So, the $625 would be the increased amount in your salary which is equal to 2.5% of your old salary (i.e. 25,000).
In order to find out the amount of your new salary that you will be receiving, you have to add the increased amount to the amount of your old salary, as follows:
amount of the new salary = amount of the old salary + percent increase
= $25,000 + $625
= $ 25,625
When an increase of 2.5% is made in your salary which is now $25,000, then your new salary becomes $25,625.
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Find three consecutive even integers such that the sum of twice the first and three times the third is twenty more than four times the
second. What is the SECOND number?
Answer:
18
Step-by-step explanation:
let the consecutive integers be n , n + 2, n + 4 , then
2n + 3(n + 4) = 4(n + 2) + 20 ← distribute parenthesis and simplify both sides
2n + 3n + 12 = 4n + 8 + 20
5n + 12 = 4n + 28 ( subtract 4n from both sides )
n + 12 = 28 ( subtract 12 from both sides )
n = 16
1st number = 16
2nd number = n + 2 = 16 + 2 = 18
3rd number = n + 4 = 16 + 4 = 20
the three consecutive even integers are \(\(16\), \(18\) (16 + 2), and \(20\) (16 + 4)\). The second number in this sequence is 18.
Let's denote the three consecutive even integers as x, x+2, and x+4, where x is the smallest even integer.
According to the given information, we have the following equation based on the problem statement:
\(\[2x + 3(x+4) = 4(x+2) + 20\]\)
Now, let's solve this equation to find the value of x:
\(\[2x + 3x + 12 = 4x + 8 + 20\]\)
Combine the terms on both sides of the equation:
\(\[5x + 12 = 4x + 28\]\)
Subtract 4x from both sides:
\(\[x + 12 = 28\]\)
Subtract 12 from both sides:
x = 16
So, the three consecutive even integers are \(\(16\), \(18\) (16 + 2), and \(20\) (16 + 4).\)
The second number in this sequence is 18.
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Angie has a square dog pen with a perimeter of 20 meters. She wants to put a diagonal piece of fencing inside her pen to cut it in half because her 2 dogs have been fighting. How long of a piece of fencing will she need to buy? Hint: The formula for finding the hypotenuse of a right triangle is: a² + b² = c²
Answer: 7.07 miles
Step-by-step explanation:
Hi, to answer this, first, we have to find the length of the square dog pen.
Perimeter of a square = 4 x sides
Replacing with the value given:
20 = 4 s
Solving for s:
20/4=s
Side = 5 meters
Since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case length of the diagonal) and a and b are the other sides.
Replacing with the values given:
c^2 = 5^2 + 5^2
c^2 = 25+25
c^2 = 50
c = √50
c = 7.07 miles
Feel free to ask for more if needed or if you did not understand something.
(2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i)
Answer:
50+50iStep-by-step explanation:
Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.
Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)
On expansion
(3 - i)(3 + i)
= 9+3i-3i-i²
= 9-(-1)
= 9+1
(3 - i)(3 + i) = 10
For the expression (2 + i)(1 - i), we have;
(2 + i)(1 - i)
= 2-2i+i-i²
= 2-i+1
= 3-i
Multiplying 3-i with the last expression (1 + 2i)
(2 + i)(1 - i)(1 + 2i)
= (3-i)(1+2i)
= 3+6i-i-2i²
= 3+5i-2(-1)
= 3+5i+2
= 5+5i
Finally, [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]
= 10(5+5i)
= 50+50i
Hence, (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i
Which system of equations is represented by the graph ?
A. y=x^2+2x+1
2x+y=2
B. y=x^2-2x+1
2x+y=2
C. y=x^2+2x+1
2x+y=2
D. y=x^2-2x+1
2x-y=2
option D, y=x^2-2x+1 , 2x-y=2 represents system of equations .
Given:
points (1,0) and (3,4)
line equation is y - y1 = m(x-x1)
y - 0 = 4-0/3-1(x - 1)
y = 2(x-1)
y = 2x - 2
2x - y =2.
The vertex of the given upward parabola is in the first quadrant so the coefficient of \(x^{2}\) must have positive values.
so y = \(x^{2} -2x+1\)
Therefore option D y=x^2-2x+1 , 2x-y=2 is correct.
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T(x,y)=38xy−24x^3−19y^2 on the closed square region 0≤x≤1,0≤y≤1 Absolute maximum value is , attained at (x,y)=?
The absolute maximum value is 0, attained at (x, y) = (0, 0).
To find the absolute maximum value of the function
T(x, y) = 38xy - 24x^3 - 19y^2 on the closed square region 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, we need to evaluate the function at the critical points and the endpoints of the region and compare the values.
First, let's find the critical points by taking the partial derivatives of T(x, y) with respect to x and y and setting them equal to zero:
∂T/∂x = 38y - 72x^2 = 0
∂T/∂y = 38x - 38y = 0
Solving these equations, we find two critical points: (x, y) = (0, 0) and (x, y) = (1, 1).
Next, let's evaluate the function at the endpoints of the region:
T(0, 0) = 0
T(1, 0) = -24
T(0, 1) = -19
T(1, 1) = -5
Comparing these values, we can see that the absolute maximum value of T(x, y) is 0, which is attained at (x, y) = (0, 0).
Therefore, the absolute maximum value is 0, attained at (x, y) = (0, 0).
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Please help me
Are these similar and how?
ifferentiate the following functions:
(a) f(x)=6x3+2x2−x+12 (4 Pts) (b) f(x)=4x (4 Pts) (c) f(x)=e−x(x−2) (4 Pts)
(d) f(x)4x3/(2x2−x) (4 Pts)
(e) f(x)=ln(x−3) (4 Pts)
Answer. I think is A
Step-by-step explanation:
Let U = {(x, y, z) € R^3 | x + 2y – 3z =0}. a) (2pt) Show directly (by verifying the conditions for a subspace) that U is a subspace of R^3. You may not invoke results learned in class or from the notes. b) (2pts) Find a basis for U. You must explain your method. c) (1pt) Using your answer from part b) determine Dim(U).
a) U is subspace of R^3.
b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.
c) 2.
a) To show that U is a subspace of R^3, we need to verify the following three conditions:
i) The zero vector (0, 0, 0) is in U.
ii) U is closed under addition.
iii) U is closed under scalar multiplication.
i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.
ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:
x1 + 2y1 - 3z1 = 0 (by definition of U)
x2 + 2y2 - 3z2 = 0 (by definition of U)
Adding these two equations, we get:
(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0
which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.
iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:
x + 2y - 3z = 0 (by definition of U)
Multiplying both sides of this equation by c, we get:
cx + 2cy - 3cz = 0
which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.
Since U satisfies all three conditions, it is a subspace of R^3.
b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:
x = 3z - 2y
y = (x - 3z)/2
Substituting z = t into these equations, we get:
x = 3t - 2y
y = (x - 3t)/2
Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:
(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)
Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.
c) Since the basis for U has two elements, the dimension of U is 2.
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Since
∠
AOB
is a right angle, it is
90
∘
.
∠
AOB
is supplementary to
∠
BOC
, so
m
∠
AOB
+
m
∠
BOC
=
180
∘
. By the substitution property of equality,
90
∘
+
m
∠
BOC
=
180
∘
. Applying the subtraction property of equality,
m
∠
BOC
=
90
∘
.
What statement is missing from the proof?
A.
∠
AOB
and
∠
BOC
form a linear pair.
B.
∠
AOB
and
∠
DOC
are vertical angles.
C.
∠
COD
and
∠
AOD
form a linear pair.
D.
∠
DOA
and
∠
BOC
are vertical angles.
The missing piece of information in the proof is that m ∠ DOA and m ∠ BOC are vertical opposite angles.
What is meant by subtraction property of equality?According to the equality's subtraction property, equality is unaffected by removing the same amount from both sides of an equation. When the same quantity or value is removed from both sides of an equation, the resultant difference is also identical on both sides.
Both the equality's addition and subtraction properties are related. The same integer added to or subtracted from both sides of an equation maintains equality on both sides.
To prove that m ∠ BOC = 90°.
Given that m ∠ AOB exists a right angle triangle.
Therefore; m ∠ BOC must also be equivalent to 90°.
Since m ∠ BOC and m ∠ AOB are right angles, it follows that m ∠ DOA and m ∠ BOC are also vertical opposing angles and, as such, are equal.
So, the fact that m ∠ DOA and m ∠ BOC are vertical opposing angles is the crucial piece of information missing from the proof.
The complete question is:
Given: AOB is a right angle
Prove: m BOC = 90°
Since AOB is a right angle, it is 90°. AOB is supplementary to BOC,
so m AOB + m BOC = 180°. By the substitution property of equality,
90 + m BOC = 180°. Applying the subtraction property of equality,
m BOC = 90%. What statement is missing from the proof?
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Help please 43 points
Answer:
Get the data from the table:
40, 45, 50, 55, 75, 80, 85Median is the middle number:
55Mean is the average:
(40+ 45+ 50+ 55+ 75+ 80+ 85)/7 = 61.42Rachel and Sarah spent:
80 + 85 = 165Rabbit Population The rabbit population in a certain area is 200% of last year's population. There
are 700 rabbits this year. How many were there last year?
There were rabbits last year.
♡
Answer:
Kinda confusing, (probably just me) but I think it may be 1,400 rabbits last year.
Melissa built a square pyramid out of sand. The base of the pyramid has a side length of 18 centimeters. The height of the pyramid is 26
centimeters.
What is the volume of the pyramid?
A. 624 cm3
B. 1,872 cm
C. 2, 808 cm
D. 4,212 cm
E. 8, 424 cm
Answer:
C. 2, 808 cm^3
Step-by-step explanation:
Given that
The base of the pyramid is 18 centimeters
And, the height of the pyramid is 26 centimeters
We need to find out the volume of the pyramid
As we know that
The volume of the pyramid is
= 1 ÷ 3 × base^2 × height
= 1 ÷3 × 18^2 × 26
= 2,808 centimeter^3
Hence, the correct option is c.
Ball 1 is launched with an initial vertical velocity v
1
=145ft/sec. Ball 2 is launched 2.7 seconds later with an initial vertical velocity v
2
. Determine v
2
if the balls are to collide at an altitude of 257ft. At the instant of collision, is ball 1 ascending or descending?
The initial velocity of Ball 2 is 158.69 feet/sec.
Take downside is positive so here θ is negative here.
Initial velocity of Ball 1 is = v₁ = 145 ft./sec = 44.196 m/sec
The balls are to collide at an altitude of 257 ft that is,
H = 257 feet = 78.3336 m
Using Equation of Motion we get,
v² = u² + 2as
Now here v₀ is the final velocity of the Ball 1
u = v₁ = 44.196 m/sec
a = g = 9.8 m/s²
s = H = 78.3336 m
So,
v₀² = v₁² + 2gH
v₀² = (44.196)² + 2 (9.8) (78.3336)
v₀² = 3488.625
v₀ = √3488.625
v₀ = ± 59.06 m/s
Now calculating time for each velocity using equation of motion we get,
v₀ = v₁ + gt
t = (v₀ - v₁)/g
t = (59.06 - 44.196)/(-9.8)
t = - 1.51 second
Time cannot be negative so t = 1.51 second.
When v₀ = - 59.06 m/s
v₀ = v₁ + gt
t = (v₀ - v₁)/g
t = (-59.06 - 44.196)/(-9.8)
t = 10.53 second
Since the second ball throws after 2.7 seconds of ball 1 so we can avoid the case of t = 1.51 second.
So at the time of collision the velocity of ball 1 is decreasing.
Time of fling of ball 2 is given by
= t - Initial time after ball 2 launched
= 10.53 - 2.7
= 7.83 seconds
Height travelled by Ball 2 is, H = 257 feet = 78.3336 m.
Now we need to find the initial velocity of Ball 2 using equation of motion,
S = ut + 1/2 at²
H = v₂t - 1/2 gt² [Since downside is positive so g is negative]
v₂ = H/t + (1/2) gt
Substituting the values H = 78.3336 m; t = 7.83 seconds; g = 9.8 m/s²
v₂ = 48.37 m/s = 158.69 feet/sec.
Hence the initial velocity of Ball 2 is 158.69 feet/sec.
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