Answer:
Step-by-step explanation:
On this page, an interesting example is presented that allows the student to obtain expressions for a general case after examining the first two or three situations. It is an exercise in geometric progressions, a common topic in elementary-level Mathematics courses.
Bounces in the horizontal plane
Balon7.gif (2174 bytes)
When a ball bounces off a rigid board, the component of the velocity perpendicular to the board decreases in value, leaving the parallel component unchanged
v x = u x
v y = -e u y
Heights of successive bounces
Suppose a ball is dropped from an initial height h . We are going to calculate the heights of the successive bounces.
1.-First bounce
The velocity of the ball before it hits the ground is calculated by applying the principle of conservation of energy
The velocity of the ball after the collision is (in modulus) v 1 = e u 1
The ball ascends with an initial velocity v 1 , and reaches a maximum height h 1 which is calculated by applying the principle of conservation of energy
2.-Second bounce
The velocity of the ball before it hits the ground is calculated by applying the principle of conservation of energy
The velocity of the ball after the collision is v 2 = e u 2
The ball ascends with an initial velocity v 2 , and reaches a maximum height h 2 which is calculated by applying the principle of conservation of energy
3.-Bounce n
After collision n , the maximum height the ball reaches is
h n = e 2n h
Loss of energy experienced by the ball
In the first collision, the ball loses an energy
In the second collision, the ball loses an energy
In the collision n the ball loses an energy
The sum of Δ E 1 + Δ E 2 + Δ E 3 +…. Δ E n is the energy lost by the ball after n collisions. After infinite collisions the ball will have lost all its initial energy mgh . We are going to check it by adding the infinite terms of a geometric progression of ratio e 2 and whose first term is Δ E 1
Time it takes for the ball to stop.
The time it takes for the ball to reach the ground when dropped from a height h from rest is
The ball bounces and rises to a height h 1 , then falls back to the ground. The time it takes to go up and down is
The ball bounces and rises to a height h 2 , and then falls back to the ground. The time it takes to go up and down is
The total time after infinite bounces is the sum of t 0 and the terms of a geometric progression whose first term is 2 t 0 e and whose ratio is e.
If the ball is given a horizontal initial velocity v x . After infinite bounces, it moves a horiz
You have three pieces of ribbon measuring 16 cm, 24 cm, and 40 cm respectively. You want to cut them into strips of the same length. What is the longest possible length of one strip?
Answer:8
Step-by-step explanation:
(16---->1,2,4,(8),16
24----->1,2,3,4,6,(8),12,24
40----->1,2,4,5,(8),10,20,40
Because 8 is the largest common divisor
A television set is 36 inches wide and has a diagonal length of 42 inches. To the nearest inch, how tall is the set?
9
13
22
55
Jayden needs at least 3 cups of vegetable oil to make chow menu. If Jayden has 20 fluid ounces of vegetable oil , and there are 8 fluid ounces in 1 cup will he be able to make chow mein . Yes or no
Answer: No
Step-by-step explanation:
He need 3 cups which is converted into 24 ounces. There is 8 ounces in a cup and he has three. He has 20 ounces and he needs 24.
A deep sea diver dives 26 feet from the surface of the ocean. He then ascends 7 feet. What interger represents the divers present location in the sea?
Answer:
-19
Step-by-step explanation:
Previous position in sea + change in position= current position
-26+7= -19
Hope this helps! :)
Answer:
It is -19
Step-by-step explanation:
Well, you would do this -26 + 7 because the diver dove 26 feet BELOW sea level, which is also -26. He then ascends 7 feet, which means he is coming UP. So -26 + 7 = -19.
Simplify Forty eight fourths 48/4
Step-by-step explanation:
48 divided by 4, is 12
or 12/1
Please help me understand
Answer:
C. $30Step-by-step explanation:
According to the first part of the equation, hourly pay is $25, up to 38 hours.
Overtime is paid over 38 hours.
Find the hourly pay for overtime, taking x = 39 and finding the difference with the total at x = 39 and x = 38, then we have the payment for one hour.
30(39 - 38) + 950 - 38*25 = 30 + 950 - 950 = 30Correct choice is C
The sum of 3 times a number and -2, added to 5 times the number
Answer:
3x + (5x -2)
Step-by-step explanation:
X is any number so 3 times a number is 3x. -2 plus 5 times a number is the same as 5 times a number minus 2. And the sum would be 3x + (5x - 2)
Katy is older than Alex and Beth. Sarn is
younger than Alex and older than Beth.
Delores is older than Sam but younger than
Katy. Delores is Alex's older sister. If the
ages of these students are 14, 15, 16, 17,
and 18, who is 16 years old?
Oliver drove the first 90 miles of his journey in 1.5 hours and the remaining 120 in 3 hours. What was the average speed on the second part of Oliver’s journey?
Answer:
Step-by-step explanation:
90 miles + 120 miles = 210 total miles
1.5 hours + 3 hours = 4.5 total hours.
Average speed = 210 miles / 4.5 hours = 46 2/3 miles per hour
Answer:
40
Step-by-step explanation:
I know meth
Given N1 = 6 and Nn+1 = 6(Nn - 4) ). Find N3.
Answer:
48
Step-by-step explanation:
N₁ = 6
N(n+1) = 6*(Nn -4 )
N₍₁₊₁₎= 6* (N₁ - 4)
N₂ = 6 *(6-4) = 6*2
N₂ = 12
N₍₂₊₁₎ = 6*(N₂ - 4)
N₃ = 6*(12 -4) = 6* 8
N₃ = 48
Solve for x.
(5x - 9)°
(2x + 21)°
A. 5
B. 10
C. 22
D. 24
Answer:
D. 24
Step-by-step explanation:
5x - 9 + 2x + 21 = 180
7x + 12 = 180
7x = 168
x = 24
Suppose a supplier estimate that a new products will generate the following revenue stream. period. revenue year 0= 0 year 1=$62500 year 2 =$89 400 year 3=$ 136 200 year4 =$ 128300 year5=$ 112000 If the required rate of return is 11%, determine the value of all these cash flows at year 2.
Answer:
9834
Step-by-step explanation:
11*100*89400.
URGENT HELP PLEASEE SBDHHDS
Answer:
17800
Step-by-step explanation:
a= (t-g)/-0.0035
(-32.3-30)/-0.0035 = 17800
Can someone help me and explain me how you do this and not only give me the answer?
Answer:
just add the terms -154+8850= 8696 m
A soda company had sales of 35,107 million in 2010 and $45,99 million in 2014. Use the Midpoint Formula to estimate the sales in 2012. that the sales followed a linear pattern
Answer:
40,550
Step-by-step explanation:
That is the mid point
I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!
Answer:
Infinitely many solutions
Step-by-step explanation:
6x+18=2(3x+9)
6x+18=6x+18
Since both sides are equal to each other, then there are infinitely many solutions because no matter what x is, both sides will be equal to each other.
Answer:
infinite many solutions, (C)
Step-by-step explanation:
Once you distribute you get 6x+18 on both sides. Meaning that the answer is this has infinite many solutions.
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Find the equation of the tangent line to the curve y=x sqrtx at point (4,8)
Y=?
Answer: I think y is 32 im not good at this tho
Step-by-step explanation:
Evaluate each function for the given input values. For f (x)=2/3x+ 3, find f (x) when x= 9 and when x=-3
Answer:
Step-by-step explanation:
f(x) = 2/3 x + 3
x = 9
f(9) = 2/3 * 9 + 3 Divide 9 by 3
f(9) = 2 * 3 + 3 Combine 2 * 3
f(9) = 6 + 3 Combine
f(9) = 9 The answer is just a coincidence. The answer for the next one shouldn't be - 3
f(-3) = 2/3 *(-3) + 3 Divide 3 into - 3
f(-3) = 2*(-1) + 3
f(-3) = -2 + 3
f(-3) = 1
How was this done?
You should observe that whatever value you see on the left in the brackets, appears where the x is on the right. This is a very important concept. You should do your best to understand it because algebra is sort of based on it.
The path of a skateboarder can be modeled by the equation (x – 3)2 = –4(y – 9), where distance is in feet and air resistance is insignificant. If the skateboarder makes a jump from a ramp at x = 0, what is her maximum height and how far is she horizontally from the end of the ramp when she lands?
Answer:
The correct answer would be: "Maximum height 9 feet; horizontal distance 9 feet".
Step-by-step explanation:
I know this not only because I already took the test, BUT by graphing the equation (you can use graphing apps) it'll give you the answer.
Her maximum height is 9 feet & she is horizontally 9 feet from the end of the ramp when she lands.
What is skateboarders maximum height ?
The path of the skateboarder can be modelled by the equation,
(x-3)² = -4(y-9)
Now, from the equation, solving y,
(x-3)² = -4(y-9)
⇒ y-9 = -[tex]\frac{1}{4}[/tex](x-3)²
⇒ y = -[tex]\frac{1}{4}[/tex](x-3)² + 9
∴ Maximum height is 9 feet.
How far is she horizontally from end of ramp ?We have to take y = 0,
Now, -[tex]\frac{1}{4}[/tex](x-3)² + 9 = 0
⇒ -(x²-6x+9)+36 = 0
⇒ -x²+6x-9+36 = 0
⇒ x²-6x-27 = 0
⇒ x²-9x+3x-27 = 0
⇒ (x-9)(x+3) = 0
⇒ x = 9 or x = -3
Neglecting the negative value we get, x = 9
So, Her horizontal distance from end of the ramp is 9 feet.
Learn more about quadratic problems here :
https://brainly.com/question/16073165
#SPJ2
A street sign is in the shape of an isosceles triangle that has a base of 6.5 inches bigger than either of the equal sides. If the perimeter of the triangle is 65 inches, what is the length of the equal sides?
Answer:
19.5
Step-by-step explanation:
side is 6.5 bigger, so minus the 6.5 from the total perimeter of 65 and divide by 3.
65- 6.5 = 58.5
58.5 ÷ 3 = 19.5
equal sides are 19.5
longer side is 19.5 + 6.5
Answer:
19.5 inches
Step-by-step explanation:
You can interpret this problem as x + x + (x + 6.5)=65, with x being the length of the equal sides.
Simplified, this equation becomes 3x+6.5=65.
Solving, this becomes 3x+6.5-6.5=65-6.5 which comes out as 3x=58.5. Next, we divide this equation by 3 on both sides, which then comes out to x=19.5. Therefore, the length of equal sides are 19.5.
Check: There are two equal sides, so 19.5+19.5. Since the base is 6.5 inches bigger than either of the equal sides, the base is equal to 19.5+6.5=26. Adding these values all together comes out to 19.5+19.5+26=65.
Help pls? Thank you! I suck at time......
Answer:
20 minutes after 3:00
Step-by-step explanation:
Answer:
The answer would be 20 minutes after 3:00
What is 1/3 - 1/7 = ?
Answer:
[tex]\frac{4}{21}[/tex]
Step-by-step explanation:
In order to find the answer you need to find the common denominator of the two fractions multiply the fractions to receive that common denominator and then subtract to find your answer.
[tex]\frac{1}{3} -\frac{1}{7}[/tex]
Find the common denominator:
[tex]CD=21[/tex]
[tex]1\times7=7[/tex]
[tex]3\times7=21[/tex]
[tex]=\frac{7}{21}[/tex]
[tex]1\times3=3[/tex]
[tex]7\times3=21[/tex]
[tex]=\frac{3}{21}[/tex]
[tex]\frac{7}{21} -\frac{3}{21}[/tex]
Subtract numerators
[tex]7-3=4[/tex]
[tex]=\frac{4}{21}[/tex]
Hope this helps.
convert 0.10606060606......... to a fraction
Answer:
7/66
Step-by-step explanation:
On a trip, a student drove 42 miles per hour for 3 hours and then drove 26 miles per hour for 5 hours. What is the student’s average rate of speed, in miles per hour, for the whole trip? *
1. 126 MPH
2. 32 MPH
3. 130 MPH
4. 8.5 MPH
Answer:
34 mph
Step-by-step explanation:
Average speed = total distance / total time
Total distance = ( 40 × 2 + 30 × 3 )
= 170 miles
Total time = 5 h
So, avg speed = 170/5 = 34 mph
what's the answer for this?
9514 1404 393
Answer:
x = (y +2)/3
Step-by-step explanation:
The flowchart is trying to help you see that you "undo" what is done to x, in reverse order.
x is first multiplied by 3, then -2 is added.
First, we want to undo the addition of -2, so we add the opposite of that to y:
y = 3x -2 ⇒ y +2 = 3x
Then we want to undo the multiplication by 3, so we divide by 3:
y +2 = 3x ⇒ (y +2)/3 = x
The solution for x is ...
x = (y +2)/3
_____
Additional comment
In your diagram, each box has the inverse operation of the one in the box above it. The inverse of subtracting 2 is adding 2. The inverse of multiplying by 3 is dividing by 3. The arrows connecting the boxes are intended to show you that these inverse operations occur in the reverse order of the original operations, as we described above. (The small box at bottom center might contain "3x".)
100 POINTS!!! & Brainliest
A cat weighing 12.1lb needs insulin at 2.0 international units (IU)/kg. The insulin comes in a concentration of 10 IU/mL. How much insulin do you give the cat? Please show work!
Answer:
[tex]1 \: lb = 0.453 \: kg \: \\ first \: lb \: convert \: to \: kg \\ cat \: weight \: 12.1 \times 0.453 = 5.4813 \: kg \\ how \: much \: iu \: isulincat \: need \\ we \: must \: multiply\: the \: weight \: of \:cat \: to \: 2 \\ \\ 5.4813 \times 2 = 10.9626 \: iu[/tex]
good luck
carry out the following subracting involving rational number 13/36-2/40
Answer:
14/45
Explanation:
Make the denominator of both fractions the same
13/36=130/360
2/40=18/360
130/360-18/360=112/360
112/360=14/45
What is the value of v?
4/5 is a fraction
4/5 (v−7)=2
Answer:
v = 9.5
Step-by-step explanation:
[tex] \\ \tt \frac{4}{5} (v - 7) = 2[/tex]
[tex] \\ \tt \mapsto \frac{4(v - 7)}{5} = 2[/tex]
[tex] \\ \tt\mapsto \frac{4v - 28}{5} = 2[/tex]
[tex] \\ \tt \mapsto4v - 28 = 2 \times 5[/tex]
[tex] \\ \tt \mapsto4v - 28 = 10[/tex]
[tex] \\ \tt \mapsto4v = 10 + 28[/tex]
[tex] \\ \tt \mapsto \: v = \frac{38}{4} [/tex]
[tex] \\ \tt \mapsto \: v = 9\frac{2}{4} \: or \: 9.5 [/tex]
When simplified what is the answers?
Answer:
-1
Step-by-step explanation:
1. To simplify this expression, let's go through the orders of operations:
|2 - 5| - (12 ÷ 4 - 1)^2|-3| - (12 ÷ 4 - 1)^23 - (12 ÷ 4 - 1)^23 - (3 - 1)^23 - (2)^23 - 4-1Therefore, the answer is -1.
Triangle A, B, C, is shown. Angle C, A, B is 70 degrees. Angle A, B, C is 70 degrees.
Find the missing angle A C B
Answer:
40°
Step-by-step explanation:
<CAB=70°
<ABC=70°
<ACB+ <CAB+ <ABC=180(sum of angles in a triangle)
<ACB +70+70=180
<ACB+140=180
<ACB=180-140
<ACB=40°