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1.The man in the figure at left has a mass of 50 kg, and launches horizontally from a trapeze at ...

m/s. After landing on the trampoline, which has a “spring” constant of 17 kN/m, the trampoline deflects downward 0.7 m, and the man bounces up and to the left.
a) How much farther to the left does he travel after bouncing off the trampoline?
b) What is the maximum height he will reach after the bounce?
c) What will his velocity be upon landing?

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2.The question is "A dog is looking at the top of a steeple that is sitting on top of a ...

ight of the church, not including the steeple is 20 feet. The line of sight between the dog and the top of the steeple is 29 feet. What is the height of the steeple? Round your answer to the nearest tenth

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3.A skier starts from rest at the top of a hill. The skier coasts down the hill and up a ...

as the drawing illustrates. The crest of the second hill is circular, with a radius of 28.6m. Neglect friction and air resistance. What must be the height of the first hill so that the skier just loses contact with the snow at the crest of the second hill?

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4.Q1) (15 points) In the diagram below, M1 = 50 Kg, M2 = 20 Kg, mass and radius of the ...

g and 30 cm each, respectively. Both M1 and M2 rest on frictionless surfaces and the system starts from rest.
(a) Draw the fbd for each of M1, M2 and the pulley.
(b) Write the equations of motion for each of M1, M2 and the pulley.
(c) Calculate the linear acceleration of the two masses, as well as the angular acceleration of the pulley.
(d) Calculate the angular velocity of the pulley after M1 and M2 have been displaced linearly by 2 m.
Q2) (10 points) A basketball is thrown with an initial speed v0 of 10.8 m/s at 400 above horizontal, and it enters the hoop from above. The ball is released at 2.00 m above the ground. The hoop is 3.05 m above the ground and 10.0 m away from the player.
(a) Find the time at which the ball passes through the hoop.
(b) Find the ball’s velocity (express in component form) just when it enters the hoop.
(c) Find the ball’s maximum height.
Q3) (5 Points) An object is thrown up from the top of a building of height of 400 m with an initial velocity of 20 m/s.
(a) Find the position and the velocity of the object 5 s later.
(b) With what velocity will it hit the ground?
(c) At the same time the first object is thrown up, a second object is thrown up from the ground at 100 m/s. Will the two objects collide? If yes, calculate when and where,

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5.A rock is thrown from a cliff. Its path may be modeled by the function h(t) = -2t^2 +6t ...

is measured in seconds and height is measured in metres. Answer each of the following algebraically.
at what time does the rock hit the ground?
for what length of time is the rock above a height of 8 metres?

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6.A force of 40.0 N is needed to compress a spring 0.200 m. A 1.00 x 10-2 kg ball ...

ring.
a) Calculate the work done to compress the spring. (2 marks)
b) What happens to the work done on the spring ? (1 mark)
c) If the spring is released, what happens to the energy of the spring? (1 mark)
d) Calculate the total mechanical energy of the ball at the instant it leaves the spring. (2 marks)
e) What will be the speed of the ball at the instant it leaves the spring? (2 marks)
f) If the ball is fired up into the air by the spring, how much gravitational potential energy will it gain? (1 mark)
g) What will be the maximum height of the ball? (2 marks

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20 s to fall past your window. The window is 1.6 m tall. From what height above the top of the win-
dow was the hammer dropped by the worker?

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8.The mean height of all the elderly women in a city is 160 cm and the variance of their heights ...

cm2. If a sample of 60 elderly women is taken, what is the probability that their mean height will be less than 158 cm?

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9.I am trying to figure out the optimal radius that will give the lowest surface area of a cylinder. I ...

have done the calculus which reveals that the surface area is at a minimum when height is double the radius. I am now trying to find an equation for the relationship between the amount of wasted surface area as a percentage of the minimum surface area and the ratio between height and radius.
If I were to plot it on a graph, the y axis would be the percentage of excess materials needed as a percentage of the minimum possible surface area, and the x axis would be height divided by radius. Since the surface area is minimized when height=2(radius), I know that when x=2, y=0.
The website https://www.datagenetics.com/blog/august12014/index.html explains what I am trying to do quite well and shows the graph below. I am trying to find the equation for this graph, but am unsure how to go about it.

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lly a math problem I gotta solve, and I have no idea how to do it cause of lack of my math skills. I am hoping someone can help me with this or I'm screwed.
Co basically I've got this table in excel, where X (row) is a width and Y is a height (column) of a wooden sauna cabin, the X;Y is the price for a sauna with said dimensions. I need to find a relationship between the size of the sauna and the price And formulate ani equation. I can't seem to find it, the price seems to grow non linearly, I can't seem to find any coeficient. Again, I suck at math, maybe solution is simple, but I just don't see it. Can anyone help me please?
Table Is at this link https://ibb.co/fGrxSvf . Thanks for any help!

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height in thousands of feet and t is time in minutes. Answer the questions below and express your reasoning to the right.
a.At what time is the rocket launched?

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nd standard deviation 6 inches.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the probability that an 18-year-old man selected at random is between 64 and 66 inches tall? (Round your answer to four decimal places.)
Correct: Your answer is correct.
(b) If a random sample of seven 18-year-old men is selected, what is the probability that the mean height x is between 64 and 66 inches? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
The probability in part (b) is much higher because the mean is smaller for the x distribution.
The probability in part (b) is much higher because the mean is larger for the x distribution.
The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

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bottom of the roof lie on the x-axis. The equation of the function describing the cross-section is h(x)=-|6x|+7, where h is the height of the roof, in metres, and x is the horizontal distance from the centre of the roof, in metres. To the nearest tenth of a metre, what is the width of the bottom of the roof?

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s 1600 cubic inches. The height of the box is 8 inches and the length of the box is 2 times longer than the width of the box. What is the width of the box?

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15.A sphere of mass M = 20kg and radius R = 10cm has its mass distributed in a way where ...

mediately guess it’s moment of inertia. To investigate whether it behaves more like a solid sphere or hollow sphere, you roll it down a rough ramp inclined at an angle of 30° with respect to the horizontal. The sphere rolls without slipping and you measure the velocity of the center of mass to be 3 m/s as it leaves the bottom of the ramp. The ramp’s length is 2 m and you release the sphere from the top of the ramp, a height of 1 m.
a) What is the moment of inertia of the sphere?
b) What is the angular speed of the sphere as it reaches the bottom of the ramp?
c) What is the frictional force on the sphere?

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16.A ball is thrown straight up from a rooftop 93 feet high with an initial velocity of 64 feet per ...

ond. The function s(t)=-16t^2 +64t +93 describes the ball's height above the ground, s(t), in feet, t seconds after it is thrown. The ball misses the rooftop on its way down and eventually strikes the ground. What is its instantaneous velocity as it passes the rooftop on the way down?

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17.The angle of depression from the top of a lighthouse to a raft on the water is 33o. The angle ...

evation from a seagull on the water to the top of the lighthouse is 38o. If the distance between
the seagull and the raft is 7m, then what is the height of the lighthouse? Use the sine law to answer
the problem.

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rts to the fireworks platforms: one part is on the ground and the
other part is on top of a building. You are going to graph all of your results on one
coordinate plane. Make sure to label each graph with its equation. Use the following
equations to assist with this assignment.
• The function for objects dropped from a height where t is the time in
seconds, h is the height in feet at time it t, and 0 h is the initial height is
2
0 ht t h ( ) 16 =− + .
• The function for objects that are launched where t is the time in seconds, h is
the height in feet at time t, 0 h is the initial height, and 0 v is the initial velocity
in feet per second is 2
0 0 ht t vt h ( ) 16 =− + + .
Select the link below to access centimeter grid paper for your portfolio.
Centimeter Grid Paper
Task 1
First, conduct some research to help you with later portions of this portfolio
assessment.
• Find a local building and estimate its height. How tall do you think the
building is?
• Use the Internet to find some initial velocities for different types of fireworks.
What are some of the initial velocities that you found?
Task 2
Respond to the following items.
1. While setting up a fireworks display, you have a tool at the top of the
building and need to drop it to a coworker below.
a. How long will it take the tool to fall to the ground? (Hint: use the first
equation that you were given above, 2
0 ht t h ( ) 16 =− + . For the building’s
height, use the height of the building that you estimated in Task 1.)
b. Draw a graph that represents the path of this tool falling to the
ground. Be sure to label your axes with a title and a scale. Your graph
should show the height of the tool, h, after t seconds have passed.
Label this line “Tool”.

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19.1. A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. ...

ance is negligible, what is the ball’s speed at the instant it reaches its maximum height from the ground?
A. - 20 m/s
B. 0 m/s
C. + 17.3 m/s
D. + 10 m/s
E. + 20 m/s
2. A rhino charges full speed at a car with an initial velocity of 15 m/s. When the rhino collides with the car, it crumples in by 1 m before the rhino comes to a complete stop. What acceleration did the rhino feel as it came to a stop?
A. - 112.5 m/s^2
B. - 7.5 m/s^2
C. - 30 m/s^2
D. + 112.5 m/s^2
E. + 30 m/s^2
F. + 7.5 m/s^2
3. Two students want to determine the speed at which a ball is released when thrown vertically upward into the air. One student throws the ball into the air while the other student measures the total time that the ball is in the air. The students use a meterstick to measure the release height of the ball. Which of the following equations should the students use to determine the speed at which the ball was released? *
A. Use y final = y initial+ v initial *t + (1/2)*a*t^2 from the moment in time in which the ball was released to the moment in time in which the ball reaches its highest point.
B. v final^2 = v initial ^2 + 2a(????y) from the moment in time in which the ball was released to the moment in time in which the ball hits the ground.
C. Use y final = y initial+ v initial *t + (1/2)*a*t^2 from the moment in time in which the ball was released to the moment in time in which the ball hits the ground.
D. v final^2 = v initial ^2 + 2a(????y) from the moment in time in which the ball was released to the moment in time in which the ball reaches its highest point.

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20.If a ball is thrown straight up into the air with an initial velocity of 75 ft/s, it’s height in ...

eet after t seconds is given by y=75t-16t^2. Find the average velocity for the time period beginning when t = 2 and lasting.
1) 0.1 seconds
2) 0.01 seconds
3) 0.001 seconds
Finally based on the above results, guess what the instantaneous velocity of the ball is when t=2.

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21.An object is dropped from 99 meters above the ground. What is the object's height after 3 seconds?

n, y = 0.2x2 – 0.4x – 0.6, where x and y are measured in metres.
a) Find the x intercepts
b) Find the vertex.
c) What is the minimum height of the hammock?

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is the time in seconds, and h(t) is the height of the ball
a. How long does it takes for the golf ball to be 30 feet above ground?
b. How long does it take for the golf ball to hit the ground after it has been hit by Jennifer?
c. What is the golf ball's height 4 seconds after it was hit?

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is launched from a height of 6 feet with an initial upward velocity of 64 feet per second. The T-shirt is caught 41 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?

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27.The volume of a cylinder with height h and radius r can be found using the formula V = π ...

Suppose the volume of a cylinder is 402.12 ft3 and the height is twice the radius what is the radius of the cylinder. Determine the radius, rounded to the nearest whole foot.
The radius is____ ft?

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28.An object is launched upward at 64 ft/sec from a platform that is 80 feet high. What is the objects ...

maximum height if the equation of height (h) in terms of time (t) of the object is given by h(t) = -16t^2+ 64t + 80?

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29.An object is launched upward at 64 ft/sec from a platform that is 80 feet high. What is the objects ...

maximum height if the equation of height (h) in terms of time (t) of the object is given by h(t) = -16t^2 + 64t + 80?

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30.A quarterback throws a football. The height, h metres, of the ball is given by the equation h = −5t2 ...

t2 + 20t +2 where t is the time in seconds after the ball is thrown.
a) Graph the equation using desmos (if you can take a screen shot of it and include it)
b) Why do we use only positive values of h and t?
c) What is the height of the ball 1 second after it is thrown?
d) What is the maximum height of the ball?
e) How long does it take for the ball to reach the maximum height?
f) For how long is the ball more than 10 m above the ground?

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a tilebased game,
2D rectangle tiles with a size of 5000X5000 pixels per rectangle.
I make every rectangle know the 4 neighbouring rectangles in the map so starting from one you can generate an essentially infinite map.
I want to move this map around instead of moving the player around, the player stays centered on screen and since the map moves under him it looks like he's the one doing the moving.
So I know the following things:
Width and height of a single section:
5000X5000 pixels
the x and y location of the center section can be a value anywhere from -5000,-5000 to 5000,5000
The visible screen real estate is 1920 X 1080 pixels big
0X,0Y always stars top left, bottom right is 5000X5000
What I need to end up with:
A percentage value of howmuch this specific section is visible on screen, "inside the rectangle that is the scfeen)

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32.What is the height of a triangle whose area is 4 square meters and whose base is 2 1/2 meters long?

d 5 cm wide. The area of the rectangle is 15cm squared. What is the height of the rectangle?
The second question is on another rectangle, the height is a and the width is 3a. The perimeter is 24cm. What is the length of the shortest side.
PLEASE HELP

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34.2. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value ...

s of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
5. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
9. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
22. What is the greatest value of c for which the roots of the equation x^2 + 4x + c = 0 are real?
24. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
7, 24 and 25
A._________________ (smaller value)
B._________________ (larger value)

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35. 1. What is the greatest value of c for which the roots of the equation x^2 + 4x + ...

2. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
A._______________________ (Smaller Value)
B. _______________________ (Larger Value)
3. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
4. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
5. If 8 ounces of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
6. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value of x?

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36. Value: 1 equation image indicator a. (x - 2)2(x - 3)2 b. (x2+ 4)(x2+ 9) c. (x - 2)(x + ...

2)(x - 3)(x + 3)
d. (x2 - 4)(x2+ 9)
Value: 1
The table below shows the cost of purchasing a standard stapler at five office supply stores, A through E. If the median cost of purchasing a standard stapler for these stores was $17.99, which of the following could NOT have been the cost of the stapler for Store A?
staplergraph.jpg
a. $19.95
b. $18.95
c. $16.95
d. $19.25
Value: 1
If equation image indicator then x =
a. 7
b. 1/5
c. 5
d. 1/7
Value: 1
A six−sided die, with sides numbered 1,2, 3,4,5, and 6, is tossed. What is the probability of tossing a number less than three?
a. 1/3
b. 0
c. 1/2
d. 1/4
Value: 1
If 6m + 4 = 8m, then 4m =
a. 6
b. 2
c. 8
d. 4
Value: 1
In the xy-plane, what is the y-intercept of the graph of the equation equation image indicator?
a. 2
b. 4
c. 16
d. There is no y-intercept.
Value: 1
Which of the following equations has both 2 and −4 as solutions?
a. x2 + 6x + 8 = 0
b. x2 - 2x - 8 = 0
c. x2 + 2x - 8 = 0
d. x2 - 2x + 8 = 0
Value: 1
The perimeter of a square is 20 ft. If you increase the length of the square by 2 feet and decrease the width by 1 foot, what is the area, in square feet, of the new figure?
a. 22
b. 28
c. 35
d. 40
Value: 1
(3x-2y4)-3 =
a. equation image indicator
b. equation image indicator
c. equation image indicator
d. equation image indicator
Value: 1
A softball is tossed into the air upward from a first floor balcony. The distance of the ball above the ground at any time is given by the function, distance function.png, where h(t) is the height of the softball above the ground (in feet) and t is the time (in seconds). What was the maximum height, in feet, of the softball above the ground after it was thrown?
a. 28
b. 30
c. 32
d. 34
Value: 1
A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening?
a. 20
b. 50
c. 70
d. 80
Value: 1
The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank?
a. 21
b. 15
c. 19
d. 9
Value: 1
In the xy−coordinate plane shown below, point P has coordinates (8, −6). Which of the following is an equation of the line that contains points O and P?
O and P graph.jpg
a. equation image indicator
b. equation image indicator
c. equation image indicator
d. equation image indicator
Value: 1
The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9?
a. 54
b. 6
c. 2/3
d. 3/2
Value: 1
A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees planted in each row and each row must be complete before it is planted, how many trees will be left over after planting?
a. 21
b. 11
c. 0
d. 55

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s 13 ft tall and 40 ft long and her scull has a legth of 5 feet. If the length of the museum scale model scull is 3 feet 3 inches, what is the height and the legth of the museum scale model?
a: in feet?
b: in meters?
(1 foot= 12 inches; 1 meter = 3.23 feet)

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el has run out.
a) what was the acceleration of the missile before the fuel has run out?
b)Do base on the given graph is it possible to calculate the gravitational acceleration g of the earth?If yes calculate it based on the graph.
c)when the missile get the max height from the moment it launched?
d)what is the max height the missile reached?
e)In how much time the missile will hit the ground from the moment it launched?
f)In what velocity the missile hit the ground (direction and magnitude)?

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics