Answer:
The possible value of F must be 5N.
Step-by-step explanation:
A vector quantity is a quantity that comprises of both magnitude and direction. And an example of a vector quantity is force.
In the given question, the pointing arrows are two forces in action, pushing the box in opposite directions.
If the values of both forces pointing left and right are equal, the box would not move. This implies that the two forces are balanced, so the box would be at a state of dynamic equilibrium.
If the box moves to the right, it implies that the force F is less than that pointing right i.e 6N > F.
Therefore, the possible value of F is less than 6N. Thus, F = 5N.
The roof of the Westin Tower (officially called the Westin Peachtree Plaza Hotel) in Atlanta is located at a height of 723 ft. Assume a stone is dropped from this roof. (Note: Round numerical answers to two decimal places, if necessary.)
Required:
a. Find the distance of the stone above the ground at any time t (before it hits the ground).
b. How long does it take the stone to reach the ground?
c. With what velocity does it reach the ground?
Answer:
a) The stone takes approximately 6.704 second to reach the ground.
b) The stone takes approximately 6.704 second to reach the ground.
c) The stone hits the ground at a velocity of -215.695 meters per second.
Step-by-step explanation:
a) The stone experiments a free fall, which is a uniform accelerated motion due to gravity and in which effects from air friction and Earth's rotation are negliglble. Then, the vertical distance of the stone above the ground at any time [tex]t[/tex] is represented by the following model:
[tex]y = y_{o}+v_{o}\cdot t +\frac{1}{2}\cdot g\cdot t^{2}[/tex] (1)
Where:
[tex]y_{o}[/tex] - Initial height of the stone, measured in meters.
[tex]v_{o}[/tex] - Initial velocity of the stone, measured in meters per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
If we know that [tex]y_{o} = 723\,ft[/tex], [tex]v_{o} = 0\,\frac{ft}{s}[/tex] and [tex]g = -32.174\,\frac{ft}{s^{2}}[/tex], then the distance of the stone above the ground at any time [tex]t[/tex] is represented by the following model:
[tex]y = 723 -16.087\cdot t^{2}[/tex] (2)
b) If we know that [tex]y = 0[/tex], then the time taken by the stone to reach the ground is:
[tex]723-16.087\cdot t^{2} = 0[/tex]
[tex]t = \sqrt{\frac{723}{16.087} }\,s[/tex]
[tex]t \approx 6.704\,s[/tex]
The stone takes approximately 6.704 second to reach the ground.
c) The function velocity is found by differentiating (2) once:
[tex]v = -32.174\cdot t[/tex] (3)
If we know that [tex]t \approx 6.704\,s[/tex], then the velocity when it hits the ground is:
[tex]v = -32.174\cdot (6.704)[/tex]
[tex]v = -215.695\,\frac{m}{s}[/tex]
The stone hits the ground at a velocity of -215.695 meters per second.
A group of eight people are attending the movies together.
a. Two of the eight insist on sitting side by side. In how many ways can the eight be seated together in a row?
b. Two of the people do not like each other and do not want to sit side-by-side. Now how many ways can the eight be seated together in a row?
Answer:
I think A
Step-by-step explanation:
Consider the figure below. If ∆ABC is translated using the vector (x, y)→(x−3, y+3), then rotated 180° about the origin, what will be the x-coordinate of C’ ?
Answer: -7
Step-by-step explanation:
I’m doing the test
a. What is the decimal for 1 trillionth of a second?
Answer:
Step-by-step explanation:
1 000 000 000 000 E12
Answer:
Step-by-step explanation:
0.000 000 000 001
Carla currently has $300 in her bank account. Each time she goes to the ATM,
she withdraws $20. Write an equation representing this situation:
Answer:
y = -20x + 300
Step-by-step explanation:
y is total amount of money left (because this is the answer we are trying to find.)
x is the amount of times she goes to the ATM (because this is our unknown variable.)
-20 multiplies by x because she loses $20 every time she goes to the ATM. The equation has + 300 because she already has $300 in her bank account.
what's 2+2-2-4+77 and what is the square root of the sum
Answer:
simplified it is 75 the square root of 75 is 8.66025403784
Step-by-step explanation:
Find the circumference of the circle. Round your answer to the nearest hundredth. Use 3.14 or 227 for π.
There's a picture of a circle with the radius of 21 cm
Picture of the circle:
Answer:
65.94cm
Step-by-step explanation:
The two equivalent equations to find the circumference of a circle are:
Circumference = 2 * pi * radius
Circumference = pi * diameter
Since the diameter of the circle is given, in order to find circumference, plug in 21cm into the 2nd equation:
Circumference = pi * diameter = pi * 21 cm = 3.14 * 21 = 65.94 cm
sam was charged $1050 in interest on a loan with a 2.5% interest rate. what was the original amount of the loan if he took 5 years to pay it back?
Answer:
$8,400=amount of loan
Step-by-step explanation:
Key:
P=Money borrowed
T=5 years (time passed)
R=0.025 (interest rate)
I=$1050 (interest charged)
Formula: I=P*R*T
Work:
1,050=P*0.025*5
1,050=P*0.125
1,050/0.125=8,400
Check
8,400*0.025*5=1,050
(thank you 7th grade math last year haha)
A grocery store sells a bag of 7 oranges for $3.08. What is the cost of oranges, in dollars per orange
Answer:
$0.44 each
Step-by-step explanation:
3.08/7 = 0.44
The required cost in dollars per orange is $0.44.
Given that,
A grocery store sells a bag of 7 oranges for $3.08. What is the cost of oranges, in dollars per orange is to be determined.
The ratio can be described as the proportion of the fraction of one amount towards others. e.g.- water in milk.
What is arithmetic?In mathematics, it deals with a number of functions according to the statements.
here,
Let the cost of 1 orange = $x
The grocery store sells a bag of 7 oranges for $3.08.
So for 1 orange,
x = 3.08 / 7
x = $ 0.44
Thus, the required cost in dollars per orange is $0.44.
Learn more about ratios here:
brainly.com/question/13419413
#SPJ2
1 hundred 8 million 4 hundred 4 thousand translate
Answer:
800,004,500
Step-by-step explanation:
which is the correct answer?
Answer:
i think B
Step-by-step explanation:
40 points i will crown. A, B, C, or D.
Answer:
C. x > -3
Explanation:
The circle with no filling means it can not be equal
It goes ahead of -3 so it is greater than -3
WDGWADgawYd awIdwaiudwaiudgaidgawida
Sara and Harry are putting together a puzzle. Sara put together 7/12 of the puzzle pieces. Harry put together 7/24 of the puzzle pieces. What fraction of the total number of puzzle pieces has NOT been used? Enter your answer as a fraction, in simplest form, in the box provided.
Answer:
1/8
Step-by-step explanation:
7/12= 14/24 14/24 + 7/24= 21/24
21/24= 7/8 1-7/8= 1/8
The fraction of the total number of puzzle pieces has not been used is 1/8.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Sara and Harry are putting together a puzzle. Sara put together 7/12 of the puzzle pieces. Harry put together 7/24 of the puzzle pieces.
The fraction of the total number of puzzle pieces has not been used is calculated as,
7/12= 14/24
21/24= 7/8
1-7/8= 1/8
To know more about an expression follow
https://brainly.com/question/19961687
#SPJ2
The value of y varies directly with x, and y =-10 when x=40, identify the value of y when x =-5
Answer:
I think that answer is 5 or 35
Really need help !!!!!!!!
Please help answer the first 3 boxes for brainslt
> for brainslt
y=mx+b
1st one:
m=-3 b=-2
Not sure for proportional
Negative Slope
2nd one:
m=15 b=0
Proportional
Positive Slope
3rd one:
m=-4/3 b=8
Not sure proportional or not
Negative Slope
Answer:
Work shown below!
Step-by-step explanation:
y = -3x - 2
m = -3
b = -2
Non-proportional because it doesn't pass through the origin
Negative Slope
y = 15x
m = 15
b = 0
Proportional because it passes through the origin
Positive Slope
y = -4/3x + 8
m = -4/3
b = 8
Non-proportional because it doesn't pass through the origin
Negative Slope
Find f(2) If f(x) = (x + 1)2.
Answer:
f(2)=9
Step-by-step explanation:
help meeeee pleaseeee
how many times larger is 2.4 x 10^8 than 6 x 10^7?
An automobile assembly line operation has a scheduled mean completion time, , of minutes. The standard deviation of completion times is minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of completion times under new management was taken. The sample had a mean of minutes. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the mean completion time has decreased under new management
Answer:
Step-by-step explanation:
Here are the missing values;
Mean μ = 15.5 minutes
Standard deviation = 1.7 minutes
A Random sample of 90 completion
The sample mean = 15.4 minutes
Level of significance = 0.1
Then the following analysis can be made on the above study.
Firstly, the null hypothesis is [tex]\mathbf{H_o : \mu = 15.5}[/tex]
the alternative hypothesis is [tex]\mathbf{H_a: \mu < 15.5}[/tex]
Since, the value is less than, then this is a one-tailed test.
The Z test statistics can be computed as:
[tex]Z = \dfrac{ \overline x - \mu }{\dfrac{\sigma}{\sqrt{n}} } \ \ \sim \ \ N(0.1)[/tex]
[tex]Z = \dfrac{ 15.4-15.5 }{\dfrac{1.7}{\sqrt{90}} }[/tex]
[tex]Z = \dfrac{ -0.1 }{\dfrac{1.7}{ 9.4868} }[/tex]
Z = −0.560
The critical value of Z at 0.1 level of significance is:
[tex]Z_{0.1} = -1.28[/tex]
Decision Rule: We fail to reject the null hypothesis sInce -0.560 > -1.28
Conclusion: NO, there is no evidence to support the claim that the mean completion time has decreased. We conclude that the mean completion time remains at 15.5 minutes.
Would the space in between 2 transversals be an interior angle?
Answer:
When the two lines being crossed are Parallel Lines the Consecutive Interior Angles add up to 180°. so yes
Step-by-step explanation:
in how many ways 5 passengers can sit in a compartment having 16 vacant seats
9514 1404 393
Answer:
524,160
Step-by-step explanation:
Assuming order matters, it is the number of permutations of 16 things taken 5 at a time:
16P5 = 16!/(16-5)! = 16·15·14·13·12 = 524,160
_____
The first passenger can pick any of 16 seats; the second can pick any of 15 remaining seats; and so on until all 5 passengers have chosen a seat. The number of possible different arrangements is the number shown above.
What is the common difference for this arithmetic sequence?
-6, -1,4,9, 14, ...
A. 5
B. 3
C. 6
D. 4
Answer:
A. 5
Step-by-step explanation:
-6 + 5 = -1
-1 + 5 = 4
4 + 5 = 9
9 + 5 = 14
Naomi has a lot of stuff in her pencil case. There are 18 items in her pencil case, including 9 pencils. What is the probability that a randomly selected item from Naomi's pencil case will be a pencil? Write your answer as a fraction or whole number. P(pencil) =
Answer:
p=1/2
Step-by-step explanation:
If 9 is 1 half of 18 that means there is a 50% chance of you picking a pencil out of the pencil case
Grocery store sells tangerines in 2/5 kg bags. A customer bought 4kg of tangerines for a school party. How many bags did he buy
In order to have 4 kg, he must have 20/5 kg. Each bag is 2/5 kg, so 2/5 times 10 is 20/5 or 4kg. Therefore, he bought 10 bags of tangerines for the school party.
10. What is the area of a triangle with base 4cm and
height 8cm?
A. 6cm2 B. 9cm2 C. 14cm D. 16 cm
Step-by-step explanation:
Area of triangle = 0.5(4)(8) = 16cm² (D).
Simplify:
9x/2 - 4x - 3 = ?
Answer: Um, I think is [tex]\frac{x}{2-3}[/tex].
Step-by-step explanation:
18. The radius of a circle is increasing at a constant rate of 3 cm per second. What is the rate of increase (at any point)
of the area of the circle?
Step-by-step explanation:
you should have to give more points for this answer
You can spend up to $35 on a shopping trip. You want to buy a shirt that cost $14. Write and solve an inequality that represents the amount of money you will have left if you buy the shirt
Answer:
Step-by-step explanation:
a. 35 greater than or equal to 14 + x
35 - 14 = 21
x = $21
b. If the shirt is 30% off it would cost $9.80
14 x 0.3 = 4.2
14 - 4.2 = 9.8
35 is greater than or equal to 9.80 + x
35 - 9.8 = 25.2
x = $25.20
This changes the inequality by making x greater than it was in part a
c. Yes, you do have enough money to buy the shirt that is on sale and a pair of pants. x is the amount that you have left to spend after you buy the shirt that is on sale. 25.20 is greater than the cost of the pants.