The particle's acceleration a increases at a constant rate, so that its average rate of change is equal to its instantaneous rate of change, which is equal to
(4 ft/s² - 1 ft/s²) / (1 s) = 3 ft/s³
The particles starts with acceleration a (0) = 1 ft/s², so we can determine its acceleration at time t by the fundamental theorem of calculus:
a(t) = a (0) + ∫₀ᵗ (3 ft/s³) du
a(t) = 1 ft/s² + (3 ft/s³) t
It also starts from rest, so with initial velocity v (0) = 0. Integrating again gives us the velocity function,
v(t) = v (0) + ∫₀ᵗ a(u) du
v(t) = ∫₀ᵗ (1 ft/s² + (3 ft/s³) u) du
v(t) = (1 ft/s²) t + 1/2 (3 ft/s³) t ²
Taking the particle's initial position to be x (0) = 0, compute the integral again to determine the distance it travels in 1 s:
x(t) = x (0) + ∫₀ᵗ v(u) du
x(t) = ∫₀ᵗ ((1 ft/s²) u + 1/2 (3 ft/s³) u ²) du
x(t) = 1/2 (1 ft/s²) t ² + 1/6 (3 ft/s³) t ³
→ x (1 s) = 1/2 (1 ft/s²) (1 s)² + 1/6 (3 ft/s³) (1 s)³ = 1 ft
Really need help !!!!!!!!
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)
Notes ...
The supporters at a wrestling tournament either supported the home team or the visiting
teams. 45% of the supporters cheered for the visiting tearns and 55% of the supporters
cheered for the home team. If the total number of people attending the tournament was
1200, how many people were supporters of the visiting teams at the wrestling
tournament?
X=45
55-1200
Practic...
Margaret is completing a lifeguard course and is completing the test at the end of the
course. There are 75 total questions that she needs to complete and she is 36% complete.
How many more cuestions does she need to complete
Q
Answer:
Step-by-step explanation:
For your first question,
Total percentage of people cheering for visiting team = 45%
Total percentage of people cheering for home team = 55%
Total number of people cheering = 1200
Therefore, the number of people cheering for visiting team = 45% of 1200
= [tex]\frac{45}{100}[/tex] × 1200
= 45 × 12
= 540 people
For your second question,
Total number of questions = 75
Total percentage of the number of questions he completed = 36%
Percentage of the amount of questions left = 100 - 36 = 64%
Therefore, the number of questions left to complete = 64% of 75
= [tex]\frac{64}{100}[/tex] × 75
= [tex]\frac{64}{20}[/tex] × 15
= [tex]\frac{64}{4}[/tex] × 3
= 16 × 3
= 48 questions are left
Pls helpppppp! 25 points will mark brainliest!!!!!
That is the answer. Hope it helps!
Can someone help me explain please?
Answer:
B. 16 = 4y
y = 4
Answer:
B. 16 = 4y
Step-by-step explanation:
Long block = 16Amount of blocks that make the long block (16): 4Label of the small blocks: yTotal of small blocks: y × 4y × 4 = 4yBecause the long block and the y blocks are equal, 16 = 4yI hope this helps!
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
VY=27. VZ = 18, and Ww=8, find WX
Х
W
Z
Answer:
D. 4
Step-by-step explanation:
∆VWZ ~ ∆VXY, therefore:
[tex] \frac{VW}{VX} = \frac{VZ}{VY} [/tex]
VW = 8
VX = 8 + WX
VZ = 18
VY = 27
Plug in the values
[tex] \frac{8}{8 + WX} = \frac{18}{27} [/tex]
Cross multiply
[tex] 8 * 27 = (8 + WX)*18 [/tex]
[tex] 216 = 144 + 18WX [/tex]
Subtract 144 from each side
[tex] 72 = 18WX [/tex]
Divide both sides by 18
[tex] 4 = WX [/tex]
WX = 4
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.
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
URGENT
The table shows the derivation of tan(2x). Select the
correct reason for each step.
Reason 1 is
Reason 2 is
Reason 3 is
Answer:
Reason 1 is: Addition
Reason 2 is: Tangent Sum Identity
Reason 3 is: Simplify
Step-by-step explanation: ED 2020
Answer:
Reason 1 is: Addition
Reason 2 is: Tangent Sum Identity
Reason 3 is: Simplify
Step-by-step explanation:
What are the first three terms of the Arithmetic Sequence an = 12 – 2(n – 1)?
Group of answer choices
11, 10, 9
12, 10, 8
0, 10, 20
1, 2, 3
Answer:
The first 3 choices are:
12, 10, 8
Step-by-step explanation:
n represents a variable, in which you start at 1 and increase by 1.
So, we first start at 1.
12 - 2(1 - 1) = 12 - 2(0) = 12
Now, 2.
12 - 2(2 - 1) = 12 - 2(1) = 10
Now, 3.
12 - 2(3 - 1) = 12 - 2(2) = 8
So, we result in 12, 10, and 8.
#teamtrees #WAP (Water And Plant)
Answer:
B
Step-by-step explanation:
an = 12 - 2(n - 1)
a1 = 12 - 2(0)
a1 = 12
==============
a2 = 12 - 2(2 - 1)
a2 = 12 - 2
a2 = 10
==============
a3 = 12 - 2(3-1)
a3 = 12 - 2*2
a3 = 8
I think B must be the correct answer. I don't think you can start with n = 0 but the question should qualify that.
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
if 3x+10=4, what is the value of 2+5x? please help
Answer:
-8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
3x + 10 = 4
2 + 5x
Step 2: Solve for x
Subtract 10 on both sides: 3x = -6Divide 3 on both sides: x = -2Step 3: Evaluate
Substitute in x: 2 + 5(-2)Multiply: 2 - 10Subtract: -85 plus 5 euqals what number help
Answer:
10
Step-by-step explanation:
lol
...its 10
Step-by-step explanation:
1+1+1+1+1= 5
1+1+1+1+1= 5
5+5=10
Please help do right don't do just for points please
Answer:
-100
75
Step-by-step explanation:
Please help! I’ll give brainlest. Idk the answer bruh it’s for a grade :/
Which scenario could be represented by this graph?
A. After realizing that the house is cold Harry turns up the thermostat the temperature of the house gradually increases at constant rate the x-axis represents time the y-axis represents temperature
B. After realizing the house is too warm Harry turns on the air conditioner the temperature of the house gradually decreases at constant rate the x-axis represents time the y-axis represents temperature
C. The house temperature rises until it reaches the thermostat temperature and then it remains constant the x-axis represents time the y-axis represents the temperature
D. Harry runs the window air conditioner until the temperature falls to a comfortable level the x-axis represents time the y-axis represents temperature
Answer:
A
Step-by-step explanation:
Process of elimination.
It can't be B or D cause those say that the temp go down while in your graph it goes up, and C is saying that it rises and becomes constant while in your graph it's the other way around.
Answer:
A.
Step-by-step explanation:
I said so
(2x + y = 14
5x - y = 28
Which ordered pair represents the solution
Answer:
D (6,2)
Step-by-step explanation:
2x6+2=14 2x6= 12 12+2= 14
5x6-2=28 5x6=30 30-2=28
There are y boats on a lake.
There are 6 people in each boat.
Write an expression, in terms of y, for the total number of people in the boats.
Answer:
I hope this may help u
Step-by-step explanation:
6×y
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.
What is the area of the trapezoid?
Answer:
a+b/2×h=56
Step-by-step explanation:
thanks needed.......
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
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Create the f(x) function based on the table. Answer should be in function notation
Answer:
It will be
f(x)=x+4
Suppose that in one week in November in St. Louis, the temperature dropped by an average of 4 degrees every day. The temperature at the beginning of the week was 65 degrees. Write an equation that relates the temperature (t) to the number of days that have passed (d). helpppp
Answer:
t = 65 - 4d
Step-by-step explanation:
Linear Modeling
The temperature in St. Louis dropped by 4 degrees every day in one week.
When d days have passed, the temperature will have dropped by 4d degrees.
We know the temperature t at the beginning of the week was 65 degrees.
Thus, when d days pass, the linear model for the temperature t is:
t = 65 - 4d
If you borrow $400,000 at an APR of 4% for 15 years, you will pay more per month than if you borrow the money for 30 years at 4%. However, you will pay much more in interest over the life of the loan. Answer the questions below (10 points) a. What is the monthly payment on the 15-year mortgage, to the nearest cent? (Be sure to use Excel to calculate the monthly payment.) b. What is the total interest paid on the 15-year mortgage? C. What is the monthly payment on the 30-year mortgage, to the nearest cent? d. What is the total interest paid on the 30-year mortgage? e. How much more interest in paid on the 30-year loan?
Answer:
If if i did the match correctly then you would be paying $53.33
Step-by-step explanation:
hope this helps!!!!!!! :D
Help please an someone explain this to me i'm confused
Answer:
Jesus I can't help, I would take the educational guess if I was you
Step-by-step explanation:
Considering only the factors of the form x - k, what is the relationship between the k values and the zeros?
Given:
Considering only the factors of the form x - k.
To find:
The relationship between the k values and the zeros?
Solution:
We know that, if (x-c) is a factor of a function f(x), then x=c is a zero of function f(x), i.e., f(c)=0, where, c is a constant.
It is given that, only the factors of the form x - k. Then by using the above theorem we can say that, k values are the zeros of the function.
The relationship between the k values and the zeros is defined as
k values = Zeros of the function
Therefore, the k values are to zeros of the function.
Simplify using the laws of exponets.
Answer:
2*5
Step-by-step explanation:
when youre dividing with powers you have to subtract them so 2*5-2*4=2*1. When the power is in brackets you multiply the whole power. So 2*1 x 5 = 2*5.
which is the correct answer?
Answer:
i think B
Step-by-step explanation:
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Write the equation of the line with a slope of -1.6 and a y-intercept of 4 in slope-
intercept form.
Answer:
y = -1.6x + 4
Step-by-step explanation:
y = mx + b
y = (-1.6)x + (4)
y = -1.6x + 4
The equation of line with a slope of -1.6 and a y-intercept of 4 in slope- intercept form is,
⇒ y = - 1.6x + 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Slope of the line (m) = - 1.6
And, The y - intercept = 4
We know that;
The slope intercept form of an equation of line is,
⇒ y = mx + b
Where, 'm' is slope of the line and 'b' is y - intercept of the line.
Hence, The equation of line with a slope of -1.6 and a y-intercept of 4 in slope- intercept form is,
⇒ y = mx + b
⇒ y = - 1.6x + 4
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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