PLEASE HELP ASAP !!
A particle moves in a a straight line along the x-axis. Its displacement (distance from 0 along the x-axis) is given by the following equation: f(t) = 3(t)^4 - 5(t)^3 + 6(t) - 7; t >= 0, where t is measured in seconds and f is measured in meters. Find the velocity of the function after 2 seconds.
Answers
The velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s
What is velocity?Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Here we have a displacement function:-
F(t)=3t⁴-5t³+6t-7
So to find out the velocity we will differentiate the above equation with respect to t.
d(F(t)/dt=12t³-15t²+6
V=12t³-15t²+6
Put the value of t=2 seconds
V=12x(2x2x2)-15x(2x2)+6
V=42 meters per second
Hence the velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s
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Related Questions
Each of 4 ladies randomly chooses a woolen overcoat from 15 different styles. What is the probability that at least 2 ladies choose the same type of overcoat?
Answers
Answer:
1/2
total No-4
required number-2
=No of required outcome
No of Normal outcome
=2/4
=2
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Spencer is draining his swimming pool. The expression - 720x + 4,000 represents the amount of water, in gallons, remaining in the pool
after x hours. What does 4,000 represent?
A the time left until the pool is empty
B the gallons of water initially in the pool
Cthe total hours required to drain the pool
D the amount of water being drained per hour
Answers
Using linear function concepts, it is found that the representation of the value of 4,000 is given by:
B the gallons of water initially in the pool.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the amount of water in the pool after x hours is modeled by:
y = -720 x + 4000.
4000 is the y-intercept, which is the initial amount of water in the pool, hence option B is correct.
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Evaluate.
11! over 9!(11 - 9)!
Answers
Answer:
220 is ans by many hardworking But I don't knows which
Answer:
[tex]\huge{\boxed{\sf 55}}[/tex]
Explanation:
[tex]\sf Combination \ Formula = \ _n C_r=\dfrac{n !}{r ! (n-r) !}[/tex]
Here given:
n = 11r = 9[tex]\bf _{11} C_9[/tex]Evaluate:
[tex]\rightarrow \sf \dfrac{11 !}{9 ! (11-9) !}[/tex]
[tex]\rightarrow \sf \dfrac{39916800}{ 362800 (2)}[/tex]
[tex]\rightarrow \sf \dfrac{39916800}{725760}[/tex]
[tex]\rightarrow \sf 55[/tex]
What is limit of startfraction x squared x minus 12 over x squared minus 3 x endfraction as x approaches 3? 0 startfraction 7 over 3 endfraction 4 dne
Answers
The limit of the expression [tex]f(x) = \frac{x^2 - 12}{x^2 - 3}[/tex]a s x approaches 3 is -1/2
How to determine the limit?The expression is given as:
[tex]f(x) = \frac{x^2 - 12}{x^2 - 3}[/tex]
As the variable x approaches 3, the limit is represented as:
[tex]\lim_{x \to 3} f(x)[/tex]
So, we have:
[tex]\lim_{x \to 3} = \frac{3^2 - 12}{3^2 - 3}[/tex]
Evaluate the exponents
[tex]\lim_{x \to 3} = \frac{-3}{6}[/tex]
Evaluate the quotient
[tex]\lim_{x \to 3} = -\frac{1}{2}[/tex]
Hence, the limit of the expression as x approaches 3 is -1/2
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Answer:
B. 7/3
Step-by-step explanation:
Took the final test and this was the correct answer
In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4. 1 cm. Which compound inequality represents the situation? r > 4 and r ≤ 4. 1 r > 4 or r ≤ 4. 1 r < 4 and r ≥ 4. 1 r < 4 or r ≥ 4. 1.
Answers
Answer:
see the attachment!
i hope this can help you!
Find the inverse of the function f(x) = 2x - 4.
O
8(x) = -1/x--1/4
O
8(x) = -x-1-1/
O g(x) = 4x + 2
O
1
g(x) = = x + 2
Answers
Answer:
y = 4 - x / 2
Step-by-step explanation:
y = 2x - 4
x = 2y - 4
y = 4 - x
----------
2
If an airplane descends 15 feet every 1.45 seconds, how far would the airplane travel in three and a half minutes? The equation is y=-40x+58
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here we go ~
The air plane descends 15 feels every 1.45 seconds, so it's unit rate is :
[tex]\qquad \sf \dashrightarrow \: \dfrac{15}{1.45} \: \: ft / sec[/tex]
Now we have to calculate the descent in 3.5 minutes ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{15}{1.45} \: \: \times 3.5 \times 60[/tex]
[tex]\qquad \sf \dashrightarrow \: 2172.41 \: \: ft[/tex]
So, the airplane descends 2172.41 feels in three and a half minutes ~
Jayson uses a hose to fill a 45-gallon tank with water in 15 minutes. How many gallons of water does Jayson add to the tank per minute?
Answers
Draw a line of best fit on the graph below. Explain how you knew where to draw the line of best fit.
Where does your line of best fit cross the y-axis?
Answers
Answer:
The line should be a negative sloping line that looks something like this:
Solve the following equation x2+6x=27 x = and
Answers
Answer:
Step-by-step explanation:
Assuming the question is x^2 + 6x = 27x, subtract 6x from both sides. x^2 = 21x. Then, divide both sides by x and you get x= 0, 21
In the diagram,
B (5,9)
A (2,3)
the points A, B and C lie on the straight line y = 2x-1
The coordinates of A are (2, 3).
The coordinates of B are (5, 9).
Given that AC = 3AB, find the coordinates of C.
0
y=2x+1
C
Answers
Answer:
C = (11, 21)
Step-by-step explanation:
The relation AC = 3AB can be used to find the coordinates of C given those of A and B.
__
C -A = 3(B -A)
C = 3B -2A . . . . . add A to both sides
C = 3(5, 9) -2(2, 3) = (15 -4, 27 -6) . . . . use the given points for A and B
C = (11, 21)
51% of a university's freshman class are majoring in Economics. If 4590 students in the freshman class are Economics majors, how many students are in the freshman class?
Answers
Answer:
2340
Step-by-step explanation:
4590*.51=2340.9
Because you can not have .9 people, you round down to 2340
2341 students are in the freshman class.
What is percentage?Percentage is defined as ratio expressed as a fraction of 100.
Total no. of students in the freshman Economics majors = 4590
51% students of a university's freshman class,
Let x no. of students in the freshman class,
x = 51/100×(4590)
x = 0.51×(4590)
x = 2340.9
x = 2340.9 ≈ 2341
Hence, 2341 students are in the freshman class.
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The midpoint of overline AB is M(-4, 0)M If the coordinates of A are (-6, 6) what are the coordinates of B?
Answers
Answer:
(-2, -6)
Step-by-step explanation:
Equating A and B to the Midpoint (M) :
(-4, 0) = (-6 + x / 2, 6 + y / 2)Equations formed :
-6 + x / 2 = -4-6 + x = -8x = -22. 6 + y / 2 = 0
6 + y = 0y = -6Midpoint : (x , y)
(-2, -6)Solve for X. Round to the nearest tenth, if necessary.
Answers
Answer:
still don't get it
Step-by-step explanation:
but please write it in an understanding meaning
Explain how you can determine which angle of a scalene triangle is the largest and which is the smallest.
Answers
Answer:
use The Law of Cosines first to calculate the largest angle. then use The Law of Sines to find another angle. and finally, use the angles of a triangle add to 180° to find the last angle.
Step-by-step explanation:
The scalene triangle is a type of triangle with sides of three different lengths and angles of three different measurements. In every scalene triangle, the shortest side is opposite the smallest angle and the longest side is opposite the largest angle.
On a coordinate plane, kite w x y z has points (1, 1), (3, 4), (5, 1), (3, negative 3). kite wxyz is graphed on a coordinate plane. what is the area of the kite? 7 square units 8 square units 14 square units 16 square units
Answers
The area of the kite will be C. 14 square units.
How to calculate the area?From the information given, on coordinate plane, kite w x y z has points (1, 1), (3, 4), (5, 1),
The area of the kite will be;
= 2(1/2 × 7 × 2)
= 2 ×7
= 14 units²
Therefore, the area of the kite will be 14 square units.
In conclusion, the correct option is C.
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Answer:
14 square units
Step-by-step explanation:
3. Which model shows the fraction
A.
B.
C.
D.
as a multiple of a unit fraction?
Answers
Answer:
A is the answer
Step-by-step explanation:
because 3 is shaded
and there is 5 rows with three shaded
In the shape below, find the value of d, rounded to one decimal place.
Answers
Answer: 128.7
Step-by-step explanation:
What is the value of the expression below when t = 6?
Answers
Answer:
C. -18
I hope that this helped you.
Answer:
C. -18
Step-by-step explanation:
The value of the expression is found by substituting the given value for the variable and following the Order of Operations to evaluate it.
__
[tex]\dfrac{2(4(6-t)^2+t-3(t+5))}{3}\qquad\text{given}\\\\=\dfrac{2(4(6-6)^2+6-3(6+5))}{3}=\dfrac{2(4(0^2)+6-3(11))}{3}=\dfrac{2(6-33)}{3}\\\\=\dfrac{2(-27)}{3}=\dfrac{-54}{3}=\boxed{-18}[/tex]
_____
Additional comment
In this instance, the Order of Operations can be shortcut a bit by factoring 3 from the numerator and denominator early in the evaluation.
= 2(2 -11) = 2(-9) = -18
Area of triangle = 24
Answers
Answer:
[tex]x=-2\pm2\sqrt13[/tex]
Step-by-step explanation:
The area of the triangle is;
[tex]A=\frac{1}{2} \times b\times h[/tex]
[tex]b=x+4[/tex]
[tex]h=x[/tex]
[tex]Area=A=24[/tex]
[tex]A=\frac{1}{2}\times[(x+4)\times x] \\24=\frac{x^{2} +4x}{2} \\24\times2=x^{2} +4x\\48=x^{2} +4x\\x^{2} +4x-48=0\\[/tex]
This can only be solved by the quadratic formula.
[tex]x=\frac{-b\pm\sqrt {b^{2}-4ac }}{2a}[/tex]
where;
[tex]a=1\\b=4\\c=-48[/tex]
and we get,
[tex]x=-2\pm2\sqrt13[/tex]
Three friends just out of culinary school have applied for a loan to open a new restaurant in the heart of New York City. The bank gives them a loan in the amount of 1.3 million dollars. The three friends estimate that their business will be able to make a profit of approximately $0.7 million per year. They keep track of their debts, profits, and overall financial status on a balance sheet. They enter the debt as a negative value and all profits as positive values. Define a unit for the amount of time since the company began. Enter a variable for the amount of time since the company began and use this variable to write an expression for the expected financial status. 1. What was the financial status of the company when it began? 2. If the estimates were correct, how many years was it before the financial status of the company was 14.8 million dollars?
Answers
Answer:
The answer is 0.3 million per year
Step-by-step explanation:
ok
First one to answer, i will mark brainlist
Answers
Answer:
WX < YW < XY
Step-by-step explanation:
Angle sum propertySum of all angles of triangle = 180
114 + 53 + ∠y = 180
167 + ∠Y = 180
∠Y = 180 - 167
∠Y = 13
The side opposite to smallest angle is shortest.
Angles in ascending order: ∠Y < ∠X < ∠W
Sides in ascending order: WX < YW < XY
mike has some candies and gave 15 of them to his friend, Late his mom bought him twice the amount of candies he had at the beginning how many candies did he have in the beginning if he has 60
Answers
Answer:
30
Step-by-step explanation:
gave 15 to his friend 30-15=15 his mom bought mom 60 candies so 30
The area of a rectangle is 49d + 91
The length is an integer higher than 1, but is a known number.
Find the width of the rectangle.
Answers
Assuming that L and d are known numbers, we can write.
[tex]W = \frac{49d + 91}{L}[/tex]
How to get the width of the rectangle?
Remember that for a rectangle of width W and length L, the area is given by:
A = L*W
In this case, the area is 49d + 91, and the length is a known number, so we know the value of L.
Then we can write:
A = L*W = 49d + 91
To get the value of W, we need to isolate it on one side of the equation.
We can do that by dividing both sides by L.
[tex]W = \frac{49d + 91}{L}[/tex]
We assume that d and L are known, so with the above rational expression, we have W totally determined.
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4.
—-
——
help please
math geniuses pls help!!!
pls check other questions too!
Answers
Answer:
Always in the range zero to one
Step-by-step explanation:
Option c is the answer
Dog in a Ditch
Oscar and Rasheed are identical twins. They are both 6 feet tall. They are on opposite sides of
a ditch that is 30 feet wide. Their dog, Earl, is at the bottom of the ditch and is walking away
from Oscar towards Rasheed. Earl can get out if he wants to. When Oscar looks at Earl, his line
of sight makes a 75° angle below the horizontal. When Rasheed looks at Earl, his line of sight
makes a 40° angle below horizontal. Earl has walked % of the way across the ditch. How deep
is the ditch?
Answers
The ditch is 14.54 feet deep.
What is application of Trigonometry?Trigonometry can be used to roof a house, to make the roof inclined ( in the case of single individual bungalows) and the height of the roof in buildings etc. It is used naval and aviation industries. It is used in cartography (creation of maps). Also trigonometry has its applications in satellite systems.
As, both brother have height of 6 feet.
We will use the concept of application of trigonometry to find the depth of ditch.
The explanation is attached below
Now, by solving both equations we get
0.8391y= (2+√3)(30-y)
4.5711y=111.96
y= 24.49 feet.
Now,
x= 14.54 feet.
Hence, the depth of ditch is 14.54 feet.
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The dance committee hired a DJ for the fall dance. The DJ charges
$125 per hour in addition to $55 for an assistant. The committee
wants to keep the total cost under $600. Which inequality represents
the maximum amount of hours the DJ will play at the dance?
Answers
Answer: 4 hours
Step-by-step explanation:
4 Hours
Explanation:
Make h = hours
You add the $55 extra cost for the assistant
$125h + $55 = $555
Use additive inverse to isolate the term with the variable
$125h + $55 - $55 = $555 - $55
Use multiplicative inverse to isolate the variable
[tex]\frac{125h}{125}[/tex] = [tex]\frac{500}{125}[/tex]
Hours would be: 4 Hours.
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PRESS THE IMAGE BELOW WHICH ONE DO I SELECT?
50 POINTS!!!
Answers
Answer:
No, corresponding angles aren't congruentStep-by-step explanation:
We have a transversal and lines intersecting with it.
The angle measures formed by the lines and the transversal are not all equal to each other.
Four of the angles measure 85° and one 79°.
These are corresponding angles (the angles which occupy the same relative position at each intersection where a straight line, transversal, crosses two or more others).
If corresponding angles are equal, the lines are parallel.
In our case all the lines intersecting the transversal are parallel apart from the one with different angle measure.
Therefore, correct answer choice is:
No, corresponding angles aren't congruentRalph needs 1/4 cup of butter to make a cake. He has 5 cups of butter. How many cakes can Ralph make using 5 cups of butter? A) 1 B) 5 C) 20 D) 4
Answers
Answer:
b
Step-by-step explanation:
Please help...a counselor wishes to examine the benefits of a parenting class on parenting
skills. he decides to administer a questionnaire to the 10 parents who have
attended the most recent class. how could this study be improved?
select all that apply.
a. administer a questionnaire to parents who have not attended the
class.
b. use a random sample of all patients, who have attended the
class.
c. increase the sample size.
d. give parents some sample responses, prior to administering the
questionnaire.
Answers
explanation