For time measured in seconds, where t is greater than or equal to zero, the velocity of a particle
Answers
Answer: So, to find velocity we take the first derivative of the equation.
just in case you do not know how to take a derivative or a polynomial
the derivative of axn = naxn-1 where a is a coefficient and n is the exponent.
s' = 3t2 - 24t +36 this is your velocity in time t.
to solve for your velocity at t = 3 seconds we will plug 3 seconds into any t in the velocity equation.
s' = v this is just stating that s' is equal to your velocity
v = 3(3)2 - 24(3) + 36
v = 27 - 72 + 36
v = -9 m/s
to find when the particle is at rest we must consider the at rest velocity which is 0. An object at rest has no velocity(only applies to Newtonian mechanics)
so, we will change v to 0 and solve for t
0 = 3t2 - 24t + 36
to solve this we need to factor to quadratic equation.
to solve this we first will factor out 3 from the equation.
0 = 3(t2 - 8t + 12)
now we can factor. we need two numbers that when multiplied together give 12 but when added give -8. since the addition is negative and the multiplication is positive we know that we are dealing with two negative integers.
we end up with
0 = (t-2)(t-6) the three was divided on both sides to eliminate it from the equation.
so, the particle is at 0 at t = 2 seconds and t = 6 seconds.
Now, just because the particle has 0 velocity does not mean it has no acceleration. However, I do not believe the acceleration is important for this problem.
To find when the particle is moving forward you must consider again when it is at 0. When it is at 0 a speed change is happening. So, to find out if velocity is positive or negative we will test a number before 2 after 2 but before 6 and after 6.
So, we can start with t = 0 for the before 2 number
v = 3(0) - 24(0) + 36
we get v = 36 which is positive. So, the particle was moving forward before 2 seconds.
now we have already used 3 seconds and we got a negative velocity. So, the particle is moving backwards at t = 3 seconds.
So the last one to check is after 6 seconds. We will choose 10 for this one because it is easy to multiply with.
v = 300 - 120 + 36 = a positive number. You do not actually need to know what number as long as you know it is positive. That means the particle was moving forward after 6 seconds.
to find the total distance traveled we must break up the distance equation by direction of travel. So, we must take the distance traveled by the particle in pieces using the original equation.
s = t3 -12t2 + 36t
first we will solve for the distance traveled in 2 seconds.
s = 8 - 48 + 72 = 32 meters
Now we will solve for 6 seconds and figure out the distance traveled from 32 meters in the opposite direction. Then we will add the two numbers together.
s =216 - 432 + 192 = -24 meters
To find the distance travelled between 2 and 6 seconds we add the absolute value of the values together.
We end up with distance traveled between 2 and 6 seconds was
56 meters
we then add this to the original 24 meters to get the distance traveled from 0 to 6 seconds of
88 meters
then we solve for the distance at 8 seconds
s = 512 - 768 + 288 = 32 meters
so, again we add the absolute values of the previous time interval with the one we just calculated for.
24 + 32 = 56 meters. So, the particle traveled back up at this point.
We add the new 56 with the current total of 88 meters to get
total distance traveled = 144 meters
this shows us that the particle is moving in a wave pattern from 0 to 8 seconds. So, if you were to draw a graph you would have a particle start at s = 0 and t = 0, then the particle would move much like the graph of sine instead of stopping at 1 it would stop at s = 32 then drop down to s = -24 and rise up continuously after that.
Step-by-step explanation:
Related Questions
Which statement is true about the ordered pair (1 , 7)? A. To plot the ordered pair (1 , 7), travel seven units to the right on the x-axis and one unit up on the y-axis, from the origin. B. To plot the ordered pair (1 , 7), travel one unit to the right on the y-axis and seven units up on the x-axis, from the origin. C. To plot the ordered pair (1 , 7), travel one unit to the right on the x-axis and seven units up on the y-axis, from the origin. D. To plot the ordered pair (1 , 7), travel seven unit to the right on the y-axis and one units up on the x-axis, from the origin.
Answers
Answer:
C is the correct answer.
Step-by-step explanation:
You're trying to find a true statement about the point (1,7)
A. To plot the ordered pair (1 , 7), travel seven units to the right on the x-axis and one unit up on the y-axis, from the origin.
B. To plot the ordered pair (1 , 7), travel one unit to the right on the y-axis and seven units up on the x-axis, from the origin.
C. To plot the ordered pair (1 , 7), travel one unit to the right on the x-axis and seven units up on the y-axis, from the origin.
D. To plot the ordered pair (1 , 7), travel seven unit to the right on the y-axis and one units up on the x-axis, from the origin.
_____________________________________________________
Solving:
A is incorrect because it shows the point (7,1).
D is incorrect because that isn't the proper way to graph a coordinate.
B is incorrect because it says travel one unit to the right on the y axis which is the incorrect axis to graph the point (1,7).
C is your correct answer because you need to move 1 unit to the right on the x-axis to get to the coordinate (1,0). Then, you need to go 7 units up on the y-axis to reach (1,7).
Explain the difference between a polygon that is regular and a polygon that is not regular
Answers
Regular polygons have equal sides
Irregular polygons have unequal sides
Answer:
regular polygons have sides and interior angles that are the same and irregular polygons have sides and interior angles that are different
Step-by-step explanation:
each row describes a proportional relationship between the number of pounds of tomatoes used and the number of pints of tomato juice produced. complete the table by writing the constant of proportionally for each situation.
Answers
Considering the table given, the constant of proportionality of the proportional relationship is of k = 0.8.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching the problem on the internet, the set of values is as follows: (4,5), (8,10), (12,15), ...
Hence the constant is given by k = 4/5 = 8/10 = 12/15 = ... = 0.8.
More can be learned about proportional relationships at https://brainly.com/question/10424180
The pounds of tomatoes and the pints of tomato juice illustrates a proportional table
The constant of proportionality of the table is 1.25
How to determine the constant of proportionality?From the complete question, we have the following value
(x,y) = (4,5)
The constant of proportionality for a proportional table is calculated using:
y = kx
Make k the subject
k = y/x
So, we have:
k = 5/4
Evaluate
k = 1.25
Hence, the constant of proportionality of the table is 1.25
Read more about constant of proportionality at:
https://brainly.com/question/1835116
sin x=0.6, x lies in quadrant two.
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here we go ~
[tex]\qquad \tt \dashrightarrow \: \sin(x) = 0.6[/tex]
[tex]\qquad \tt \dashrightarrow \: \sin(x) = \dfrac{6}{10} [/tex]
[tex]\qquad \tt \dashrightarrow \: \sin(x) = \dfrac{3}{5} [/tex]
[tex]\qquad \tt \dashrightarrow \:x = \sin {}^{ - 1} ( \dfrac{3}{5} ) [/tex]
[tex]\qquad \tt \dashrightarrow \:x = 37 \degree[/tex]
Now, since we have to find the value of x in quadrant 2, we have to subtract the given value from 180°
that is :
[tex]\qquad \tt \dashrightarrow \:x = 180 - 37[/tex]
[tex]\qquad \tt \dashrightarrow \:x = 143 \degree[/tex]
Solve.
18,923,612 - 9,089,689
A. 9,833,023
B. 9,833,923
C. 9,933,923
D. 27,613,301
Answers
Answer:
B
Step-by-step explanation:
9833923
Which situation could be represented by the expression 1.40x?
Answers
Answer:
B. the area of a rectangle with side lengths 1.40 and x
Step-by-step explanation:
To find the area of a rectangle, multiply the length by the width.
If 1.40 is the length, x is the width.
1.40×x=1.40x
So B is the correct answer.
A tour bus in Jaipur serves 400 customers a day. The charge is Rs 50 per person. The owner of the bus service estimates that the company would lose 10 passengers a day for each Rs 5 fare increase.
(i) How much should the fare be in order to maximize the
Answers
What is the mean of the values in the dot plot?
Enter your answer in the box.
Answers
Answer:
the mean is 46.
Step-by-step explanation:
The total is 460 and divided by the amount of numbers(10) is 46.
Pls help!!!!!!!!!!!!!!!!!!!!!!!
Answers
I ONLY GOT 1 MIN!!!! PER QUESTION HELP
Chase wrote this description.
I saw a four sided figure. It had one pair of congruent sides that were not parallel. It also had one pair of parallel lines.
What shape has Chase described?
a parallelogram
a rhombus
a trapezoid
a kite
Answers
Answer:
options c
trapezoid
saw a four sided figure. It had one pair of congruent sides that were not parallel. It also had one pair of parallel lines.
saw a four sided figure. It had one pair of congruent sides that were not parallel. It also had one pair of parallel lines.What shape has Chase described?
trapezoidThe boundary line on the graph represents the equation x-3y=5. Write an inequality that is represented by the graph.
Answers
Answer:
y > 1/3x - 5/3
x-3y < 5
Step-by-step explanation:
We simplify x-3y=5, to y = 1/3x - 5/3
We notice the boundary line is dotted, we know the inequality must be < or > rather than ≤ or ≥.
The shading is above the line which indicates that in y-intercept form we must use >.
y > 1/3x - 5/3
or x-3y < 5
Either of these show the exact same thing.
What’s the domain and range?
Answers
Answer:
D [-1,3] and R [5,27]
Step-by-step explanation:
I explained the process of finding the domain and range in your previous questions therefore I will only give you the answer for this one.
D [-1,3] or [tex]-1\leq x\leq 3[/tex]
R [5,27] or [tex]5\leq y\leq 27[/tex]
How many edges does this shape have?
A. 6
B. 12
C. 16
D. 18
Answers
Answer:
B. 12
Step-by-step explanation:
Edges are the straight lines
243+222 Based on the passage, which statement is fact rather than fictio
Answers
Answer:465
Step-by-step explanation:
Answer: the answer is d) several players have asthma .
243+222=465
Step-by-step explanation:
which is true because players do have asthma and ii also took the test and made a 100 .
The probability of getting a yellow gumball from
a gumball machine is. The probability of getting
a yellow piece of candy from a piñata is. If a
gumball is taken from the gumball machine and a
piece of candy is pulled from the piñata, what is the
probability that both will be yellow?
Answers
A car rental agency has 42 cars (each an identical model). the owner of the agency finds that at a price of $32 per day, all the cars can be rented; however, for each $1 increase in rental cost, one of the cars is not rented. what should the agency charge to maximize income?
Answers
Answer:
increase to 38 and have the unused ones in for maintenance
How would I solve the equation’s by cross multiplying number 4,5,9,10
Answers
Answer:
4) a = 6
5) m = 1
Step-by-step explanation:
4) use FOIL, First Inside Outside Last, when you cross multiply.
[tex]\frac{a+4}{a-1} =\frac{a-2}{a-4}[/tex]
[tex](a+4)(a-4) = (a-1)(a-2)[/tex]
I'm going to do the left side first.
[tex](a+4)(a-4)\\a^2-4a+4a-16\\a^2-16[/tex]
Now I'm going to do the right side.
[tex](a-1)(a-2)\\a^2-2a-1a+2\\a^2-3a+2[/tex]
Next I'm going to rewrite back as the equation and solve for a.
[tex]a^2 - 16 = a^2 -3a +2\\a^2 - a^2 -16 = a^2-a^2-3a+2\\-16-2=-3a+2-2\\-18=-3a\\-18/-3=-3a/-3\\a=6[/tex]
5) I'm going to use distributive propoerty when I cross multiply. Then I will setup an equation like number 4 and solve for m.
[tex]\frac{5m-2}{3}=\frac{8-3m}{5} \\[/tex]
[tex]5(5m-2)=3(8-3m)\\25m-10=24-9m\\25m+9m-10=24-9m+9m\\34m-10=24\\34m-10+10=24+10\\34m=34\\34m/34=34/34\\m=1[/tex]
Calculate the surface area. Be sure to show how the area of each face is calculated.
Answers
Answer:
Surface area of the cubiod is 186.34 cm²Step-by-step explanation:
Given:
Shape = cubiodLength of cubiod = 10cmWidth of cubiod = 4.1 cmHeight of cubiod = 3.7 cmTo Find:
Surface areaSolution:
We can find the total surface area of cubiod by summing up the area of the six faces of the cubiod:
Area of the top and bottom face = lw+ lw = 2lwArea of the front and back face = lh+ lh = 2lhArea of the two side faces = wh+ wh = 2whSurface Area = 2(lw+ wh + hl)
Substituting the required values:
➝ Surface Area = 2(10 × 4.1) + (4.1 × 3.7) + (3.7 × 10)
➝ Surface area= 2(41 + 15.17 + 37)
➝ Surface Area = 2(93.17)
➝ Surface Area = 186.34 cm²
Hence,
Surface area of the cubiod is 186.34 cm²It took Azul 1.75 hours to bike The Blue Mountain Trail
Azul averaged 12.5 miles per hour. What is the best
estimate for the length of the trail?
Answers
=> 1.75x12.5 = 21.875 miles
Based on your answer choices
Between 12 and 26 is the most correct answer
AnsweA jar contains 15 red marbles, 30 blue marbles, 10 green marbles, and 35 orange marbles. Find the probablilty of picking a green marble.r:
Step-by-step explanation:
7. A spherical balloon has a circumference of 25 cm.
a.) What is the approximate surface area of the balloon to the nearest square centimeter?
b.) What is the approximate volume of the balloon to the nearest cubic centimeter?
Answers
Answer:
surface area of the balloon is 199 cm^2
Water is pouring into a conical vessel of diameter 5.2m and slant height 6.8m (as shown in the adjoining figure), at the rate of 1.8 m per minute. How long will it take to fill the vessel?
Answers
Answer:
31.6m
Step-by-step explanation:
First, find area of the vessel [ (πr2h)/3 ]
Radius = 5.2/2= 2.6
Using Pythagorean theorem, find the height of the cone:
[tex]\sqrt{6.8^{2} -5.2^{2} }[/tex] = 4.38
Area of vessel = [tex]\frac{ (PI * 2.6 * 2 * 4.38)}{3}[/tex] = 56.88 [tex]cm^{3}[/tex]
Do cross multiplication using ratios:
1.8 = 1
56.88 = [tex]x[/tex]
[tex]\frac{56.88}{1.8}[/tex]= 31.6
Is this just a fancy way of saying to graph the point (2,-6) or am I supposed to graph a line?
Answers
Answer:
I do know what that is saying it's saying the rise of the line is going to be -6 and the run is going to be 2.
Step-by-step explanation:
Your supposed to graph a line I don't exactly remember how to do it but yeah you're supposed to graph the line.
Find the value of each trigonometric ratio. Simplify
Answers
Tan A = 16/12
From a set of whole numbers from 1 to 32, what is the probability of randomly choosing a number either divisible by 5 or divisible by 3?
A) 1/2
B) 7/16
C)15/32
D)5/8
Answers
Using it's concept, it is found that the probability of randomly choosing a number either divisible by 5 or divisible by 3 is given by:
B) 7/16
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
There is a total of 32 numbers.Those that are divisible by 3, 5 or both are: {3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30}, that is, 14 numbers.Hence the probability is given by:
p = 14/32 = 7/16.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
What is the volume of the cardboard container
Answers
Explanation: The volume of a pentagonal prism is equal to the area of the base times the height of the pentagonal prism. The area of the base here is 43 centimeters squared and the height of the pentagonal prism is 12 centimeters. So we get 43 multiplied by 12, which equals 516, and the volume of a pentagonal prism is always written in cubes units, so our answer is that the volume of the cardboard container is 516 centimeters cubed.
Instructions: Find the missing side. Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
x is the adjacent side of 30°
Hypotenuse = 22
[tex]Cos \ 30^ \circ = \dfrac{adjacent \ side}{hypotenuse}\\\\\\0.866 = \dfrac{x}{22}\\\\\\0.866*22 = x\\[/tex]
x = 19.1
Answer:
cosθ=Adjacent/ hypotenuse
[tex] \cos(30) = \frac{x}{22} \\ \\ \frac{ \sqrt{3} }{2} = \frac{x}{22} \\ \\ 2x = 22 \sqrt{3} \\ \\ x = \frac{22 \sqrt{3} }{2} \\ \\ x = 11 \sqrt{3} = 19.05 = 19.1[/tex]
Do number 5 pleaseee
Answers
Answer:
A
Step-by-step explanation:
16 × 2 = 32
20 × 2 = 40
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Determine which sets of lengths can form a right triangle
Answers
10,24,26 can make a right triangle
6,14,18 cannot make a right triangle
I hope this helps
This is for 25 points please don't spam.
Answers
Answer:
D.
Step-by-step explanation:
REarranging the fromula:
F = m . a
M is in grams and acceleration is in meters / second squared
grams . metres per second squared.
Answer:
D) grams · meters per second squared
Step-by-step explanation:
[tex]\sf a=\dfrac{F}{m} \implies F=ma[/tex]
If a has units of [tex]\sf ms^{-2}[/tex]
If m has units of [tex]\sf g[/tex]
Then as F is the product of m and a, then
F has units of [tex]\sf g \cdot ms^{-2}=gms^{-2}[/tex]
WILL GIVE BRAINLIEST
Select the decimal that is equivalent to \dfrac{111}{250}
250
111
start fraction, 111, divided by, 250, end fraction.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
0. 3760. 3760, point, 376
(Choice B)
B
0. 3\overline{76}0. 3
76
0, point, 3, start overline, 76, end overline
(Choice C)
C
0. 4440. 4440, point, 444
(Choice D)
D
0. \overline{444}0.
444y
0, point, start overline, 444, end overline
(Choice E)
E
None of the above
Answers
Answer:
0.444
Step-by-step explanation:
im a bit confused with the anwser choices, so just pick which ever one contains states 0.444 as it's answer choice.
hope this helps :)
Answer:
0.444
Step-by-step explanation:
1.) A rational number in the form of a fraction can be represented as a decimal by dividing the numerator by the denominator.
2.) Now let's divide 111.000000... by 250. Find enough decimal digits in the numerator so we can see whether the decimal terminates or starts to repeat. [tex]111/250 = .444[/tex]. Since the remainder is 000, this is a terminating decimal.
3.) The terminating decimal is [tex]\frac{111}{250} = 0.444.[/tex]
