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:
Tanya's father travels every week for business. He has traveled around the
world many times. Over the past 10 years, he has accumulated approximately
460,000 frequent flyer miles. How is that number expressed in scientific
notation?
A. 4.6 × 103
B. 4.6 × 10 4
C. 4.6 × 10 5
D. 46 × 10 5
The correct answer would be: 4.6 x 10^5
The volume of a square pyramid with a height of 12m is 100 m find the Length of the square base.
The difference of x and a number is 6. What is the other number?
Answer:
Answer: The other number is y = x + 6.
Step-by-step explanation:
What is p(x)? I need help ASAP
Answer:
Option C
Step-by-step explanation:
you just subtract the functions from each other.
hence,
15x - 7x - 20
p(x) = 8x - 20
Which of the following expressions are equivalent to -2(5 – 3)?
Choose all answers that apply:
A
-10 - 6
B
-10 + 6
None of the above
Peno
Sos
Answer:
It's B
-10 + 6
Step-by-step explanation:
Here, we gotta use the distributive property.
the -2 will distribute to the 5, which will make the -10
then, the -2 will also distribute to the -3 (the minus is the negative) which will make the 6
So, that should give you the -10 + 6, which is B
hope this helped :)
Answer:
[tex]\boxed{\sf{B.-10+6}}[/tex]Step-by-step explanation:
Use the distributive property.
Distributive property:
→ A(B+C)=AB+AC
→ -2(5-3)
Multiply.
→ -2*5=-10
→ -2*3=-6
Rewrite the problem down.
→ = -10+6
Therefore, the correct answer is B. -10+6.I hope this helps you! Let me know if my answer is wrong or not.
Linear Sequences
Please help with this question
Put either a,b,c,d
It is on linear sequences
35 points up for grabs
Answer:
please help the question
Step-by-step explanation:
How tall is this building?
Answer:
The building is 86.6 m tall.
Step-by-step explanation:
Coh Cah Toa
Coh: sin(theta) = Opp/Hyp
Cah: cos(theta) = Adj/Hyp
Toa: tan(theta) = Opp/Adj
Using Toa.
tan(theta) = Opp/Adj
tan(60°) = x/50
x = 50 * tan(60°)
x = 50 * √(3)
x ≈ 86.60254038
x = 86.6 m
Please help me with algebra question will mark brainliest to first person with a real answer
Answer:
367/90
Step-by-step explanation:
As [tex]4.\bar{7}=4\frac{7}{9}[/tex], this means that [tex]0.4\bar{7}=4\frac{7}{90}=\frac{367}{90}[/tex], 1/10th of 4.7 repeated.
What’s the scale factor? Quick
This is on ixl and I have to get at least a 90
Answer:
4
Step-by-step explanation:
We start with the smaller shape. We look at each coordinate and we multiply by 4. That will give us the coordinates for the bigger shape.
if a-1/a=5 then find the value of a square +1/asquare
Answer:
3
Step-by-step explanation:
Calculating a
a - 1 / a = 5a - 1 = 5a4a = -1a = -1/4Substitute in the 2nd equation
a² + 1 / a²(-1/4)² + 1 / (-1/4)²1/2 + 1 / 1/23/2 / 1/235. Cole worked for a concrete company last weekend. On Saturday, his gross income was $350
and his net income was $307.05. On Sunday, his gross income was $280 and his net income
was $246.35. What amount did Cole pay in payroll tax last weekend?
PLS HELP ASAP a wheel makes 13 revolutions to cover a distance of 65 m find the radius of the wheel
Circumference:-
65/135mRadius:-
2πr=5πr=2.5r=2.5/πr=0.797mAnswer:
radius = 0.8 m (nearest tenth)
Step-by-step explanation:
One revolution of the wheel means one complete turn. Therefore, the distance of one revolution is the circumference of the wheel.
First, find the distance of one revolution (the circumference) by dividing the total distance by the given number of revolutions:
[tex]\sf circumference=\dfrac{65}{13}=5\:m[/tex]
Formula
[tex]\textsf{circumference of a circle}=\sf 2 \pi r \quad \textsf{(where r is the radius)}[/tex]
[tex]\implies \sf radius=\dfrac{circumference}{2 \pi}[/tex]
Substituting the found value of the circumference into the formula to find the radius:
[tex]\implies \sf radius=\dfrac{5}{2 \pi}=0.8\:m\:(nearest\:tenth)[/tex]
A car traveled 1010 miles at an average speed of 3030 miles per hour
and then traveled the next 1010 miles at an average speed of 5050 miles
per hour. What was the average speed, in miles per hour, of the car for the
2020 miles?
The average speed, in miles per hour, of the car for the 20 miles is 37.5 mph
Average speedAverage speed v = d/t where
d = total distance and t = total timeMaking t subject of the formula, we have
t = d/v
Time to cover first 10 milesNow when the car travels 10 miles at an average speed of 30 miles per hour,
d = 10 mi and v = 30 mph.So, t = d/v
= 10/30
= 1/3 h
Time to cover next 10 miles
Also, when the car travels the next 10 miles at an average speed of 50 miles per hour,
d' = 10 mi and v' = 50 mph.So, t' = d'/v'
= 10/50
= 1/5 h
Time to cover 20 miles
The total time for the 20 miles is T = t + t'
= 1/3 h + 1/5 h
= (5 + 3)/15 h
= 8/15 h
Average speed for 20 miles
So, the average speed for the 20 miles is v = D/T where
D = 20 miles and T = 8/15 h.So, v = D/T
v = 20 mi ÷ 8/15 h
v = 20 × 15 mi/8 h
v = 2.5 × 15 mi/h
v = 37.5 mph
So, the average speed, in miles per hour, of the car for the 20 miles is 37.5 mph
Learn more about average speed here:
https://brainly.com/question/24739297
can someone help me with this question
Answer:
(4,2)
Step-by-step explanation:
It's parallel, so all of them have to be on the same way.
The last point has to be at the same distance from the one right above it
Answer:
C. (4, 2)
Step-by-step explanation:
(x, y)
if you put the last dot on (4, 2) and connected all of them, it would create a perfect parallelogram
What is the slope of the line through the points (-2, -1) and (4, 3)?
2/5
5/2
3/2
2/3
Answer:
2/3
Step-by-step explanation:
We can use the slope formula to find the slope
m = ( y2-y1)/(x2-x1)
= ( 3- -1)/ ( 4 - -2)
= ( 3+1)/ ( 4+2)
= 4/6
= 2/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{The formula for slope of a line is: }\large\boxed{\mathsf{m = \dfrac{y_2 - y_1}{x_2 - x_1} \ or\ easier \ way\ m = \dfrac{rise}{run}}}[/tex]
[tex]\large\textsf{NOW LETS ANSWER THE GIVEN EQUATION}[/tex]
[tex]\large\text{THE GIVEN EQUATION: \boxed{\rm{m = \dfrac{3 - (-1)}{4 - (-2)}}}}\\\large\boxed{m \rm{= \dfrac{3 + 1}{4 + 2}}}\\\\\\\large\boxed{m \rm{= \dfrac{4}{6}}}\\\\\\\large\boxed{m \rm{= \dfrac{4\div 2}{6\div 2}}}\\\\\\\large\boxed{m = \rm{\dfrac{2}{3}}}\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{Option\ D. \dfrac{2}{3}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Xaviera went out to play soccer at 5:31 and returned home at 7:00 how long was she playing soccer
Step-by-step explanation:
she played for about 1 hour 29 minutes
Answer:
1 hour and 29 minutes or 89 minutes
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
See picture for full problem. Please and thank you so very much!
Answer:
Step-by-step explanation:
i need help with this quick pls , please solve 5a
Answer:
Step-by-step explanation:
If you use de morgan's laws to write out [tex]-(PvQ)[/tex], it returns -P ^ -Q
And if ^ means 'and', it is showing that (P and Q) and (-P and -Q) which isn't possible since there can't be something that is both true and false. Therefore, it is a contradiction since something can not be true a nd false at the same time.
Do number 2 please. Please bots don’t answer! I just trying to get help :(
Answer:
no 2. cube a' will be smaller because it was multiplied by a fraction
no 3. c
65 brainleiest! Can someone help?!
Answer:
m∡EFG = 139°, and m∡ IFH = 49°
Step-by-step explanation:
We know that vertical angles are congruent so we can say that
∡EFG ≅∡DFH and that ∡EFD≅∡GFH
Congruent angles have the same measure therefore
∡EFG = ∡DFH = 6x+25 and
∡EFD = ∡GFH = 2x+3
Use that all those angles add up to 360° to find x
∡EFG +∡GFH +∡DFH + ∡EFD = 360°, substitute the given measures
6x+25 +2x+3 + 6x+25 +2x+ 3 = 360 , combine like terms
16x + 56 = 360, subtract 56 from both sides
16x = 304, divide both sides by 16
x = 19
m∡EFG = 6x +25 , substitute x with 19 and calculate
m∡EFG = 6·19 +25
m∡EFG = 139°
m∡ IFH = 90°- m∡GFH, substitute m∡GFH with 2x+3
m∡ IFH = 90°- (2x +3), substitute x with 19
m∡ IFH = 90°- (2·19 +3)
m∡ IFH = 90°- 41
m∡ IFH = 49°
What is the area of the shape?
Answer:12 units^2
Step-by-step explanation:
2*2=4
2*2*1/2=2
2*6*1/2=6
4+2+6=12
12 units^2
Use the picture I provided to help me answer the question.
The wheel of a bike has a diameter of 26 inches. What is the circumference of the wheel?
Answer:
C ≈81.64 inches
Step-by-step explanation:
Formula : C ≈ πd
Where:
C = circumference
π ≈ 3.14 {About}
d = diameter
As Given :
Wheel of a bike has a diameter of 26 inches.
Solution:
Note - Given that diameter = 26
π ≈ 3.14 {About}
C ≈ 3.14 (26)
C ≈ 81.64
Therefore the circumference of the wheel is 81.64 inches
Kavinsky
is 627 divisible by 3
Answer:
yes.
Step-by-step explanation:
If you divide 627 by 3, you get 209 which is a whole number.
Hope this helped! Have a nice day!
Please give Brainliest when you can!
-Jaron
Answer:
technically speaking, yes. but if you don't want any remainders, (or decimals) then no.
Step-by-step explanation:
7 isnt divisable by anything, unless you have remanders or decimals, fractions ext. so yeah.
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?
The approximate surface area of the balloon is 199 cm².
The approximate volume of the balloon is 262 cm³
What is the surface area and the volume of the balloon?Radius of the balloon = circumference / 6.2832
25 / 6.2832 = 3.98cm
Surface area = 4πr²
4 x 22/7 x 3.97² = 199 cm²
Volume = 4/3πr³
4/3 x 22/7 x 3.97³ = 262.20 cm³
To learn more about the volume of a sphere, please check: https://brainly.com/question/13705125
Pleaseeeeee helppp!!!!! Will mark brainliest!!
Answer:
the first one (3x-2)(2x-3)
Compare using >, < or =
7 x 5/4 _ 7
How do you know your answer is correct?
Choose 1 answer:
A. Because we are multiplying 7 by a fraction that is less than 1.
B. Because we are multiplying 7 by a fraction that is equal to 1
C. Because we are multiplying 7 by a fraction that is greater than 1.
I think the answer will be:
C but i not that sure
Answer:
C. Because we are multiplying 7 by a fraction that is greater than 1.
Step-by-step explanation:
- Sumin -
What is the measure of the unknown angle?
A 72°
B 74°
C 76°
D 79°
Answer:
C. 76 degrees.
Step-by-step explanation:
n = 180 - 104
= 76.
Answer:
C
Step-by-step explanation:
a straight line is 180 degrees
so we can say that n is equal to 180 - 104
n is equal to 76 degrees
If you can help me with this please and thank you
Answer:
Nnnnnnnnnnnn
Step-by-step explanation:
L bozo
Does anybody know this ?
Answer:
0, 1, 2, 3, 4
Step-by-step explanation:
Multiply each x value by 1/3 then add 2. Since the numerator is 1, you would multipy by one and divide by the denominator of 3, so you really need to divide each x value by 3 then add 2.
-6:
-6/3 = -2
-2 + 2 = 0
-3:
-3/3 = -1
-1 + 2 = 1
0:
0/3 = 0
0 + 2 = 2
3:
3/3 = 1
1 +2 = 3
6:
6/3 = 2
2 + 2 =4