Step-by-step explanation:
Given that,
The positions of the first particle,[tex]s_1=4t-t^2[/tex]
Velocity,
[tex]v_1=\dfrac{ds_1}{dt}\\\\v_1=\dfrac{d(4t-t^2)}{dt}\\\\v_1=4-2t[/tex]
Position,
[tex]s_2=5t^2-t^3[/tex]
[tex]v_2=\dfrac{ds_2}{dt}\\\\v_2=\dfrac{d(5t^2-t^3)}{dt}\\\\v_2=10t-3t^2[/tex]
Hence, this is the required solution.
Write the product as a single power. 6^(5) * 6^(2) * 6^(5)
Answer:
6^12
Step-by-step explanation:
add up all the exponents
[tex]\displaystyle\bf \boxed{a^m\cdot a^n=a^{m+n}}\\\\6^5\cdot 6^2\cdot6^5=6^{5+2+5}=\boxed{6^{12} }[/tex]
A college with a graduating class of 4000 students in the year 2010 predicts that its graduating class will grow 5% per year.
Using an exponential function to model the number of students y in the graduating class t years after 2010 to predict the number
of students in 2017?
Hello,
[tex]u_0=4000\\u_1=4000*1.05 (for\ year\ 2011)\\\\u_n=4000*1.05^n\\So:\\year\ 2017: u_7=4000*1.05^7=5628,401690625\ \approx{5628}[/tex]
Using an exponential function, the number of students y in the graduating class 7 years after 2010 i.e. in 2017 will be 5628.4
What is an exponential function?y = abˣ, where a is the initial population, b is the rate, and x is the time, is the standard exponential function.
How to solve this problem?Here initial student population = 4000.
Rate = 5% = (100 + 5)/100 = 1.05
Time = 7 years.
Now, in 2017, the population will be y = 4000 * (1.05)⁷ = 5628.401691 ≅ 5628.4.
Therefore, using an exponential function, the number of students y in the graduating class 7 years after 2010 i.e. in 2017 will be 5628.4
Learn more about exponential function here -
https://brainly.com/question/14551308
#SPJ2
A soccer team made $575.75 from selling popcorn at a concession stand during a tournament. The popcom cost the
team $65.00. What is the amount of money earned for each player if the profit is divided equally among the 15
players? Round to the nearest cent.
O S34.05
0 $42.72
57.661.25
59.611.25 hurry I'm being timed!
Answer:
$34.05
Step-by-step explanation:
I don’t know the answer so ignore the checked box
Answer:
CDHG
Step-by-step explanation:
Because you can go in that order and be able to get to the next letter. In the other option you cannot
PLEASE HELP NEED HELP W ALGEBRA 2 QUESTION!!
the graph of f(x) = 3 sqr root x+8 is shown which statement is true
1. The function is only increasing x > -8
2. The function is only increasing when x > 0
3. The function is always decreasing
4. The function is always increasing
Pls say what number choice in your answer! Thanks!
Answer:
2. increasing when x > 0
the result of root is a positive number
and since there is no value of neg number in roots so it's increasing when x>0
plus in zero it self has a positive number (0,8)
but u cannot find either it's increasing or decreasing in zero bcoz in first derivative test
when x =0
y= not defined
What is the largest prime number less than 200?
Answer:
199Step-by-step explanation:
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.
A prime number is a number that has only two divisors: 1 and itself.
Exaples:
2, 3, 5, 7, 11, 13, 17, 19, 23 ...
We know: all primes except 2 are odd.
Let's check the number 199:
We know:
13² = 13 · 13 = 169 < 200
17² = 17 · 17 = 289 > 200
199 : 3 is not an integer
199 : 5 is not an integer
199 : 7 is not an integer
199 : 11 is not an integer
199 : 13 is not an integer
199 : 17 is not an integer
Therefore 199 is thelargest prime number less than 200.
Find the perimeter of ΔNOP. Round your answer to nearest tenth if necessary. Figures are not necessarily drawn to scale
Answer:
P = 157.5 units
Step-by-step explanation:
hi can you help me in mate plis simplify the following algebraic expressions
Answer:
[tex] \frac{3 {x}^{2} }{ {y}^{2} {z}^{6} } [/tex]
Step-by-step explanation:
I have attached the explanation above. hopefully this will help
what s the equation of the line through the origin and (-2, 3)
Answer:
y=[tex]\frac{-3x}{2}[/tex]
Step-by-step explanation:
Hi there!
We need to find the equation of the line that passes through the origin (the point (0,0)) and (-2,3)
There are 3 ways to write the equation of the line, although the most common way is slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
So we need to find the slope of the line first
The formula for the slope (m) calculated from two points [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are points
We have the needed information to calculate the slope, but let's label the values of the points to avoid any confusion
[tex]x_{1}[/tex]=0
[tex]y_{1}[/tex]=0
[tex]x_{2}[/tex]=-2
[tex]y_{2}[/tex]=3
Now substitute their values into the equation and find m
m=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m=[tex]\frac{3-0}{-2-0}[/tex]
subtract
m=[tex]\frac{3}{-2}[/tex]
so the slope of the line is [tex]\frac{3}{-2}[/tex]. It can also be rewritten as [tex]\frac{-3}{2}[/tex]
Here is the equation of the line so far:
y=[tex]\frac{-3x}{2}[/tex]+b
we need to find b
As the equation passes through both (0,0) and (-2,3), we can use either one of them to solve for b
Let's take (0,0) for this case
Substitute 0 as x and 0 as y
0=-[tex]\frac{3}{2}[/tex](0)+b
multiply
0=0+b
add 0 to both sides
0=b
So b is 0
The equation of the line therefore is y=[tex]\frac{-3x}{2}[/tex]
Hope this helps!
Hello can someone help me with this problem
A 4-column table with 4 rows. Column 1 is labeled number of friends with entries 3, 5, 7, 9. Column 2 is labeled Carnival Cost with entries 51.5, 75.5, 99.5, 123.5. Column 3 is labeled Aquarium Cost with entries 43.5, 72.5, 101.5, 130.5. Column 4 is labeled Wave Pool Cost with entries 50.25, 61.25, 85.75, 110.25.
Gale wants to compare the cost of the events.
Aquarium: $14.50 each ticket
Carnival: c = 15.5 + 12f
Wave pool: $16.75 each, but $12.25 each for groups larger than 4
Which of the claims Gale makes is true?
The table represents all possibilities.
The carnival always costs the least.
The Aquarium always costs the most.
(7, 101.5) is an ordered pair used to represent the aquarium cost.
Answer:
D.(7, 101.5) is an ordered pair used to represent the aquarium cost.
Hope it helps :)
Step-by-step explanation:
Answer: it is d - (7, 101.5) is an ordered pair used to represent the aquarium cost
Step-by-step explanation: got it right on edge 2022
find the next four terms of the sequence 5, 4, 9, 13, 22
Answer:
38
Step-by-step explanation:
The first term of the given sequence is 9.
The second term is 13
= 9 + 4 . = 9 + 2 × 2.
The next number is 22.
= 13 + 9 . = 13 + 3 × 3 .
In the same way the next number of the given sequence will be
22 + 4 × 4 .
= 22 + 16 = 38.
A company uses two vans to transport
workers from a free parking lot to the
workplace between 7:00 and 9:00 a.m.
One van has 6 more seats than the other.
The smaller van makes two trips every
morning while the larger one makes only
one trip. The two vans can transport 57
people, maximum.
How many seats does the larger van have?
Answer:
The larger van has 23 seats
Step-by-step explanation:
Create a system of Equations:
1. Define variables.
> let x=small van and y=larger van
2. create 2 equations based on the information given.
> y = 6 + x
> 2x + y = 57
3. Use any method to solve
Substitution: 2x + (6 + x) = 57. x=17
now plug x in to the original equation to solve for y (the larger van)
y = 6 + 17 and y = 23
Elimination: 2y = 12 + 2x
y = 57 - 2x
3y = 69 and y = 23
Find the measure of the indicated angle.
2x + 40 = 180
2x = 140
x= 70
answer is 70
can anyone answer this? (2y²-3xy)÷y.
Answer:
2y - 3x
Step-by-step explanation:
Given
(2y² - 3xy) ÷ y
Divide each term on the numerator by y , that is
[tex]\frac{2y^2}{y}[/tex] - [tex]\frac{3xy}{y}[/tex] ( cancel y on numerator/ denominator of both fractions )
= 2y - 3x
If y is proportional to x, find the missing number.
A. 15
B. 12
C. 16
D. 18
HELPPP!!!!
Answer:
C. 16
Step-by-step explanation:
5 is half of 10, so 8 should be half of the next number.
Answer:
C. 16
Step-by-step explanation:
[tex] \frac{y}{x} = \frac{10}{5} = \frac{?}{8} \\ \frac{2}{1} = \frac{?}{8} [/tex]
cross multiplying
[tex]16 = ?[/tex]
so the missing number is 16
Drag the tiles to the correct location on the image.Not all tiles will be used.
Answer:
Given,
side=4√5 millimetres
=4×4√5
=16√5
Perimeter= 16√5 milimetre
Area= side× side
=4√5 × 4√5
=80
Area= 80 square milimeters
------------------------------
hope it helps...
have a great day!
Answer:
solution:-Given,
side=4√5 mm
=4×4√5
=16√5
Perimeter= 16√5 mm
Area= side× side
=4√5 × 4√5
=80
Area= 80 square milimeters
------------------------------
hope it is helpful to you
stay safe healthy and happy
please tell me the answer to this, thanks
Step-by-step explanation:
Hey there!
The equation is: 2x + 3y -12=0 (i)
From the given equation;
Slope (m) = (-coeff.of X)/(coeff.of y)
m = -2/3
Now; Let the missing component be "a".
The equation also can be written in;
The equation also can be written in;(y-8) = -2/3(x-a) (using one point formula)
3y - 24 = -2x + 2a
2x +3y -2a -24 = 0………(ii)
Since both equation are made from same coordinates, equating equation (i) and (ii).
2x + 3y -12= 2x +3y -2a -24
Cancel like terms,
-2a - 24 = -12
or, -2a = 12
or, a = -6.
Therefore, the missing value is -6.
Check:
Putting the value "a" in equation (ii).
2x + 3y -2(-6) -24 = 0
or, 2x+3y -12 = 0 (which is equal to equation (i).
Hope it helps!
What is the slope of the line represented by the equation y-6 = 5(x-2)?
O A. 6
O B. 5
O C. -5
O D. 2
Answer:
B
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 6 = 5(x - 2) ← is in point- slope form
with slope m = 5 → B
Find x if : (-3/7)^-19 ÷ (-3/7)^8 = (-3/7)^- 2x+1
Answer:
x=14
Step-by-step explanation:
(-3/7) power (-19-8)= (-3/7) power -2x+1
-19-8= -2x+1
-27= -2x+1
-27-1= -2x
-28= -2x
x=28/2
x=14
PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS ANSWERRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
Answer:
ssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
¼. 1000
Step-by-step explanation:
25% = 25/100
= 1/4
Therefore,
25% of 1,000 is the same as
1/4. 1000
Which equation in slope-intercept form represents a line that is parallel to y=-4x-5 and passes through the points (0,0)?
Answer:
y = 0x
Step-by-step explanation:
y=-4x-b
0 = -4(0) + b
0 = 0 + b
0
Hello, Brainly community!
This question is for all of those Calculus people out there.
The volume of a swimming pool is changing with respect to time, such that the volume is given by W(t), where W(t) is measured in cubic centimeters and t is measured in seconds. A tangent line is shown for W(t) at t = 3 seconds. Determine the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
(I've narrowed down the answer choices to 2, and just really need to find the right way of thinking to find the answer)
(A) W(lim t) as t goes to 3.
(B) [W(3.1) - W(2.9)] / 0.2.
Thank you in advance!
Answer:
(B) [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]
General Formulas and Concepts:
Calculus
Limits
Derivatives
The definition of a derivative is the slope of the tangent line.Derivative Notation
Instantaneous Rates
Tangent Line: [tex]\displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}[/tex]Step-by-step explanation:
Since we are trying to find a rate at which W(t) changes, we must find the derivative at t = 3.
We are given 2 close answer choices that would have the same numerical answer but different meanings:
(A) [tex]\displaystyle \lim_{t \to 3} W(t)[/tex](B) [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the rate at which the volume would be changing and it is not a derivative.
If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a derivative at t = 3, and a derivative tells us what rate something is changing.
∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
How do I solve for X HELP
Answer:
x = 4 degrees
Step-by-step explanation:
The two angles have the same measurement. They are opposite angles.
26x + 7 = 31x - 13
Group like terms:
26x - 31x = -13 - 7
-5x = -20
x = 4
Check if you want to make sure.
Step-by-step explanation:
[tex]here \: is \: your \: solution : - \\ \\ both \: angles \: are \: equal \: (vertical \: anges) \\ \\ 26x + 7 = 31x - 13 \\ \\ solving \: the \: equation \: \\ \\ 26x - 31x = - 13 - 7 \\ \\ - 5x = 20 \\ \\ x = -20 \div 5 \\ \\ x = \: 4 \: degrees \: \: \: \:(Answer ✓✓✓( \\ \\ \huge\mathcal\blue{happy \: life (. ❛ ᴗ ❛.) }[/tex]
PLEASE HELP.
if v1….
please answer
HCF of 16 and 40
Answer:
8
Step-by-step explanation:
3. Una forma de dividir facilmente entre 4 es dividiendo dos veces entre 2.Observa el ejemplo y aplica el procedimiento utilizado
Ejemplo: 568÷4=(568÷2)÷2
= 284 ÷2
= 142
a) 936÷4= c)2 812÷4=
b) 2 084÷4= d)3 720÷4=
3
49:51
What is the solution to the system that is created by the equation Y =-X+6 and the graph shown below?
10
8
6
4
-10-8-6-44
2
4 6
8 10 x
4
46
-8
10
O (-8,-4)
O (-4,-2)
(4.2)
(6.3)
Mark this and retum
Save and Exit
Next
Submit
PLEASE HELP I'LL MARK BRANLIEST!
Activity Gina is playing dominoes with her family. She and her brother, Greg, are playing as a team (team A) against their parents (team B). The table shows how many points the two teams have scored in each round. Gina is keeping track of the scores and wants to know which measures of center and spread best represent each team’s data.
Team A: 15 20 15 5 10 15 10 15 5 20
Team B: 20 15 25 30 20 25 0 15 25 30
Part B What is the mean score for team A? Show your calculation.
Answer:
Mean of team A is 13
Step-by-step explanation:
I hope it helps:)
Help please
If the measure of angle 6 is 140 degrees and the measure of angle 7 is (x + 30) degrees, what value of x will guarantee n ∥ m?
Answer:
x = 10
Step-by-step explanation:
If n // m , then angle 6 and angle 7 are co interior angles and they are supplementary.
∠6 + ∠7 = 180
140 + x +30 = 180
x + 170 = 180
x = 180 - 170
x = 10
