Answers
(a) Differentiate [tex]s(t)[/tex] to get the velocity.
[tex]s(t) = \cos(t^2 - 1)[/tex]
Use the chain rule.
[tex]u = t^2 - 1 \implies \dfrac{du}{dt} = 2t[/tex]
[tex]s(u) = \cos(u) \implies \dfrac{ds}{du} = -\sin(u)[/tex]
[tex]\implies \dfrac{ds}{dt} = \dfrac{ds}{du} \dfrac{du}{dt} = \boxed{-2t\sin(t^2-1)}[/tex]
(b) Evaluate the derivative from (a) at [tex]t=0[/tex].
[tex]\dfrac{ds}{dt}\bigg|_{t=0} = -2\cdot0\cdot\sin(0^2-1) = \boxed{0}[/tex]
(c) The object is stationary when the derivative is zero. This happens for
[tex]-2t \sin(t^2 - 1) = 0[/tex]
[tex]-2t = 0 \text{ or } \sin(t^2 - 1) = 0[/tex]
[tex]t = 0 \text{ or } t^2 - 1 = n\pi[/tex]
(where [tex]n[/tex] is any integer)
[tex]t = 0 \text{ or } t = \pm\sqrt{n\pi + 1}[/tex]
We omit the first case. In the second case, we must have [tex]n\ge0[/tex] for the square root to be defined. Then in the given interval, we have two solutions when [tex]n=\in\{0,1\}[/tex], so the times are
[tex]t_1 = \sqrt{1} = \boxed{1}[/tex]
[tex]t_2 = \boxed{\sqrt{\pi + 1}} \approx 2.035[/tex]
(d) A picture is worth a thousand words. See the attached plot. If you're looking for a verbal description, you can list as many features of the plot as are relevant, such as
• intercepts (solve [tex]s(t)=0[/tex] to find [tex]t[/tex]-intercepts and evaluate [tex]s(0)[/tex] to find the [tex]s[/tex]-intercept)
• intervals where [tex]s(t)[/tex] is increasing or decreasing (first derivative test)
• intervals where [tex]s(t)[/tex] is concave upward or concave downward (second derivative test; at the same time you can determine any local extrema of [tex]s(t)[/tex], which you can see in the plot agrees with the critical points found in (c))
Related Questions
R, S, and T are collinear. S is between R and T. RS =2w + 1, ST = w - 1, and RT = 18. Use the Segment Addition Postulate to slove for w. Then determine the lenght of RS.
Answers
R, S, and T are collinear . Then 13 is the length of RS.
What do collinear points mean?
Collinear points are those that are situated along a single or shared straight line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either near or far from one another.The question to know
RS + ST = RT
RS = w + 1 , ST = w - 1
RT = 18
2w + 1 + w - 1 = 18
3w = 18
w = 18/3
w = 6
RS = 2 * 6 + 1 = 13
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[tex]\sqrt{180x^{25}y^{23}z^{39}[/tex]
Answers
[tex]6[/tex][tex]x^{12}[/tex][tex]y^{11}[/tex][tex]z^{19}[/tex][tex]\sqrt{5xyz}[/tex]
How do you define the square root of a number?
In mathematics, a square root of a number x is a number y such that y^2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 42 = (−4)2 = 16.
[tex]\sqrt{180x^{25 } y^{23} z^{39}[/tex]
[tex]180 = 2*2*3*3*5\\x^{25} = x*x*x........*x 25 times\\y^{23}= y*y*y.........*y 23 times\\ z^{39} = z*z*z........*z 39 times[/tex]
we have
square terms comes out
x is 25 times so we can write x as [tex](x^{12})^{2}[/tex] [tex]*[/tex][tex]x[/tex] therefore [tex]x^{12}[/tex] comes out and only left inside is x
similarly [tex](y^{11})^{2}[/tex] [tex]*y[/tex] therefore [tex]y^{11}[/tex] comes out and only left inside is y
[tex](z^{19})^{2} *z[/tex] therefore [tex]z^{19}[/tex] comes out and left inside is z
then the expression become
[tex]6[/tex][tex]x^{12}[/tex][tex]y^{11}[/tex][tex]z^{19}[/tex][tex]\sqrt{5xyz}[/tex]
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Complete the sentence. The distance between 4 and 17 is
Answers
Answer:
13
Step-by-step explanation:
You just have to minus 17 with 4 to get the answer!
Distance = 17 - 4 = 13 units
Read the problem below and find the solution. Draw a diagram on your own
paper to help solve it.
A group of 29 friends gets together to play a sport. First, people must be
divided into teams. Each team has to have exactly 4 players, and no one can
be on more than one team. How many teams can they make? (It is possible
that not everyone can be on a team.)
(Do not include units in your answer.)
Answer here
Answers
Answer:
yes
Step-by-step explanation:
28/4 = 7 teams
1 is left without a team
Find the slope of the line passing through the points (-7, 8) and (2, -8).
Answers
-16/9
Help please I cant find my answer
Answers
Answer:
see explanation
Step-by-step explanation:
1
4(5 + 3n) - 7 ← distribute parenthesis by 4
= 20 + 12n - 7 ← collect like terms
= 12n + 13
2
6 - (10n + 8) ← distribute parenthesis by - 1
= 6 - 10n - 8 ← collect like terms
= - 10n - 2
combining (adding) the 2 expressions
12n + 13 - 10n - 2 ← collect like terms
= 2n + 11
If the sum of squares for a sample containing 51 items equals 400, what is the standard deviation? 8.00 7.84 4.47 2.83
Answers
The standard deviation is 2.83 if the sum of squares for a sample containing 51 items equals 400 option (D) is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{n-1}[/tex]
SD is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
∑(x(i) - X)² = 400
n = 51
SD = √(400/51-1)
SD = √8
SD = 2.828 ≈ 2.83
Thus, the standard deviation is 2.83 if the sum of squares for a sample containing 51 items equals 400 option (D) is correct.
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Help please Algebra
Answers
Answer: y=-x+17
-1 ==> slope
(0, 17)
Step-by-step explanation:
x+y=17
x-x+y=17-x
y=-x+17
-x/x=-1 ==> slope
y=-x+17
y=-(0)+17
y=17 ==> (0, 17)
Evan invested $2500 in the stock market.
Four months later, the value of the
investment dropped to $2248. Find the
average monthly change in the value of
the investment.
Answers
Answer:
63
Step-by-step explanation:
Value dropped = 2500 - 2248 = 252
divide 252 across 4 months
252/4 = 63
The average monthly change in the value of the investment is $63.
Given that, Evan invested $2500 in the stock market. Four months later, the value of the investment dropped to $2248.
What is the investment?Investment definition is an asset acquired or invested in to build wealth and save money from the hard earned income or appreciation. Investment meaning is primarily to obtain an additional source of income or gain profit from the investment over a specific period of time.
Now, change in investment is
2500-2248 = 252
The average monthly change
= 252/4
= 63
Hence, the average monthly change in the value of the investment is $63.
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Noah is trying to bisect angle BAC. He draws circles of the same radius with centers B and C and then uses one of the points of intersection for his ray. What mistake has Noah made in his construction
Answers
The mistake done by Noah in his construction is that; length of the line segment AB and AC should be equal.
How to bisect an angle?
The steps in bisecting an angle say PQR is as follows;
Start with angle PQR that we will bisect.
1. Place the compasses' point on the angle's vertex Q.
2. Adjust the compasses to a medium wide setting. The exact width is not important.
3. Without changing the compasses' width, draw an arc across each leg of the angle.
4. The compasses' width can be changed here if desired. Recommended: leave it the same.
5. Place the compasses on the point where one arc crosses a leg and draw an arc in the interior of the angle.
6. Without changing the compasses setting repeat for the other leg so that the two arcs cross.
7. Using a straightedge or ruler, draw a line from the vertex to the point where the arcs cross.
8. This is the bisector of the angle ∠PQR.
Therefore, the mistake done by Noah is that length of the line segment AB and AC should be equal in order to bisect it.
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14) Out of the following options, pick the one that
can be expressed as a rational number.
a) 1.16321632...
b) 0.00120345...
c) 5.672101234 ...
d) 2.75757575...
i have no idea what this means
Answers
PLEASE HURRY UP
Lamar needs to buy plastic forks. Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3.97.
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
Round your answers to the nearest cent.
Answers
Answer:
A = .05 and B = .08 so A is the better buy
Step-by-step explanation:
In each case, divide total cost by number of units to get unit cost.
tommy do this instead then
Answers
Answer: (2) 1010025
Step-by-step explanation:
Let's find the sum of 1+3+5+7+...+2007+2009
Let's use the formulas for an arithmetic progression:
[tex]a_1=1\ \ \ a+2=3\\d=a_2-a_1\\d=3-1\\d=2[/tex]
[tex]a_1 =1\ \ \ \ a_n=2009\\a_n=a_1+(n-1)d\\\Rightarrow\ 2009=1+(n-1)2\\\Rightarrow \ 2009=1+2n-2\\\Rightarrow\ 2009=-1+2n\\\Rightarrow\ 2010=2n\\[/tex]
Divide both parts of the equation by 2:
[tex]1005=n[/tex]
Hence,
[tex]\displaystyle\\S=\frac{a_1+a_n}{2} n\\\\S=\frac{1+2009}{2}1005\\\\S=\frac{2010}{2} 1005\\\\S=1005*1005\\\\S=1010025[/tex]
A particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s. find its displacement during this time interval. answer in units of m\
Answers
For a particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s, the displacement is -11.53 m
For given question,
A particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s.
We can observe that, for t1 = 1.82 s and t2 = 3.81 s
object is moving from right to left along the x axis.
We know that, the displacement of a particle moving in a straight line is the change in its position.
so, d = 4.97 - 16.5
d = -11.53
The negative sign indicates that the object is moving from right to left along the x axis for t1 = 1.82 s and t2 = 3.81 s
Therefore, for a particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s, the displacement is -11.53m.
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In a recent national football league season tom brady philip rivers and aaron rodgers throw a total of 94 touchdown passes if we first had two more touchdowns and roger and six fewer than brady how many did brady have
Answers
Answer:
88 is the answer to the question
Initial estimates of the probabilities of events are known as _____ probabilities.
Answers
Initial estimates of the probabilities of events are known as prior probabilities.
Prior probability, in Bayesian statistics, is the probability of an event before new data is collected. This is the best rational assessment of the probability of an outcome based on the current knowledge before an experiment is performed.
The prior probability of an event will be revised as new data or information becomes available, to produce a more accurate measure of a potential outcome. That revised probability becomes the posterior probability and is calculated using Bayes' theorem. In statistical terms, the posterior probability is the probability of event A occurring given that event B has occurred.
The prior probability is the probability assigned to an event before the arrival of some information that makes it necessary to revise the assigned probability. The revision of the prior is carried out using Bayes' rule. The new probability assigned to the event after the revision is called posterior probability.
Initial estimates of the probabilities of events are known as prior probabilities.
To know more about " Prior Probabilities"
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The domain and the range of the reciprocal function are the set of all real numbers. True or false?.
Answers
False. All real numbers, with the exception of 0 because f (0) = 1 0, fall inside the reciprocal function's domain and range. Y cannot be 0 if x cannot, either.
What are real numbers?In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are used in measurements of continuously varying quantities such as size and time. They are distinguished from imaginary numbers, which use the symbol I or the square root of 1, by the word "real." A complex number has a real (1) and an imaginary I component, like 1 + i. The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.
Contrary to rational numbers, whose decimal expansions always contain a digit or group of digits that repeats itself, such as 1/6 = 0.16666... or 2/7 = 0.285714285714, irrational numbers have decimal expansions that do not repeat themselves. Since there is no regularly repeating group in the decimal produced as 0.42442444244442, it is irrational.
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the points (-3,1), (-1,1), (0,-1), (-1,-3), (-3,-3) and (-4,-1) are vertices of a polygon. what type of polygon is formed by these points?
Answers
Answer:
10
Step-by-step explanation:
Bxhwbdjnqbxkabxjb iqbdnannsmxns
What is your monthly take home pay if your take home pay is $897.84 every monday
Answers
I need help 10-25 please help asap step by step
Answers
please help me please
and thx for who will help or he did and its ok if u don't know the ans
Answers
Answer:
I graphed the two equations for you. The point one which is selected is the solution to the system of equations.
Step-by-step explanation:
Please see attachment below.
Hope this helps!
Please mark as brainliest if this helps!
Frank was born in 1933 and died in 1946 at the age of 57. How can this be?
Answers
Answer:
Frank was born in 1933 and died in 1946 at the age of 57. 1933 and 1946 are not years but just room or ward numbers.
EXPLANATION:
The numerical 1933 and 1946 do not signify the year of birth or death. No where in the question is the word 'years' mentioned. Thus 1933 signifies either the room number or the ward number of the hospital Frank was born in.
Similarly 1946 is the room or ward number where Frank died. Hence his age is irrelevant with respect to 1933 and 1946. His related age of 57 thus has nothing to do with them.
Answer:
The numerical 1933 and 1946 do not signify the year of birth or death. Nowhere in the question is the word ‘years’ mentioned. Thus 1933 signifies either the room number or the ward number of the hospital Frank was born in.
Step-by-step explanation:
help help help help help help help help help help help help help help help help help help help help help help help help help help
Answers
Answer:
1. [tex](x-6)^{2}[/tex]
2. [tex](x +11)^2[/tex]
3. [tex](x-4y)^{2}[/tex]
4. [tex](5x - y)^2[/tex]
Step-by-step explanation:
1. [tex]x^{2} -12x +36[/tex] ---> [tex](x-6)^{2}[/tex]
2. [tex]x^{2} +22x + 121[/tex] ---> [tex](x +11)^2[/tex]
3. [tex]x^{2} -8xy+16y^{2}[/tex] ---> [tex](x-4y)^{2}[/tex]
4. [tex]25x^2-10xy + y^2[/tex] ---> [tex](5x - y)^2[/tex]
PLEASE HELP ASAP!!
Answers
The equation of the graph is (x-3)(x+1), the y-intercept of y=[tex]x^{2} -5x+4[/tex] is "4" and the factors of y=[tex]x^{2} -5x+4[/tex] are (x-4) ad (x-1)
Given that a graph touch x-axis at 2 points i.e. 2 roots are there for given graph.The graph touches the x-axis at (3,0) and (-1,0) it implies x=3 and x=-1 are the solutions the equation,(x-3) and (x+1) are factors of equation
Therefore,the equation of graph is (x-3)(x+1).
Given the equation y=[tex]x^{2} -5x+4[/tex]
The y-intercept is defined as the graph passing a fixed point at x=0 line
i.e.(0,c) pass through it . c is the y-intercept
c=0-0+4
c=4
Therefore,The y-intercept of the equation y=[tex]x^{2} -5x+4[/tex] is 4
Factorising y=[tex]x^{2} -5x+4[/tex]
⇒ y=[tex]x^{2} -5x+4[/tex]
⇒y=[tex]x^{2} -x-4x+4[/tex]
⇒y=x(x-1)-4(x-1)
⇒y=(x-4)(x-1)
Therefore, the factors of y=[tex]x^{2} -5x+4[/tex] are (x-4) and(x-1)
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Better taxi service charges $3.00 for the first mile plus $0.20 for each additional mile. Best
taxi service charges $6.00 for the first two miles plus $0.10 for each additional mile. How
many miles will a person travel in order to spend an equal amount of money using either
service?
PLEASE AN EXPERT THIS IS WORTH 50 POINTS!!!!!!!!!
Answers
Can someone help me on this
Answers
Answer:
one solution
Step-by-step explanation:
-7 works
7 does not
(5x+3)(5x-3) what is the answer if multiplied
Answers
Answer:
25x^2 -9
Step-by-step explanation:
(5x+3)(5x-3)
FOIL
first 5x*5x = 25x^2
outer 5x*-3 = -15x
inner 3*5x = 15x
last = 3*-3 = -9
Add them together 25x^2 -15x+15x -9
Combine terms 25x^2 -9
Answer:
[tex] \sf25 {x}^{2} - 9[/tex]
Step-by-step explanation:
We can use Foil method to find the answer for this expression.
(5x + 3) (5x - 3)
That is:
F --> First ---> (5x)(5x)
O --> Outside ---> (5x) (-3)
I --> Inside ---> (3)(5x)
L --> Last ---> (3) (-3)
And now we have to add those terms together while combining like terms.
[tex] \sf(5x)(5x) + (5x)( - 3) + (3)(5x) + (3)( - 3) \\ \sf25 {x}^{2} - 15x + 15x - 9 \\ \sf25 {x}^{2} - 9[/tex]
Please help with algebra!
Answers
Answer:
[tex]x=29[/tex]
Step-by-step explanation:
These two angles add up to 180 degrees. We can make an equation saying that [tex](2x+6)+4x=180[/tex]. Simplifying, we get [tex]6x+6=180\\[/tex].
Now when we subtract 6 from both sides we get [tex]6x=174[/tex]. Then we divide both sides by 6 to get our final answer: [tex]x=29[/tex]
Hope this helps!
What is 0.2302 to the thousands place
Answers
0.7+y=−1.34 Please solve it I tried 0.64 and it said it was incorrect.
Answers
Answer:
-2.04
Step-by-step explanation:
it'll be
-1.34 - 0.7 = y
- 2.04 = y
