Answers
Answer:
y=-x+pi/3+sqrt(3)/2
Step-by-step explanation:
*I assume you are asking for help on part a because the other question is a calculator question.*
We want to find tangent line to y=2sin(x)cos(x) at x=pi/3.
First I prefer to use y=sin(2x). (Double angle identity: sin(2x)=2sin(x)cos(x) .)
Differentiate using chain rule:
y'=2cos(2x)
y' gives us the slope for any tangent along our curve.
So at x=pi/3, the slope is 2cos(2×pi/3)=2cos(2pi/3)=2(-1/2)=-1.
We also need to know a point our line to find the equation of our line.
At x=pi/3, y=sin(2×pi/3)=sin(2pi/3)=sqrt(3)/2.
So a point on our line is (pi/3, sqrt(3)/2).
So by point-slope form of a line we have
y-y1=m(x-x1)
y-sqrt(3)/2=-1(x-pi/3)
Distribute:
y-sqrt(3)/2=-x+pi/3
Add sqrt(3)/2 on both sides:
y=-x+pi/3+sqrt(3)/2
Answer:
y= -x+(pi/3)+(sqrt3)/2
Step-by-step explanation:
The given is y=2sin(x)*cos(x)
to take the derivative we will need to use the constant rule (which says when taking the derivative of any constant multiplied by an expression you take the derivative of the function and multiply it by the constant) and the multiplication rule to get
y'=2(sin(x)*-sin(x)+cos(x)*cos(x))
this would simplify to be
y'=-2sin^2(x)+2cos^2(x)
We then substitute in the given x value to find the slope of the tangent line at that point and get
-2sin^2(pi/3)+2cos^2(pi/3)
which simplifies to
-2*3/4+2*1/4
which is -1
Since we have the slope we need to find the y value to go with the original x so that we have a point to use in point slope form. When we substitute pi/3 into the given equation we get (sqrt 3)/2 and have the point (pi/3, sqrt3/2)
now we write the point slope form equation
y-(sqrt3)/2= -(x-pi/3)
y-(sqrt 3)/2 = -x+pi/3
y= -x+pi/3+(sqrt3)/2
you could simplify the last two terms, but I think it is simplest to understand this way.
For b, enter both equations into graphing software or a calculator
Related Questions
URGENT!! A train travels at the rate of 120 km per hour
11. What is its speed in meters per second?
Answers
Answer:
33.333
Step-by-step explanation:
I looked up the answer
Find the surface area 5 8 10
Answers
Answer:
340
Step-by-step explanation:
last time I got this type of question, I either just multiplied it or sum, try doing different methods if u can because I got this question right and I forgot how I did it, but I feel like I multiplied something
Answer:
340
Step-by-step explanation:
which is the result of the surface area
Please please help me I will give you brainless please
Answers
Answer:
[tex]f(x) = 2x - 1 \\ g(x) = 3x \\ h(x) = {x}^{2} + 1 \\ f( g(x)) = 2(3x) - 1 = 6x - 1 \\ f( g( - 3)) = 6( - 3) - 1 = - 19 \\ h(f(x)) = {(2x - 1)}^{2} + 1 \\ h(f(0)) = {(2(0) - 1)}^{2} + 1 \\ h(f(0)) = 2[/tex]
maths is not my thing
Answers
Answer:
If you are looking for the number of faces/sides….
Step-by-step explanation:
1:6
2: 5
3: 8
4:5
5:5
6:5
Hope this helps
Dont forget to smash that heart at the bottom <3
Have a great day,you’re amazing !
Plz Mark Brainliest
Lmk if its right I’m not sure whether number 2 is 4 or 5
I haven’t done shapes in a while .-.
12.5 miles per hour to meters per second
What would it be if you change 12.5 miles per hour to meters per second?
Answers
Answer:
12.5 mph = 5.588 m/s
Step-by-step explanation:
To convert a mile per hour measurement to a meter per second measurement, multiply the speed by the conversion ratio.
Since one mile per hour is equal to 0.44704 meters per second, you can use this simple formula to convert:
Simplify these expressions
а) xxxxx
b) ухухухуху
Answers
[tex]a) \: x \times x \times x = x {}^{3} \\ b) \: y \times y \times y \times y \times y = y {}^{5} [/tex]
Answer:
a) x³
b) [tex]y^{5}[/tex]
What is the name of the property used when multiplying polynomials?
Answers
Answer:
the distributive property
Step-by-step explanation:
it allows us to multiply each term of the first polynomial by each term of the second
PLS mark Brianliest
HELPPPPPPPPPPP. please explain how u got the answer
Answers
Step-by-step explanation:
the key is x = 0.
also I see in the first table no "run-away" effect of some values, so my first suspicion is : it is linear.
let's test it.
a linear function is a line :
y = ax + b
remember, x = 0 is a key element.
y = a×0 + b
-3 = a×0 + b
-3 = b
so, we know, the line function is
y = ax - 3
now, for the a. let's use the next xy pair (1, 1).
1 = a×1 - 3
4 = a
aha ! our line function is therefore
y = 4x - 3
verify with the next 2 points (2, 5) and (3, 9)
5 = 4×2 - 3 = 5 correct
9 = 4×3 - 3 = 9 correct
linear type and equation confirmed.
the second table :
yes, we see relatively big y values compared to the x values.
and the y values follow the powers of 2
so it seems to to be exponential.
64 = 2⁶
32 = 2⁵
16 = 2⁴
8 = 2³
so, while x increases, the powers of 2 decrease. so, we must build something like y = 2^x, but it must run contrary to the increase in x.
the old trick : c-x.
again, x= 0 is key. when x = 0 we get the biggest y (64). that means that gives us c.
64 = 2^(c-x) = 2^(c-0) = 2^c = 2⁶
=> c = 6
so, we suspect the exponential function
y = 2^(6-x)
let's verify with the other points
(1, 32)
32 = 2^(6-1) = 2^(5) = 32 correct
(2, 16)
16 = 2^(6-2) = 2^(4) = 16 correct
(3, 8)
8 = 2^(6-3) = 2^(3) = 8 correct
so, yes, it is the exponential function
y = 2^(6-x)
Ratios
Alexander has a Collection of baseball cards he wants to organize it’s way book use the table to determine how many pages he will hold 234 cards
Answers
Step-by-step explanation:
setup a porportion. Make it pages/cards. Solve for the number of pages, p.
[tex] \frac{3}{18} = \frac{p}{234} [/tex]
reduce the fraction 3/18
[tex] \frac{1}{6} = \frac{p}{234} [/tex]
cross multiply
[tex]6p = 234[/tex]
divide by 6
[tex] \frac{6p}{6} = \frac{234}{6} [/tex]
[tex]p = 39 \: pages[/tex]
There are 39 pages he will hold for 234 cards.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent
to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
Alexander has Collection of baseball cards which he wants to organize.
Now, By the given table;
The ratios for Pages to cards are,
Number of pages : Number of cards
⇒ 3 : 18
After simply;
⇒ 1 : 6
And, 6 : 36 = 1 : 6
Thus, Let number of pages for the given cards = x
Then, By the definition of ratio we get;
x : 234 = 1 : 6
Solve for x as;
x / 234 = 1/6
x = 234/6
x = 39
Thus, There are 39 pages he will hold for 234 cards.
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If y varies directly as x and y = 3 when x = 10, find x when y = 8.
Answers
Answer:
x=26.6 when y=8
Step-by-step explanation:
y=Kx, k=y/x, when y is 3 and x is 10,
k=3/10= 0.3
but when y is 8, x will be given by
x=y/k
x=8/0.3
x=26.6 approximately 27
Graph thee line that represents this equation:
y+2=1/2(x+2)
Answers
Answer:
[tex]y = \frac{1}{2} x - 1[/tex]
Explanation:
The first pic shows the line graphed, while the second pic shows how to turn the equation into proper slope-intercept form.
The only steps the second pic is missing however, is flipping the sides around to be better understood (optional), and more importantly subtracting 2 on both sides in order to move it to the other side, to get 2y = x - 2. And dividing the 2 on both sides to get y by its self, to get:
y = (x-2)/2 , or y = 1/2 x - 2/2 , which if you notice 2/2 makes it equal to one whole so your answer is y = 1/2 x - 1 .
If you like this answer can you please mark me brainliest? :)
There are 40 runners in a race. How many ways can the runners finish first, second, and third?
Answers
Answer:
117600
Step-by-step explanation:
50 x 49 x 48 = 117,600 ways
You have 50 possible for 1st, 49 for 2nd, 48 for 3rd
or
Permutations 50P3 = 117,600
There are total 59280 ways that can the runners finish first, second and third in a race.
What is permutation?
A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
Formula for permutation[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]
Where,
[tex]nP_{r}[/tex] is permutation.
n is total number of objects.
r is number of objects selected.
According to the given question
Total number of runners, n = 40
Total number of runners to be selected for first, second and third position is 3 i.e. r = 3
Therefore,
The number of ways can the runners finish the first, second and third is given by
[tex]40P_{3} = \frac{40!}{((40-3)!} =(40)(39)(38)=59280[/tex]
Hence, there are total 59280 ways that can the runners finish first, second and third in a race.
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PLEASE HELP ME ITS ALGEBRA 2 THANK YOUUUU
Answers
Answer:
10
Step-by-step explanation:
Proprotions:
81/9 = 90/c(?)
so
81c= 9(90)
81c=810
810/81=
10
so c=10
Hope it helped!!
A school counts the number of students taking AMDM and find 225 students taking AMDM. They also count the number of students taking Physics and find 248 students taking the Physics. When they compare the two lists they find 98 student taking AMDM and Physics. What is the probability of a student taking AMDM given they are taking Physics. (Answer in decimal form rounded to the thousandth)
Answers
The probability of a student taking AMDM given they are taking Physics is 39.51%.
Since a school counts the number of students taking AMDM and find 225 students taking AMDM, and they also count the number of students taking Physics and find 248 students taking the Physics, and when they compare the two lists they find 98 student taking AMDM and Physics, to determine what is the probability of a student taking AMDM given they are taking Physics, the following cross multiplication calculation must be performed:
248 = 100 98 = X 98 x 100/248 = X 9800/248 = X 39.51 = X
Therefore, the probability of a student taking AMDM given they are taking Physics is 39.51%.
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slope of the line that passes though (-4.5,7/5) and (3,3.5)
Answers
Answer:
5
Step-by-step explanation:
y2-y1
--------
x2-x1
8/1.5=5
(-10) + 3 please help
Answers
Answer:
The answer is -7 the answer is-7
Answer:
-7
Step-by-step explanation:
(-10)+3
-10+3=-7
-4-6=-10
-10+7=-3
A 35-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces
Answers
Answer:
5 inch - first board
10 inch - second board
20 inch - third board
Step-by-step explanation:
x = first board
board two = 2x
board three =4x
x+2x+4X=35
7x=35
x=5 inch - first board
10 inch - second board
20 inch - third board
√3(√6+√15)
simplify to the simplest form possible
Answers
Answer:
√3(√6+√15)
= 3**1/2(6**1/2 + 15**1/2)
= 3**1/2 · 6**1/2 + 3**1/2 · 15**1/2
= 18**1/2 + 45**1/2
= (2×9)**1/2 + (5×9)**1/2
= 2**1/2 · 9**1/2 + 5**1/2 · 9**1/2
= 2**1/2 · 3 + 5**1/2 · 3
= 3(√2 + √5)
Step-by-step explanation:
A rare disease has been discovered that affects 2 out of every 10,000 trees in a forest, what percent of trees are affected? Plz show work if you can
Answers
Craig likes to collect vinyl records. Last year he had 10 records in his collection.Now he has 12 records.What is the percent increase of his collection
Answers
Answer:The percent increase is 20%.
Step-by-step explanation:
It's fairly simple.
Multiply 10 by (100/10) which is 10 to get 100.
Multiply 12 by 10 to get 120.
120 - 100 = 20
Help please don’t know what to do???!
Answers
Answer:
81.75
Step-by-step explanation:
First, find the median of all the answers.
78.25, 77.75, and 84 = 80 (median)
now that we know 80 is the median, we will add it to our solution.
And still, there is no OTHER TEST in to make this stay 80.
78.25, 77.75, 84, and 80 = 79.125
since this is incorrect, we go higher.
78.25, 77.75, 84 and 81 = 79.625
since this is also incorrect, we go higher.
78.25, 77.75, 84 and 82 = 80.125
since this is higher and incorrect, we will go lower to 81.5.
78.25, 77.75, 84 and 81.5 = 79.875
since this is lower AND 82 is not the correct solution, we will go up by 0.25.
78.25, 77.75, 84 and 81.75 = 80
To check, we will do the problem again.
78.25, 77.75, 84 and 81.75 = 80
So, the solution is 81.75
Find the axis of symmetry for this parabola:
y = -3x2 + 6x + 1
Write your answer as an equation.
Answers
The graph of the given Quadratic equation is attached in the Answer, where we can se that the axis of symmetry is :
x = 1The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing?
Answers
Given :
The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 7 cm and the width is 4 cm .To find :-
how fast is the area of the rectangle increasing?Solution :-
As we know that :-
A = lbTo find the rate :-
d(A)/dt = d(lb)/dt .Differenciate :-
dA/dt = l (db/dt ) + b (dl/dt )Substitute :-
dA/dt = 6*7 + 4* 8 dA/dt = 42 + 32 cm²/s dA/dt = 74 cm²/sGiven f(x)=2x+5, find f(1)
Answers
Answer:
2
Step-by-step explanation:
Anna and Ravi are members of different clubs. Anna's club charges $25 per month. Ravi's club
charges $15 per month but has an annual fee of $40. After how many months will Anna and
Ravi have paid the same total amount?
Pls helppp
Answers
Let:
x = # of months
Anna: 25x
Ravi: 15x + 40
We set them equal to each other as they’d pay the same amount, and solve for x.
25x = 15x + 40
25x - 15x = 15x - 15x + 40
10x = 40
10x/10 = 40/10
x = 4
Tìm đạo hàm Y' = Y'(x) tại X0 = π/4 của hàm số y -= y(x) được cho bởi phương trình tham số
X= arctan t
y = ln t
Answers
about it ok to my house and Elsa and Anna and I are going to my house and I don't know what it's like to my
hello there
im looking for some help here thanks.
Answers
Answer:
divide 2 by 9
the result is 0.2 (repeats so need a bar over the 2) is a repeating decimal.
divide 3 by 10
the result is 0.3, is a terminating decimal.
both are rational and real numbers
Answer:
To change 2/9 to a decimal, divide 2 by 9.
The result, 0.222..., is a repeating decimal.
To change 3/10 to a decimal, divide 3 by 10.
The result, 0.3, is a ____ decimal. (I don't know the answer choices, but it would be the one that is the decimal not repeating).
Both 2/9 and 3/10 are irrational numbers.
Step-by-step explanation:
Write the slope-intercept equation of the line with slope -3/4 passing through the point (-4,5). If necessary, answer using fractions, not decimals.
Answer:
Answers
Answer:
y = -3/4x + 2
Step-by-step explanation:
y = -3/4x + b
5 = -3/4(-4) + b
5 = 3 + b
2 = b
To the nearest hundredth, 11.6/0.95 is about
Answers
Answer:
12.21
Step-by-step explanation:
please answer this, i am so confused
Answers
The bag of dog food would last for 21 days.
The bag contains 42 cups of dog food. If the dog eats [tex]2\frac{1}{3}[/tex] cups everyday, the amount of cup in the bag decreases by [tex]2\frac{1}{3}[/tex] cups everyday. This can be represented with this expression: 42 - [tex]2\frac{1}{3}[/tex]d. Where d represents the number of days.
In order to determine the number of days in which the bag would be emptied, this equation can be used:
Number of days the dog food would last = number of cups in the cup / amount the dog eats each day
42 ÷ [tex]2\frac{1}{3}[/tex]
42 ÷ [tex]\frac{7}{3}[/tex]
42 x [tex]\frac{3}{7}[/tex] = 21 days
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