The approximation using the Trapezoidal Rule and the exact answer using the Fundamental Theorem of Calculus both make sense.
Using the Trapezoidal Rule, we have:
h = (pi - 0)/6 = pi/6
cos(0) + 2(cos(pi/6) + cos(pi/3) + cos(pi/2) + cos(2pi/3) + cos(5pi/6)) + cos(pi)
= 1 + 2(0.866 + 0.5 + 0 - 0.5 - 0.866) + (-1)
= 0
Using the Fundamental Theorem of Calculus, we have:
∫ cos 2x dx = [sin 2x / 2] from 0 to pi
= (sin 2pi / 2) - (sin 0 / 2)
= 0
Since both methods give us an answer of 0, the answer makes sense. The integral of a periodic function over one period, such as cos 2x over [0, pi], evaluates to 0.
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The answers make sense since the integral of cos 2x over [0, pi] is negative and our approximations are also negative. Additionally, the Fundamental Theorem of Calculus confirms our approximation.
Using the Trapezoidal Rule with n=6, we have:
delta_x = (pi - 0) / 6 = pi/6
x_0 = 0, x_1 = pi/6, x_2 = 2pi/6, x_3 = 3pi/6, x_4 = 4pi/6, x_5 = 5pi/6, x_6 = pi
f(x_0) = cos(20) = 1
f(x_1) = cos(2pi/6) = sqrt(3)/2
f(x_2) = cos(22pi/6) = 0
f(x_3) = cos(23pi/6) = -1
f(x_4) = cos(24pi/6) = 0
f(x_5) = cos(25pi/6) = -sqrt(3)/2
f(x_6) = cos(2*pi) = 1
Using the Trapezoidal Rule formula, we have:
integral cos 2x dx = (delta_x/2) * [f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + 2f(x_4) + 2f(x_5) + f(x_6)]
= (pi/36) * [1 + 2sqrt(3)/2 + 2(0) + 2(-1) + 2(0) + 2(-sqrt(3)/2) + 1]
= (pi/36) * [-2 + sqrt(3)]
≈ -0.471
To check our solution, we can use the Fundamental Theorem of Calculus:
F(x) = (1/2) * sin(2x)
F(pi) - F(0) = (1/2) * (sin(2pi) - sin(20)) = 0
F(pi) - F(0) ≈ -0.471
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if f (x) = x² – 3, then find f (8) =
Answer:
61
Step-by-step explanation:
[tex]f(8)=8^2-3=64-3=61[/tex]
Solve equation 3 + p = 8
Answer:
The answer is 5
Step-by-step explanation:
You can do inverse operation which is Subtraction.
8-3 = 5
Answer:
5
Step-by-step explanation:
if its not that i have no idea what to say
You deposit $300 in a savings account. The account earns 10% simple interest per year.
a. What is the interest earned after 8 years?
The interest earned is $? after 8 years.
b. What is the balance after 8 years?
The balance is $?
after 8 years.
Answer:
Step-by-step explanation:
The interest after 8 years is $240
The balance after 8 years is $540
Hope this helps!
Plz, Mark Brainliest!
The interest after 8 years is $240 and the balance after 8 years is $540.
What is Simple interest?Simple interest is calculated by multiplying the daily interest rate by the principal, by the number of days that elapse between payments.
Given that, You deposit $300 in a savings account. The account earns 10% simple interest per year.
SI = P*R*T/10
Where P = principal
R = rate
T = time
a) The interest earned after 8 years:-
SI = 300*10*8/100 = $240
b) The balance after 8 years:-
Amount = 300+240 = $540
Hence, The interest after 8 years is $240 and the balance after 8 years is $540.
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I am trying to find the measure of angle KRD angle KRD: 5r+42 angle: DRB: 4r+66 I don't really understand this
Based off what you have I can't solve it
Step 1: Give an example of an equation that has a variable on both sides. (YES YOU GET TO MAKE UP YOUR OWN EQUATION) Step 2: After you create your equation, explain with words how you would solve your equation. Make sure you explain each step and the properties you would use. Your answer should be in paragraph form. *
Answer:
3m = 3m
Step-by-step explanation:
Divide both sides by 3, and you get m = m
disappointing but this was all i could think of sorry
Examine this expanded form.
1
(a)(a)(a)(a)(a)(a)
Which is the expression in exponential form?
6-a
6a
a-6
6a-1
Answer:
*drumroll* It's C. a-6,babes <33
Step-by-step explanation:
Did this in Edge,hope it helps >3<
Answer:
C
Step-by-step explanation:
edge 2021
Sushil rolls a fair dice 138 times.
How many times would Sushil expect to roll an even number?
Answer:
69?
Step-by-step explanation:
Find the circumference for the circle below. Round your answer to the nearest
tenth
radius = 17
Amanda has $56.10 in her bank account in March. In May she has 4 times as much money in her account than she did in March. In June she adds $75.22 to her account. How much money does Amanda have in her account in June?
Answer:
$299.62
Step-by-step explanation:
Amanda has $56.10 in his bank account in march
In May he has 4 times this money
= 56.10×4
= 224.4
In June she add $75.22 to the money
= 224.4 + 75.22
= 299.62
Hence in June Amanda has $299.62 in her account
(3)
23
-1
2
0
d
2
e
4.
f
d =
e-
f=
Answer:
Step-by-step explanation:
this is the formula using a calculator hit 2nd then x^2 and the number you want then enterPlease help I’ve been on for 1/2 hours
1/2a-4 * = times
1/2*(a-8)
I am very behind in edge, is anyone willing to help me?
Answer:
Whats the question?
Answer:
Yeeeee
Step-by-step explanation:
The cost of 7 scarves is $85.75. What is the unit price
Answer:
The cost of 1 scarf is $12.25 each.
Step-by-step explanation:
3 A pair of vertical angles is formed as shown.
175°
(5x + 30)
Which best represents the value of ?
A 29
B 1
C31
D41
Answer:
A - 29
Step-by-step explanation:
5x + 30 = 175
5x +30 -30 = 175 - 30
5x = 145
5x ÷ 5 = 145 ÷ 5
X = 29
40 is what % of a
Plz help
Answer:
Step-by-step explanation: To calculate the percentage, multiply this fraction by 100 and add a percent sign. 100 * numerator / denominator = percentage . In our example it's 100 * 2/5 = 100 * 0.4 = 40 .
in 10 years time a father Will be twice as old as his daughter.10 years ago he was six time as old as his daughter.How old is each now
Answer:
Step-by-step explanation:
let fathers age now be x
daughters age now be y
10 years hence
(x+10)= 2(y+10)
x+10 = 2y+20
x-2y=10
10 years ago
(x-10)= 6(y-10)
x-10 = 6y-60
x-6y=-50
x-2y=10
x-6y=-50
subtract the equations
4y=60
y=15 daughter's age now
substitute y in x-2y=10
so x=40 present father's age
pls mark brainliest
Answer:
Let the age 10 years ago of daughter be ( x years ) and age of father would be ( 6x years )
After 10 years, age of father = ( 6x + 10 + 10 )
= ( 6x + 20 ) years
And Age of daughter will be = ( x + 10 + 10 )
= ( x + 20 ) years
ATQ,
6x + 20 = 2( x + 20 )
=> 6x + 20 = 2x + 40
=> 6x - 2x = 40 - 20
=> 4x = 20
=> x = 5
Hence, Present age of daughter = ( x + 10 )
= ( 5 + 10 )
= 15 years
Present age of father = ( 6x + 10 )
= 6( 5 ) + 10
= 30 + 10
= 40 years
Step-by-step explanation:
your answer Miss.
TWENTY POINTS
PLEASE HELP ASAP DONT STEAL POINTS
Multiplying the radical by a number between 0 and 1 causes the graph of the parent function ( f(x)= √x ) to ___________.
Answer:
FOR YOU LOVE
Step-by-step explanation:
If a function is defined by a radical expression, we call it a radical function. The square root function is f(x)=√x f ( x ) = x . ... A radical function is a function that is defined by a radical expression.
THE PIC IN ABOVE IS EQUATION TRY TO ANSWER IT
PLEASS MARK ME AS BRAINLIEST LOVE YOU STAY SAFE
Please help!
Given A= [2 -7 6 1] and B= [-9 5 1 -1]
IT X-A=B, what is X?
Answer:
Option A, Or Option 1
Step-by-step explanation:
-7 -2
7 0
A person walks 1/3 of a mile every half hour. How far
would the person walk in 2
hours?
Answer:
1 1/3 miles
Step-by-step explanation:
1/3 is for a half-mile, so double it to 2/3 for one mile.
Now double it again for two hours.
2/3 + 2/3 = 1 1/3 miles in two hours
Answer:
The person will walk 1 1/3 miles in 2 hours.
Step-by-step explanation:
There are 4 half-hours in 2 hour
1/3*4=4/3 or 1 1/3 miles
Enter an equation in the form y = mx + b that represents the function
Answer: no answer c
Step-by-step explanation:
can you help me with this
Answer:
[tex]140[/tex]°
Step-by-step explanation:
This polygon has [tex]9[/tex] sides, so it's a nonagon. The expression used to find the sum of the measures of the interior angles of any polygon is [tex]180(n-2)[/tex]° where [tex]n[/tex] is the number of sides the polygon has. In this case, [tex]n=9[/tex], so the sum of the measures of the interior angles of this polygon is [tex]180(9-2)=180*7=1260[/tex]°.
We are given that this is a regular polygon (with 9 sides), meaning that all of its interior angles have the same measure, and we also know that the sum of the measures of its interior angles is [tex]1260[/tex]°. Therefore, each interior angle measures [tex]\frac{1260}{9}=140[/tex]°. Hope this helps!
2x-y+8z=13
3x+4y+52=18
5x-2y-72=20
Answer:
Answer is above (In the image).
Step-by-step explanation:
I am not sure if that is what you were looking for. To convert it to decimals, just input the figures into your calculator.
In my opinion the best way to solve these equations are elimination, therefore I will be giving my answer in this way!
2x-y+8z=13 1️⃣
3x+4y+52=182️⃣
5x-2y-72=203️⃣
We first combine liked terms in equation 2 and 3.
2️⃣turns into 3x+4y=-34 let's call it 2️⃣'
3️⃣turns into 5x-2y=92 let's call it 3️⃣'
Then solve for x
3️⃣'*2
10x-4y=184
3️⃣+2️⃣
13x=150
x=150/13
Now substitute the x back into equation 2️⃣'
3*150/13+4y=-34
450/13+4y=-442/13
4y=-892/13
2y=-446/13
y=-223/13
Now we can substitute this back into 1️⃣ to solve for z
2*150/13- - 223/13+8z=169/13
523/13+8z=169/13
8z=-354/13
4z=-177/13
z=-177/52
This problem is kind of messy so let me restate my answer!
x=150/13
y=-223/13
z=-177/52
I really hoped this is correct and it helped, and would appreciate it if you give me brainlliest! If you have any more questions about my solution please ask me in the comments!
20% of what number is 479
168
0 235
O230
094
Answer:
168 hope this is right
Step-by-step explanation:
What is the fifth term in the expansion of (3x - 3y)??
X²4A
Answer:
4
Step-by-step explanation:
can someone help me pls 10 points
Answer:
They added +3x instead of subtracting it in the first step.
Step-by-step explanation:
Instead:
5x + 2 = 3x - 8
-3x -3x
----------------------
2x + 2 = -8
-2 -2
-----------------
2x = -10
/ 2 / 2
-----------
1x = -5
---------
x = -5
Select the Equivalent Expression. 3 negative 5 =? I cant find the negative sign on here lol.
Answer:
Step-by-step explanation:
do you mean 3-5=-2 ?
Answer:
3+,-5 =-2
Step-by-step explanation: you mean this if you do your welcome
look at the picture please help.
Answer:
Under 1: $3.25
Under 3: $9.75
Under 5: $16.25
Cost for 15 pounds = $48.75
Answer:
1 pound= $3.25
3 pounds=$9.75
5 pounds=$16.25
15 pounds =$48.75
Step-by-step explanation:
1x3.25=3.25
3x3.25=9.75
5x3.25=16.25
15x3.25=48.75
Find the volume of a cylinder that has the following dimensions. Do not round your answer. (Use 3.14 for TT.)
radius: 5 cm
height: 0.25 m
volume =
cm
Answer:
volume is πr^h
Step-by-step explanation:
3.14*5*5*0.25 is 1962.5cm^2
in m^2 it would be 19.625
Ada is making rice. The instructions call for 2 1/4 cups of water for 1 cup of rice. Ada is using only 1/3 cup of rice.
Answer:
3/4 cup of water
Step-by-step explanation:
2.25 (2 1/4) divided by 3 (or times 1/3) is 3/4
The required number of cups of water is 3/4 cups of water
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The number of cups of rice = 1 cup
The number of cups of water for making rice = 2 1/4 cups of water
So the equation for
The number of cups of water for 1/3 cups of rice =
Number of cups of water for making rice / 3
The number of cups of water for 1/3 cups of rice = 2 ( 1/4 ) / 3
= 9/4 / 3
= 3 / 4 cups of water
Therefore , the number is 3/4 cups of water
Hence , The required number of cups of water is 3/4 cups of water
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Which of the following equations are equivalent? Select three options.
2+x=5
X+ 1 = 4
09+X=6
X+(-4)=7
0-5+ X= -2
Answer:
2+x=5
X+1=4
0-5+X= -2
These are the answers