From calculations, the given integral ∫c x sin(y)ds is equal to [tex]20\left(-\frac{1}{3}\cos \left(4\right)+\frac{1}{9}\sin \left(4\right)-\frac{1}{9}\sin \left(1\right)\right)=0.806[/tex].
Integration
The integrals are the opposite of derivatives. They are used in several applications, like: calculations of areas, volumes and others.
For solving an integration, you should know its rules. For this question will be necessary to apply the following integration rules:
For constant function - ∫b dx = b ∫ dx= bx+CFor sin function - ∫sin(x) dx = cos(x) + CFor integration by parts - ∫u v dx = uv -∫v duFirst, you should calculate the segment from the points (0, 1) and (4, 4).
segment=(4-0,4-1)=(4,3).
After that you should parametrize the segment:
r(t)=(0,1)+(4t,3t)= (4t,3t+1), where 0≤t≤1
Now, you can find dr/dt.
r'(t)=(4,3)
Consequently, the magnitude of |r'(t)| will be:
|r'(t)| =[tex]\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25} =5[/tex]
Finally you can evaluate the integral: ∫c x sin(y)ds. From r(t), you know that x=4t and y=3t+1.
[tex]\int _0^1\:xsin\left(y\right)\:ds=\int _0^1\:4t\cdot sin\left(3t+1\right)\:\cdot 5ds=\int _0^1\:20t\cdot sin\left(3t+1\right)\:\cdot ds[/tex]
Applying the Rule Integration for a Constant.
[tex]\int _0^1\:20t\cdot sin\left(3t+1\right)\:\cdot dt\\ \\ 20\cdot \int _0^1t\sin \left(3t+1\right)dt\\ \\[/tex]
Applying the Rule Integration by Parts.
∫u v dx = uv -∫v du
u=t
dv= sin(3t +1 )dt, then v=
[tex]=20\left[-\frac{1}{3}t\cos \left(3t+1\right)-\int \:-\frac{1}{3}\cos \left(3t+1\right)dt\right]^1_0\\ \\=20\left[-\frac{1}{3}t\cos \left(3t+1\right)+\frac{1}{9}\sin \left(3t+1\right)\right]^1_0\\ \\ =20\left(-\frac{1}{3}\cos \left(4\right)+\frac{1}{9}\sin \left(4\right)-\frac{1}{9}\sin \left(1\right)\right)\\ \\ =0.806[/tex]
Read more about integration rules here:
https://brainly.com/question/14405394
The value of the integral ∫c x sin(y)ds where c is the curve is 0.806 if the line segment is from (0,1) to (4,4).
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
First, we have to calculate line segment (0,1 ) to (4, 4)
= (4-0, 4-1) = (4, 3)
Parametric form of the segment:
P(t) = (0+4t, 3t) where 0 ≤ t ≤ 1
Now differentiate the segment:
P'(t) = (4, 3)
The magnitude of the P'(t)
[tex]\rm P'(t) = \sqrt{4^2+3^2}[/tex]
P'(t) = 5
Now the integration can be evaluated from the P(t)
[tex]\rm \int\limits^1_0 {xsin(y)} \, ds = \int\limits^1_0 {4tsin(3t+1)} \, 5ds[/tex] ( x= 4t, y = 3t+1)
[tex]\rm \int\limits^1_0 {xsin(y)} \, ds = 20\int\limits^1_0 {tsin(3t+1)} \, ds[/tex]
The value of the integration:
[tex]\rm \int \limits^1_0 {tsin(3t+1)} \, ds = 0.040[/tex]
[tex]\rm \int\limits^1_0 {xsin(y)} \, ds = 20(0.04)[/tex]
[tex]\rm \int\limits^1_0 {xsin(y)} \, ds =0.806[/tex]
Thus, the value of the integral ∫c x sin(y)ds where c is the curve is 0.806 if the line segment is from (0,1) to (4,4).
Learn more about integration here:
brainly.com/question/18125359
#SPJ4
A square is cut in half and the diagonal creating two equal triangles of each triangle has an area of 4.5 in.² what is the length in inches of the original square
BRAINLIEST HURRY HURRY By your cell phone contract, you pay a monthly fee plus some money for each minute you use the phone during the month. In one month, you spent 280 minutes on the phone, and paid $23.80. In another month, you spent 340 minutes on the phone, and paid $25.90.
Let x be the number of minutes you talk over the phone in a month, and let y be your cell phone bill, in dollars, for that month. Use a linear equation to model your monthly bill based on the number of minutes you talk over the phone.
This linear model’s slope-intercept equation is_______ .
If you spent 160 minutes over the phone in a month, you would pay _____.
If in a month, you paid $30.80 of cell phone bill, you must have spent _____ minutes on the phone in that month.
Answer:Y = Co + C*x.22.45 = Co + C*200,Co = 22.45 - 200C.29.65 = Co + C*350.Co = 29.65 - 350C. = 22.45 - 200C150C = 7.20, C = 0.048/min.Co = 22.45 - 200*0.048 = $12.85/mo. = Initial cost.Y = 0.048x + 12.85.2. Y = 0.048*110 + 12.85 = $18.13.3. 34.10 = 0.048x + 12.85, X = ?.
Step-by-step explanation:
what is 5x15= what help me please to hard
Answer:
75
Step-by-step explanation:
The position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 130 feet per second and can be modeled by the function y = 130t + 1200. Solve the system of equations. Which solution represents a viable time that the trains are side by side?
A. 14 sec
B. 15 sec
C. 16 sec
D. 17 sec
Solving the system of equations, it is found that a viable time that the trains are side by side is given by:
B. 15 sec
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
[tex]y = 14t^2[/tex]
[tex]y = 130t + 1200[/tex]
They will be side by side when:
[tex]14t^2 = 130t + 1200[/tex]
[tex]14t^2 - 130t - 1200 = 0[/tex]
It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:
[tex]\Delta = (-130)^2 - 4(14)(-1200) = 84100[/tex]
[tex]x_1 = \frac{130 + \sqrt{84100}}{28} = 15[/tex]
[tex]x_2 = \frac{130 - \sqrt{84100}}{28} = -5.71[/tex]
Time is a non-negative measure, hence option B is correct.
More can be learned about a system of equations at https://brainly.com/question/24342899
Answer:
B: 15 sec
Step-by-step explanation:
I took the algebra exam
What is 3x + 2y = 12 (show your work)
Answer:
y = (-3/2)x + 6
Step-by-step explanation:
3x + 2y = 12
2y = -3x + 12
÷2 ÷2 ÷2
y = (-3/2)x + 6
Slope: (-3/2)
Y-intercept: (0,6)
I hope this helps!
Jacob had a cube. When Jacob made a cross section parallel to the base, what shape did the cross section form? trapezoid square parallel triangle
Answer: Square
Step-by-step explanation:
A cross section cut parallel to a base will be the same shape as the base itself, and the base of a cube is a square. :)
Answer:
A square because it is not diagonal.
Step-by-step explanation:
Find the value of a. Round your answer to the nearest tenth. B 10 77.5 A C 7.9
Answer:
[tex]\displaystyle 11,3[/tex]
Step-by-step explanation:
Use the Law of Cosines to find the length of the third edge:
Solving for Angles
[tex]\displaystyle \frac{a^2 + b^2 - c^2}{2ab} = cos\angle{C} \\ \frac{a^2 - b^2 + c^2}{2ac} = cos\angle{B} \\ \frac{-a^2 + b^2 + c^2}{2bc} = cos\angle{A}[/tex]
Use [tex]\displaystyle cos^{-1}[/tex]towards the end or you will throw your result off!
Solving for Edges
[tex]\displaystyle b^2 + a^2 - 2ba\:cos\angle{C} = c^2 \\ c^2 + a^2 - 2ca\:cos\angle{B} = b^2 \\ c^2 + b^2 - 2cb\:cos\angle{A} = a^2[/tex]
Take the square root of the final result or it will be thrown off!
Let us get to wourk:
[tex]\displaystyle 10^2 + 7,9^2 - 2[10][7,9]\:cos\:77,5 = a^2 \hookrightarrow 100 + 62,41 - 158\:cos\:77,5 = a^2 \hookrightarrow \sqrt{128,212541} = \sqrt{a^2}; 11,323097677... \\ \\ \boxed{11,3 \approx a}[/tex]
I am joyous to assist you at any time.
The height of a building in a drawing is 15 inches at the actual height of the building is 165 feet find the scale factor of the drawling
165 ft / 15 inches = 11
scale = 1 inch = 11 feet
which is written as 1:11
Which answers describe the shape below? Check all that apply.
A. Square
B. Trapezoid
C. Quadrilateral
D. Parallelogram
E. Rhombus
F. Rectangle
Answer:
The answers are C, D, and F
Step-by-step explanation:
Question 1
1 pts
Use the GSS file to investigate whether or not Americans use the Internet at least 7
hours per week (estimating an hour per day). Perform the One Sample T Test
procedure (as presented in SPSS Demonstration 1) to do this test with the variable
WWWHR. Do the test at the .01 significance level. What is the T [1]?
Put 40 in the
The computation of the significance level shows that the p-value is less than 0.01 and the conclusion is that Americans use the internet more than 7 hours weekly.
What is a significance level?It should be noted that the significance level simply means the probability that an event occured by chance.
From the complete question, it can be noted that at 0.01 significance level, the t statistic is 17.873 and the degree of freedom is 539.
The p-value for the right tailed test is 0. Therefore, since the p value is less than 0.01, we will reject the null hypothesis. The conclusion is that Americans use the internet more than 7 hours weekly.
Learn more about significance level on:
https://brainly.com/question/9163177
What is the difference?
74 – 26 =
47
48
52
58
48 is the correct answer
Please help! will give brainlest! locks in 30 min!
PLEASE PLEADE HELP!!
Hello and Good Morning/Afternoon:
Let's take this step-by-step:
By looking at this diagram:
[tex]\hookrightarrow \text {angle C is 45 degrees, angle A is 90 degrees}[/tex]
[tex]\hookrightarrow \text{We know that the sum of all the angles is 180 degrees in a triangle}[/tex]
[tex]a + b + c = 180\\90 + b + 45 = 180\\b + 135 = 180\\b = 45[/tex]
[tex]\hookrightarrow \text {Therefore angle B is also 45 degrees}[/tex]
With all these angles' measures:
⇒ we have a 45-45-90 triangle
⇒ which has some special properties (look at the diagram attached)
Based on the diagram:
[tex]\hookrightarrow \text{the longest side/ hypotenuse (BC)} = \text{ length of leg (AC)} * \sqrt{2} =14\sqrt{2}[/tex]
Answer: [tex]14\sqrt{2}[/tex]
Hope that helps!
#LearnwithBrainly
You and your friend buy a bag of assorted fruit that contains 3 apples, 5 oranges, and 2 bananas. You each randomly choose a piece of fruit and eat it. What is the probability you both will get a banana?
Solve. k + 6 > 19
A.
k < - 13
B.
k > 25
C.
k > 13
D.
k < - 25
Answer:
k > 13
Step-by-step explanation:
[tex]k+6 > 19\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:k > 13\:\\ \:\mathrm{Interval\:Notation:}&\:\left(13,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}[/tex]
[tex]k+6-6 > 19-6[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]k > 13[/tex]
Thus, the answer is k > 13
[RevyBreeze]
Solve and show your work for each question.
(a) What is expressed as a fraction in simplest form?
(b) What is expressed as a fraction in simplest form?
(c) What is expressed as a fraction in simplest form?
The value of 0.36 when converted to a fraction in the simplest form is 9/25.
How to calculate fractions in simplest form?Your information is incomplete. Therefore, an overview will be given. It should be noted that a fraction is in its simplest form when the numerator and denominator are prime.
From example, let's convert 0.36 to a fraction on its simplest form. This will be:
0.36 = 36/100 = 9/25
In conclusion, 0.36 is 9/25 in the simplest form.
Learn more about fractions on:
https://brainly.com/question/78672
Put the following items in order from most expensive to least expensive. Item Base Price Change Direction Blender $29. 73 9% Markdown Hat $14. 16 77% Markup Ink $20. 17 27% Markup Heater $28. 46 22% Markdown a. Blender, heater, ink, hat b. Blender, ink, hat, heater c. Ink, hat, blender, heater d. Ink, heater, blender, hat.
Putting the considered items in order from most expensive to least expensive item gives the order as shown by: Option b. Blender, ink, hat, heater
What is Markup and Markdown?Markup is the amount that will be increased in the original price of the considered thing.
Markdown is the amount that will be decreased from the original price of the considered thing.
Think of "up" and "down" as increasing and decreasing prices respectively.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, the base prices and the chage in price is given as:
Item Base Price Change Direction
Blender $29.73 9% Markdown
Hat $14.16 77% Markup
Ink $20.17 27% Markup
Heater $28.46 22% Markdown
Calculating the resultant price:
Case 1: Blender:Resultant price = 29.73 - 9% of 29.73
[tex]P= 29.73 - \dfrac{29.73}{100}\times 9\\\\P = 27.0543 \: \: \text{dollars}[/tex]
Case 2: Hat:Resultant price = 14.16 + 77% of 14.16
[tex]P= 14.16+\dfrac{14.16}{100}\times 77\\\\P = 25.0632\: \: \text{dollars}[/tex]
Case 3: Ink:Resultant price = 20.17 + 27% of 20.17
[tex]P= 20.17+\dfrac{20.17}{100}\times 27\\\\P = 25.6159\: \: \text{dollars}[/tex]
Case 4: Heater:Resultant price = 28.46 - 22% of 28.46
[tex]P= 28.46- \dfrac{28.46}{100}\times 22\\\\P = 25.0448 \: \: \text{dollars}[/tex]
Thus, putting the considered items in order from most expensive to least expensive item gives the order as shown by: Option b. Blender, ink, hat, heater
Learn more about percent here:
https://brainly.com/question/11549320
Which number is the smallest?
A. 817.9
B. 871.003
C. 817.1
D. 817.099
Answer:
D.
Step-by-step explanation:
817.099 is the smallest
please give brainliest
find the sum of first 40 terms of 11+14+17+...
Answer:
S₄₀ = 2780
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
14 - 11 = 17 - 14 = 3
this indicates the sequence is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 11 and d = 3 , then
S₄₀ = [tex]\frac{40}{2}[/tex] [ (2 × 11) + (39 × 3) ]
= 20( 22 + 117)
= 20 × 139
= 2780
Which inequality can be used to find how many $1.25 snack packs can be purchased for $10.00?
Answer:
1.25s [tex]\leq[/tex] 10.00
Step-by-step explanation:
Let's snack = s
Note:
[tex]\leq[/tex] ⇒ Less than or equal to
[tex]\geq[/tex] ⇒ Greater than or equal to
< ⇒ Less than
> ⇒ Greater than
Since we are trying to find how many $1.25 snack packs can be purchased for $10.00.. Thus, that less than or equal to $10.00 which also means we use [tex]\leq[/tex].
Thus the equation is 1.25s [tex]\leq[/tex] 10.00
`lenvy`
Answer:
8 snacks can be purchased
Step-by-step explanation:
10.00/1.25=8
help pls asap i be grateful
Answer: number a
Step-by-step explanation:4 times 2 is 8 8 times 2 is 16
1/2x12divided by 2-2 +11= what?
Answer:
The answer is 12
Step-by-step explanation:
1/2x 12 = 6
6/2-2+11 = 12
The final answer is 12
Given triangle ABC is congruent to DEC find m
Answer:
angle d = 106
In a survey of 250 voters, 3 out of 5 voters said they planned to vote for a proposed
new county library.
a) how many of these voters plan to vote for the library?
N
b) how many are not planning to vote for the library?
Mia and Carlos are hiking on a trail where they start 16 miles apart. If Mia can average 2.3 miles per hour while hiking and Carlos can average 2.5 miles per hour. How long will it take for them to meet up?
Answer:
I'm not sure but if this is on a calculus paper, this may put you on the right track?
Step-by-step explanation:
definate integral from 2.3 to 2.5 would equal 3.2, i don't know what to do with that information but i hope that helps you.
Find volume of rectangular prism shown here. 1.5 cm 2cm 8cm
Answer:
24 cm³
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying the area of the base by the height. V=lwh. V=(1.5)(2)(8)=24 cm³
Answer:
the answer should be 24
Step-by-step explanation:
1.5 x 2 = 3
3 x 8 = 24
V = L x W x H
V = 1.5 x 2 x 8
I don’t really understand this please help me.
Answer:
Top question) 12
Bottom question) 16
Step-by-step explanation:
top) you can fit 6 in the bottom of a 3x2 box if the smaller boxes are only 1 cubic foot and since it's also 2 feet high you can also fit another 6 which in total equals 12.
bottom) you can fit 8, 1 cubic foot boxes, in a larger box thats 4x2 and since it's also two feet tall you can fit another 8 in making 16 fitting in the larger box
Hope this helps! pls mark brainliest
What are the circumstances under which a person will feel disadvantage, if the parking ticket is lost
The circumstances where an individual will feel disadvantaged if they misplace or lost a parking ticket is that:
The parking attendant will find it difficult and tasking to locate your car in an absence of a parking ticket.You'll also be charged an extra expensive fee for a lost ticket.What is a parking ticket?A parking ticket is a piece of paper informing someone that they have parked a car unlawfully or for an excessively lengthy period of time and must pay a fine.
It is also know to be a notice informing a driver of a fee levied for improperly parking, usually written by a traffic officer and placed to a vehicle windscreen.
However, an individual will feel disadvantaged if they misplace or lost the ticket because:
The parking attendant will find it difficult and tasking to locate your car in an absence of a parking ticket.You'll also be charged an extra expensive fee for a lost ticket.Learn more about a parking ticket here:
https://brainly.com/question/26968718
Find the number if 2 1/2 of it is 15
(please help)
[tex]2.5x = 15[/tex]
[tex]x = \frac{15}{2.5} = 6[/tex]
Answer:
or Also
[tex] \frac{5}{2} x = 15 \\ 5x = 15 \times 2 \\ 5x = 30 \\ 5x \div 5 = 30 \div 5 \\ x = 6[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
Its A
Step-by-step explanation
just trust me