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]
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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).
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For what value of x does 3^4x=27^x-3?
0 -9
O-3
O 3
O 9
Answer:
the answer to the value of X is 0-3
The roots of the equation f(x) = 0 are 1 and -2. The roots of f(2x) = 0) are - - (A) 1 and -2 (B) and - 1 (C) and 1 2 2 (D) 2 and -4 (E) -2 and 4
Answer: B
Step-by-step explanation:
When f(x) turns into f(2x), we need to halve the value of x.
The roots of f(2x) will be equal to ( 1 / 2 ) and -1.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the root of function f(x) are 1 and -2. The roots of F(2x) will be calculated as:-
( x - 1 ) ( x + 2 ) =0
( 2x - 1 )( 2x + 2 ) =0
x = 1 / 2
x = -1
Therefore, the roots of f(2x) will be equal to ( 1 / 2 ) and -1.
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[tex] \binom{4a + 3}{5} - \binom{2a + 3}{3} [/tex]
simplify the fraction
I assume your question was to simplify the following fraction ;
[tex]{:\implies \quad \sf \dfrac{4a+3}{5}-\dfrac{2a+3}{3}}[/tex]
Taking LCM will yield ;
[tex]{:\implies \quad \sf \dfrac{3(4a+3)-5(2a+3)}{15}}[/tex]
[tex]{:\implies \quad \sf \dfrac{12a+9-10a-15}{15}}[/tex]
[tex]{:\implies \quad \boxed{\bf \dfrac{2a-6}{15}}}[/tex]
This is the required answer
I need help with this math problem!
Answer:
the value is 120 i think and 2 x-intercepts for the graph of f
Step-by-step explanation:
sorry if it's wrong
GEOMETRY HELP MEEE D:!!!
Answer:
The answer for the x would be 20.25 ft.
Step-by-step explanation:
Check the underlined writing for the 2nd easier and more efficient method
The area is 9 ft.^2, and area means length*width=area. So, if you were to multiply 4.5*2 that would equal 9, which is the area of the smaller rectangle.
Now use scale factor. If the length of the smaller rectangle is 2, you need to see how many times 2 can fit into 9. 9/2 equals 4.5, then you would multiply 4.5 by 4.5 to get 20.5 to get the width of the rectangle.
If you want to check, put 2/4.5 and 9/20.25 and you both get 0.444....= 4/9
Which means that they both have the same scale
Okay, there is a much easier method I didn't realize, the butterfly method. After you find the length and width of the smaller rectange, you can cross multiply.
2/4.5 = 9/x. (keep the numbers in line, for example both of the lengths stay in the numerator) So 9*4.5 equals 40.5, and 2*x equals 2x. Use basic algebra (divide everything by 2) and you get x=20.25 as well. This solution is much more reliable.
Hope this helps!
"The difference of six and twice a
number is five."
Answer:
x = 1/2
Step-by-step explanation:
twice a number = 2x
difference means subtract 2x - 6 = 5
2x - 6 = 5 Add 6 to both sides.
2x + 6 - 6 = 5 + 6 Combine
2x = 11 Divide by 2
2x/2 = 11/2
x = 5.5
Is the answer different if it is done the other way around for the difference?
6 - 2x = 5 Subtract 6 from both sides
-2x = 5-6 Combine
-2x = - 1 Divide by -2
-2x/-2 = -1/-2
x = 1/2
Yes they are different. Following the way the question is written, I would choose the second method.
What is the end behavior of the function f of x equals negative 4 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
The function [tex]f(x) = 4\sqrt[3]{x}[/tex] is a cube root function
The function end behavior is:
[tex]\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty[/tex]
How to determine the end behavior?The equation of the function is given as:
[tex]f(x) = 4\sqrt[3]{x}[/tex]
To determine the end behavior, we plot the graph of the function f(x).
From the attached graph of the function, we can see that:
As x approaches infinity, the function f(x) approaches infinity, and vice versa
Hence, the function end behavior is:
[tex]\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty[/tex]
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I will give brainiest find a linear inequality with the following solution set. each grid line represents one unit.
(give your answer in the form $ax+by+c>0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor other than 1.)
Answer:
Step-by-step explanation:
A survey of 100 people in New York City, NY found that.
• The probability that they take the subway each day is 0.85
• The probability that they take a Taxi each day is 0.6
• The probability that take the subway and taxi each day is 0.55
If a person is selected at random, then determine the probability thay they take either the subway or a taxi each day.
Answer: 0.9
Step-by-step explanation:
[tex]\mathrm{Total \ sample \ space \ $=100$} \\\mathrm{Event \ $A = \ taking \ subway \ each \ day}$$P(A)=0.85$$Event $B=$ taking taxi $\because P(B)=0.6$$$P(A \cap B)=0.55$$[/tex]
[tex]\begin{aligned}P(A \cup B) & \Rightarrow \text { Person taking either taxi/subway } \\&=P(A)+P(B)-P(A \cap B) \\&=(0.85-0.555)+(0.6-0.55)-0.55 \\&=1.45-0.55\\&\bf{=0.9} \end{aligned}[/tex]
Find the area of the unshaded region.
multiple choice group answers
565
555
530
560
Please help! 1/2 (18 + 14) - (18 - 14)^2
Answer:
the answer should be -185
Answer:
0
Step-by-step explanation:
1/2 (18 + 14)- (18 - 14)^2
=1/2 (32) - 4^2
=16 - 16
=0
Is this a function pls someone tell me
Answer:
No, it is not a function.
Step-by-step explanation:
In a function, each element in the domain must correspond to exactly one element in the range. That is not the case here.
Bogart has 150 stamps. 30% of them are from Africa. How many stamps are from Africa?
Answer:
There are 45 stamps from Africa
Step-by-step explanation:
10% of 150 is 15
30% of 150 is 45
15*3 = 45
A parallelogram with a right angle that is not a rectangle.
Answer:
One is a rhombus.
Step-by-step explanation:
What does the fair and accurate credit transactions act provide for consumers? a. it entitles consumers to get one free credit report per year from the big three reporting agencies. b. it entitles consumers to notify credit reporting agencies if their identity is stolen. c. it entitles consumers to file a complaint with the federal trade commission if their identity is stolen. d. it entitles consumers to find out about who has access to personal information and if it is being handled securely.
Fair and accurate credit transactions act entitles consumers to find out about who has access to personal information and if it is being handled securely.
What is fair and accurate credit transactions act?Fair and accurate credit transactions act passed in 2003 which is made to improve the protection of customer.
The objective of fair and accurate credit transactions act-
To improve the protection of customer.Ensure provisions in case of identity theft.Provide access to consumers to find out about who has access to personal information.Thus, fair and accurate credit transactions act entitles consumers to find out about who has access to personal information and if it is being handled securely.
Option d is the correct option.
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Answer: a. It entitles consumers to get one free credit report per year from the big three reporting agencies.
Step-by-step explanation: quizlet
A circular swimming pool has a radius of 20 feet. The family that owns the pool wants to put up a circular fence that is 5 feet away from the pool at all points. Which is closest to the circumference of the fence they will need?
Answer:
157.08 ft
Step-by-step explanation:
R = 20+5 = 25
Circumfrence = 2*pi*r = 2*pi*25 = 157.079 ft
NEED HELP ASAP!!!! GIVING BRAINLIEST+ 30 POINTS TO WHOEVER CAN ANSWER THESE TWO QUESTIONS THE BEST!!!
50 POINTS CORRECT ANSWER ONLY!! PLEASE HELP ASAP
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Use a recursive formula to determine the time she will complete station 5. Show your work.
Geometric Recursive Formula
f(n) = f(n − 1) • r
Answer:
ask 23
Step-by-step explanation:
(1, 2), (2, 4), (3, 8), (4, 16)
Use a recursive formula to determine the time she will complete station 5. Show your work.
Geometric Recursive Formula
f(n) = f(n − 1) • r
Answer:
f(n) = f(n − 1) • 2
Step-by-step explanation:
f(1) = 2
f(2) = 4
f(3) = 8
f(4) = 16
Geometric Recursive formula: f(n) = f(n − 1) • r
where r is the common ratio
To determine r, divide one term by the previous term:
[tex]\sf r=\dfrac{f(n)}{f(n-1)}=\dfrac{16}{8}=\dfrac{8}{4}=\dfrac{4}{2}=2[/tex]
Therefore, f(n) = f(n − 1) • 2
The first term in a sequence is 84. The pattern follows the rule add 24. What are the next four terms?
Answer: 108, 132, 156, and 180
Step-by-step explanation:
If you need to add 24 to the first term for the next 4 terms, you would have
84 + 24 = 108
108 + 24 = 132
132 + 24 = 156
156 + 24 = 180
So your sequence would be 108, 132, 156, and 180 for the next 4 terms.
What percentage of Africa is savanna?
less than ten percent
approximately twenty-five percent
almost fifty percent
close to seventy percent
Answer:
C, Almost fifty percent
Step-by-step explanation: I just got it right.
Melanie invested $9,800 in an account paying an interest rate of 4.5 compounded quarterly. Amelia invested $9,800 in an account paying an interest rate of 4.75 compounded continuously. After 20 years, how much more money would Amelia have in her account than Melanie, to the nearest dollar?
Answer:
$13,082.60 more
Step-by-step explanation:
Melanie:
[tex]A=P(1+\frac{r}{n})^(20)\\ A=9800(1+\frac{.045}{4})^(20)\\A=$12,257.36[/tex]
Amelia:
[tex]A=Pe^(rt)\\A=9800e^(.0475*20)\\A=$25,339.95[/tex]
Amelia-Melanie= $13,082.60
Use numerals instead of words. If necessary, use / for the fraction bar(s).
The measure of angle 0 is 7 pie/4. The measure of its reference angle Is _°, and tan 0 is _
Answer:
-1
Step-by-step explanation:
angle 0: 7pie/4
=7*180/4
=1260/4
=315
hence reference angle(0)= 315
now, tan 0 = tan315
= tan(360-45)
= -tan45
= -1
1. Sixty-four unit cubes were glued together to make a 4 × 4 × 4 cube. How many 1 × 1 pairs
of faces were glued together to make the larger cube?
2. A cube is painted red and then cut into 64 identical smaller cubes. How many of these cubes
are painted red on at least one face?
3. A cube is painted red and then cut into 1000 identical smaller cubes. How many of these
cubes are painted red on at least two faces?
Answer:
The answer is 56 and that is no guess
A rectangle has length 1. 5 times the width, and perimeter 12 cm. What are the dimensions of
the rectangle?
Answer:
Length = 3.6
Width= 2.4
Step-by-step explanation:
A rectangle has length 1. 5 times the width, and perimeter 12 cm. What are the dimensions of
the rectangle?
So a rectangle has 2 longer sides and 2 shorter sides.
Knowing the length is 1.5 times the width
and perimeter of 12 centimeters.
The Perimeter is the adding of all the values around a shape. A rectangle has 4 sides so you add up all the sides.
1.5w+1.5w+w+w=12
5w=12
12/5=w
w=2.4
To figure the length just multiply 1.5*2.4=3.6
And That is how you solve it :)
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Four beakers contain water as shown below.
Which two beakers of water can be combined to fill one beaker to exactly 1,000 mL?
beaker B and beaker C
beaker B and beaker C
beaker A and beaker C
beaker A and beaker C
beaker A and beaker B
beaker A and beaker B
beaker A and beaker D
beaker A and beaker D
Answer:
A&C
Step-by-step explanation:
It would be A because it has 750 mL and C because it has 250mL and 750+250=1000
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Is {(2,3), (4,5), (-2, -1), (0,1)} a function or not give a reason for your answer
Step-by-step explanation:
yes, it is a function.
the reason : every value of x (2, 4, -2, 0) has exactly one assigned value of y : 2 to 3, 4 to 5, -2 to -1, 0 to 1.
that is the definition of a function.
If claire does not make any payments, how much will she owe after ten years? $12,136.67 $3,481.24 $6,090.90 $3,232.74
The interest formulas will be used to find the amount Claire owes. If the amount has a single compounding per year, simple interest is used, otherwise, compound interest is used.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.More can be learned about interest at https://brainly.com/question/25781328
Answer:
a. $12,136.67
Step-by-step explanation:
Simplify:
4(r + 1) + 3r
A) 4r + 4
B) 5r + 1
C) 7r + 1
D) 7r + 4
Answer:
[tex]\boxed{\sf{D. \quad 7r+4}}[/tex]Step-by-step explanation:
Use a distributive property.
Distributive property:
[tex]\Longrightarrow:\sf{A(B+C)=AB+AC}[/tex]
⇒ 4(r+1)+3r
To multiply, first expand the form.
⇒ 4*r=4r
⇒ 4*1=4
Rewrite the problem down.
⇒ 4r+4+3r
Combine like terms.
⇒ 4r+3r+4
Solve.
Add similar to elements.
Add the numbers from left to right.
⇒ 4r+3r=7r
⇒ = 7r+4
Therefore, the correct answer is D. 7r+4.I hope this helps you! Let me know if my answer is wrong or not.
1/(√2+√3)-√4 pls explain i dont understand
Hey there!
1/(√2+√3)-√4
=−2−√2+√3
(Decimal: -1.682163)
A restaurant manager gives a survey to all of his customers asking them to rate the quality of the service they received. He then keeps track of how many customers return to the restaurant during the next six months. Last year, the results showed that of the customers who reported high quality service, 90% returned for additional meals. What conclusion can be drawn from this study? (6 points) Only some customers who rate their service as high quality return for additional meals. Most customers who rate their service as high quality return for additional meals. High quality services cause customers to return for additional meals. Customers who will return for additional meals report a high quality of service.
Answer: High quality services cause customers to return for additional meals.
Step-by-step explanation: The 90% crosses out the first option. Because it's 90% we don't know if all the customers reported their service. The last one just to me wouldn't make sense.