Therefore, the line integral is:
∫c xy^4 ds = 125∫[0,pi] cos(t)sin^4(t) dt = 125(48/5) = 1200
The right half of the circle x^2 + y^2 = 25 can be parameterized as c(t) = (5cos(t), 5sin(t)) for t in [0, pi], where the orientation is counterclockwise.
The line integral of xy^4 along c is given by:
∫c xy^4 ds = ∫[0,pi] xy^4 ||c'(t)|| dt
where ||c'(t)|| is the magnitude of the derivative of c with respect to t.
We have:
c'(t) = (-5sin(t), 5cos(t))
||c'(t)|| = sqrt[(-5sin(t))^2 + (5cos(t))^2] = 5sqrt(sin^2(t) + cos^2(t)) = 5
So the line integral becomes:
∫c xy^4 ds = ∫[0,pi] xy^4 ||c'(t)|| dt
= 5∫[0,pi] 25cos(t)sin^4(t) dt
= 125∫[0,pi] cos(t)sin^4(t) dt
To evaluate this integral, we can use integration by substitution. Let u = sin(t), then du/dt = cos(t) and dt = du/cos(t). So we have:
∫cos(t)sin^4(t) dt = ∫u^4 du/cos(t) = ∫u^4 sec(t) du
We can evaluate this integral as follows:
∫u^4 sec(t) du = sec(t)u^5/5 - 2/5 ∫u^2 sec(t) du
= sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 4/15 ∫u^2 du
= sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 2/5 u^3 + C
where C is the constant of integration.
Substituting back u = sin(t) and integrating over [0,pi], we obtain:
∫[0,pi] cos(t)sin^4(t) dt
= [sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 2/5 u^3]_0^pi
= (0 - 0 + 2/5(5^3)) - (1/5 - 0 + 0)
= 48/5
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Fatoumata is going to invest in an account paying an interest rate of 1.7% compounded continuously. How much would Fatoumata need to invest, to the nearest hundred dollars, for the value of the account to reach $6,300 in 5 years?
Fatoumata requires an investment of $4390.24
What is basic interest or amount?
The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest.
Rate r= 1.7%
Total A is $6300.
t = 5 years
Primary P =????
A=P(1+r)^t
6300= P(1+0.017)^5
6300= P(1.017)^5
6300= P(1.435)
P= 6300/1.435
P = 4390.24
Should be the answer. if I'm right can I get Brainiest if I'm wrong then it's fine
Answer:
$5786.63
Step-by-step explanation:
the equation for interest compounded continuously is A=Pe^rt
6300=Pe^.017(5)
then in your calculator put e raised to the .085 (which is .017 times 5)
then divide that by 6300
and P=5786.62739
A number between 55 and 101 multiple of 2, 6, and 8
Answer:72
Step-by-step explanation:
8x9=72
2x36= 72
12x6=72
ANSWER PLS!! NEED ASAP!!
Angela baked an apple pie that had a radius of 6 inches. She wants to cut the pie into eight equal slices. How wide will each piece of pie be at the outer edge?
A- 5.2 in.
B- 4.7 in.
C- 4.4 in.
D- 4.2 in.
Answer:
Angela baked A-5.2 inches of baked apple pie.
Step-by-step explanation:
which of these 3 diagrams are correct
if you can solve this that would be great
Answer:
I wish you luck
Step-by-step explanation:
PLEASE HELP!! 40 POINTS!!
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 20 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
Answer:
the second option
Step-by-step explanation:
y=mx+c
therefore y=10x+20
20 is the y intercept, 10 is the gradient
I Need help asap, This is due in less than an hour!!
Can you please copy and paste it here?
-
I cannot read it clearly.
20.25- (-5) - 11.75 + 15.
Answer:
28.5
20.25 - (-5) = 25.25
25.25 - 11.75 = 13.5
13.5 + 15 = 28.5
Step-by-step explanation:
Sorry it took so long. Hope it helps! =D
What are the 4 parts of a polygon?
The four parts of a polygon are: sides, vertices, diagonals, and interior angles.
What is polygon?Polygon is a closed figure in a plane made of of straight line or curved line that insert in pairs a polygon has at least three side of angle the height can be of any length and the angle can be of any measure polygon or classified according to the number of side they have such as triangle.
A polygon is a closed, two-dimensional shape with three or more straight sides. The four parts of a polygon are: sides, vertices, diagonals, and interior angles. The sides are the straight line segments that make up the shape. The vertices are the points where the sides meet. The diagonals are line segments joining any two non-adjacent vertices. The interior angles are the angles inside the polygon, which are determined by the number of sides the polygon has.
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How do you identify the base and exponent in an exponential notation?
We can identify the base and its exponent as the exponent indicates the number of times the base is used as a factor in an exponential notation.
What is Exponent ?An exponent is the number of times a number has been multiplied by itself. For instance, the phrase 2 to the third, which is represented as 23, means 2 x 2 x 2 = 8, not 23, and 2 x 3 = 6, respectively. Remember that every number multiplied by one is equal to itself.
Exponents are a technique of expressing extremely large numbers in terms of powers. The number of times a number has been multiplied by itself is the exponent, so to speak. For instance, the result of multiplying the number 6 by itself four times is 6 6 6 6. This can be expressed as 6⁴. Here, the exponent and base are 4 and 6, respectively.
An exponential number takes the shape of a, where an is multiplied by itself n times. The simple example is 8=23=222. In exponential notation, A is referred to as the base, whereas n is referred to as the power, exponent, or index. In scientific notation, 10, which is a specific illustration of exponential numbers, is typically always used as the base number.
Exponential notation make it easy to express powers succinctly. The exponent displays the base's multiplicative power. It can be written as 2 2 2 2=25 for the integer 32 because 2 is the "base" and 5 is the "exponent." The correct translation of this phrase is "two to the fifth power."
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Is it possible to have a triangle with sides 2cm 2cm and 5cm justify your answer?
Answer:
No, it is not possible to have a triangle with sides of 2cm, 2cm, and 5cm. This is because a triangle's sides must adhere to the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 2cm + 2cm (4cm) is not greater than 5cm, so it is not possible to form a triangle with these side lengths.
Step-by-step explanation:
Answer:
Yes u can
Step-by-step explanation:
U can create a triangle with that because 2+2 is 4 which is less than 5 meaning it would work as a triangle
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = x2 +1. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answer: The graph of f(x) = x^2 will have only one x-intercept (0,0) since it is a parabola that opens upward and its vertex is at the origin. On the other hand, the graph of g(x) = x^2 +1 is a transformation of the parent function, the graph of f(x) = x^2, where the function was shifted up by 1 unit. Therefore this function g(x) = x^2 +1 will not have any x-intercept because when x=0 the y value becomes 1 so the x-intercept will not be on the x-y plane.
In summary, the graph of f(x) = x^2 has one x-intercept, while the graph of g(x) = x^2 +1 has no x-intercepts due to the transformation of the parent function.
Step-by-step explanation:
What is true about exponential functions with a base between 0 and 1?
Answer:1 always rise to the left and approach 0 to the right.
Step-by-step explanation:
One angle of a triangle measures 70°. The other two angles are in a ratio of 4:7. What are the measures of those two angles?
The measure of the other two angles are 88 degrees and 22 degrees.
Let's call the two unknown angles x and y. Since the sum of all angles in a triangle is 180 degrees, we have:
x + y + 70 = 180
We also know that the ratio of the two angles is 4:7. We can set up a proportion to express this relationship:
x/y = 4/7
We can cross-multiply to get:
7x = 4y
We can substitute this equation into the first equation to eliminate one of the variables.
7x + y + 70 = 180
Now we have:
7x + y = 110
We can use the second equation to eliminate x:
7(4y/7) + y = 110
4y + y = 110
5y = 110
y = 22
Now that we know one of the angles is 22 we can substitute it back in the first equation
x+22+70 = 180
x = 88
Therefore, the measures of the other two angles are 88 and 22 degrees
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Maria’s height is 134 centimeters. What is her height in meters?
m
Answer:
There are 100 centimeters in 1 meter, so Maria'e height in meters would be:
1 meter and 36 centimeters, tall.
Step-by-step explanation:
Hope it helps! =D
In ΔTUV, t = 70 inches, mm∠T=99° and mm∠U=53°. Find the length of u, to the nearest inch.
The length of u is 56.60 inches. The nearest inches it is 57 inch
What is a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.
Given that ΔTUV is a triangle with m∠T=99° and m∠U=53°.
The length of t is 70 inches.
The opposite side of ∠T is t, the opposite side of ∠U is u, and the opposite side of ∠V is v.
Sine rule of ΔABC:
a/sin A = b/sin B = c/sin C
Apply sine law in ΔTUV:
t/sin T = u/sin U = v/sin V
Putting ∠T=99°, ∠U=53°, and t = 70.
70/ sin 99° = u/sin 53°
u = (70sin 53°)/ sin 99°
u = 56.60 inches
The digit after the decimal point is greater than 5, thus add 1 with the 56 to get the nearest inch.
u = 57 inches
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Can someone help me with this ? Please
Value of gof(-1) is 2. The solution has been obtained by applying the multiplication operation on the given functions.
What are operations on functions?
Just like we add, subtract, multiply and divide the terms in a function, the functions can also be added, subtracted, multiplied or divided in a similar way.
Suppose there are two functions f(x) and g(x). The notations are as follows:
For Addition: (f+g)(x) = f(x) + g(x)For Subtraction: (f-g)(x) = f(x) - g(x)For Multiplication: (f×g)(x) = f(x) × g(x)For Division: (f/g)(x) = (f(x))/(g(x))Now, gof= g(f) = 3-f
We are given f = 2+x
So, f(-1) = 2+(-1) = 1
Now, substituting the value of f(-1) in g(f) , we get
gof(-1)= 3-1=2
Hence, the value of gof(-1) is 2.
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PLEASE HELP ME I ONLY HAVE TODAY TO COMPLETE THIS ),:
What is the radical form of each of the given expressions?
Answer:
1. 7[tex]\frac{1}{2}[/tex] = [tex]\sqrt{7}[/tex]
2. 4[tex]\frac{7}{2}[/tex] = [tex]\sqrt{4} x^{7}[/tex]
3. 7[tex]\frac{1}{4}[/tex] = [tex]\sqrt[4]{7}[/tex]
4. 4[tex]\frac{1}{7}[/tex] = [tex]\sqrt[7]{4}[/tex]
Step-by-step explanation:
do -3 and 4 and -1 and 12 have a positive sum
Answer:
Yes, they do because -3+4=1 and -1+12=11
Step-by-step explanation:
Hope it helps!
Answer: If you mean + then, 12
Step-by-step explanation:
-3 + 4 = 1 -1 + 1 = 0 0 + 12 = 12
help please i need answers
The expressions that have a sum or difference equal to 3/4 are:
11/12 - 1/6 3/5 + 3/202/3 + 1/12The correct options are B, C, and E
What are sums and differences?
Sum mean the addition of numbers or expression
Difference means the subtraction of numbers or expressions.
The sum or difference of the number are as given below:
a. 1/2 + 2/4 = 4/4
b. 11/12 - 1/6 = (11 - 2) / 12
11/12 - 1/6 = 9/12
9/12 = 3/4
c. 3/5 + 3/20 = (12 + 3)/20
3/5 + 3/20 = 15/20
15/20 = 3/4
d. 7/8 - 1/2 = (7 - 4)/8
(7 - 4)/8 = 3/8
e. 2/3 + 1/12 = (8 + 1)/12
(8 + 1)/12 = 9/12
9/12 = 3/4
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Two angle measures of this triangle are 60°. Which type of triangle is it?
A.
obtuse
B.
scalene
C.
equilateral
D.
right
Answer: C. Equilateral
Step-by-step explanation:
Answer: option C is correct. two angle measures of an equilateral triangle is 60°
Step-by-step explanation: All the sides of an equilateral triangle are of equal lengths—each interior angle of this triangle measures 60°.
which of the following is not the solution of 3x+6y=12?A) (-4,4) B) (0,2)C) (8,-2)D) (3,1)
(3,1) is not the solution of the equation 3x + 6y = 12. So the option D is correct.
In the given question, we have to check which of the following is not the solution of 3x+6y=12.
To check which is not the solution of the given equation, we put the value of x and y from the given point. If for any point the condition is true then that point is the solution of the given equation. If that point doesn't satisfy the condition then that point is not the solution of the given equation.
The given equation is 3x+6y=12.
Firstly we check for the point (-4,4), where x = -4, y = 4
3(-4) + 6(4) = 12
-12 + 24 = 12
12 = 12(True)
Now we check for the point (0,2), where x = 0, y = 2
3(0) + 6(2) = 12
0 + 12 = 12
12 = 12(True)
Now we check for the point (8,-2), where x = 8, y = -2
3(8) + 6(-2) = 12
24 - 12 = 12
12 = 12(True)
Now we check for the point (3,1), where x = 3, y = 1
3(3) + 6(1) = 12
9 + 6 = 12
15 = 12(False)
Hence, (3,1) is not the solution of the equation 3x + 6y = 12. So the option D is correct.
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Write the rule for the linear function I will give brainliest
Answer:
2
Step-by-step explanation:
The rule is multiplying by 2 every time
-2 times 2 is -4
0 times 2 is 0
2 times 2 is 4
Function or not a function?
100 points
solve each system by graphing
x-y=-2
and
4x-y=4
Answer:
(2, 4)------------------------
Given system:
x - y = -24x - y = 4Rewrite equations to bring to slope-intercept form:
y = x + 2 andy = 4x - 4Plot each line and find the intersection, this is the solution.
The solution is (2, 4) as per attached graph.
8+5x=-2
show work
check
How do you find a prime number multiples?
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number can only be divided evenly by 1 and itself.
To find the multiples of a prime number, you can use the following steps:
Start with the prime number itself. This is the first multiple of the prime number.Multiply the prime number by 2. This will give you the second multiple of the prime number.Multiply the prime number by 3. This will give you the third multiple of the prime number.Repeat step 3 for larger and larger integers (4,5,6,7,8....) until you reach the desired number of multiples.For example, if the prime number is 5, the multiples of 5 are 5, 10, 15, 20, 25, and so on.
It's important to note that a prime number only has two divisors: 1 and itself. This means that a multiple of a prime number will never be a prime number.
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Classify this pair of events: A flavor of ice cream is selected at random; A
topping for the ice cream is selected at random.
A. independent
B. dependent
A A flavor of ice cream is selected at random; A topping for the ice cream is selected at random. This is B. dependent events.
What are dependent event?Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more events that are interdependent are referred to as dependent events.
If one event is accidentally altered, another is probably going to be different.
If two events are interdependent, then the result of the first event will influence the result of the second even more.
The ice cream in this case represented dependent event.
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P(x<15) round 2 decimal places
When rounded to two decimal places, numbers like 0.7035 and 2.836220364, for instance, become 0.70 and 2.84, respectively.
What is Round to Two Decimal Places?To simplify their interpretation and use in calculations, decimal numbers are frequently rounded off.
The hundredths place, which is the second place to the right of the decimal point, is where a decimal number is rounded to when it is rounded to two decimal places.
When rounded to two decimal places, numbers like 0.7035 and 2.836220364, for instance, become 0.70 and 2.84, respectively.
If you look closely, you will see that instead of 2.83, we have increased the digit in the first number's hundredths position by 1.
We did not, however, add 1 to the digit in the hundredths place for the second number (i.e 0).
The Complete Question is two decimal places.
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Complete question:
Round the function P(x<15) to 2 decimal places.
A candy store sells Nerds in two different sizes. Which is the best buy?
14 oz. for $4.20 OR 18 oz. for $5.04
Answer: 18oz
Step-by-step explanation: