To find the length l of the graph of the polar equation r = e^(2θ) for 0 ≤ θ ≤ π, we can use the arc length formula for polar curves. Answer : 0.
The arc length formula for a polar curve r = f(θ) is given by:
l = ∫[a, b] √(r^2 + (dr/dθ)^2) dθ,
where a and b are the starting and ending angles.
In this case, we have r = e^(2θ), so dr/dθ = 2e^(2θ). Substituting these values into the arc length formula, we get:
l = ∫[0, π] √(e^(4θ) + (2e^(2θ))^2) dθ
= ∫[0, π] √(e^(4θ) + 4e^(4θ)) dθ
= ∫[0, π] √(5e^(4θ)) dθ
= √5 ∫[0, π] e^(2θ) dθ.
To evaluate this integral, we can use the substitution u = 2θ, du = 2dθ:
l = √5 ∫[0, π] e^(2θ) dθ
= √5 ∫[0, 2π] e^u (du/2)
= √5 (1/2) ∫[0, 2π] e^u du
= (√5/2) [e^u] evaluated from 0 to 2π
= (√5/2) (e^(2π) - e^0)
= (√5/2) (1 - 1)
= 0.
Therefore, the length l of the graph of the polar equation r = e^(2θ) for 0 ≤ θ ≤ π is 0 units.
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Which is greater 2.6 or 2.65 ?
Answer:
2.65 is greater than 2.6
Step-by-step explanation:
if 65 is greater than 60 than 2.65 is greater than 2.60
Answer:
2.6 > 2.65
Step-by-step explanation:
what is a point-slope equation of the line with slope -12 that goes through the point (5,3)?
A. y + 3 = 12 ( x + 5)
B. y - 3 = -12 ( x -5 )
C. y - 3 = 12 ( x - 5)
D. y + 3 = -12 ( x + 5 )
Step-by-step explanation:
Equation of a straight line is given by Y=MX+C
GIVEN POINTS (5, 3) and gradient -12, therefore
in the form of y=mx+c to get the constant, it will be 3=-12(5)+c
3=-60+c
3+60=c
c=63
y=mx+c
y=-12x+63
on squared paper draw the triangle with vertices at (1,1) , (5,3) , (3,5). find the area of the triangle
Answer:
lol
Step-by-step explanation:
j
plz need help
how much black hole required force
solve by using theory of relativity
Answer:
Solving the Equations of General Relativity for Colliding Black Holes
TOPICS:AstronomyAstrophysicsBlack HoleGeneral RelativityPopularTexas Advanced Computing CenterUniversity Of Texas At Austin
By UNIVERSITY OF TEXAS AT AUSTIN NOVEMBER 8, 2020
Which set of ordered pairs is linear? A. {(2, 1), (5, 1), (6, 1)} B. {(–1, 4), (0, 0), (1, 6)} C. {(–3, 5), (1, 0), (2, 4)} D. {(0, 0), (1, 3), (2, 7)}
Answer:
merhaba ben yeni geledimde adın ne
You put $300 at the end of each month in an investment plan that pays an APR of 7%. How much will you have after 18 years? Compare this amount to the total deposits made over the time period.
Answer:
take 300 time 12 months. take that nber times 18 years. then times that number by .07.
all together there is almost a $5000 difference. that is almost the total of having put 300 in the account for another 2 years without the apr
Step-by-step explanation:
Answer:
The answer is 129,216.31. Hope it helps
Step-by-step explanation:
41,692.58
Which number is in the tenths place?
A. 2
B. 5
C. 8
D. 9
Answer:
5 is in the tenths place
Step-by-step explanation:
2 is in the ones place, 8 is in the hundredths place, and 9 is in the tens place.
Neil has 2 pounds of grapes. He uses some to make a fruit salad. Now Neil has 8 ounces of grapes. How many ounces of grapes does Neil use for the fruit salad?
Answer:
Neil uses 24 ounces of grapes for the fruit salad.
Step-by-step explanation:
Quantity of grapes = 2 pounds
Use 1 pound = 16 ounces
So,
Quantity of grapes = 2(16) = 32 ounces
Neil uses some grapes to make a fruit salad. Now Neil has 8 ounces of grapes.
Quantity of grapes that Neil use for the fruit salad = [tex]32-8=24[/tex] ounces
Therefore,
Neil uses 24 ounces of grapes for the fruit salad.
what is 3v+h v=5 h=10 which is what
Answer:
25
Step-by-step explanation:
3(5)+10 = 15 + 10 = 25
A party cap is in the form of a frustum. The radii of its ends are 10cm and 30 cm. The volume of the cap is 9100. What is the height of the cap?
Answer:
4.46cm
Step-by-step explanation:
Volume of a frustum is expressed as;
V = (1/3) * π * h * (r₁² + r₂² + (r₁* r₂))
h is the height of the frustum
r₁ and r₂ are the radii of its ends
V is the volume
Given
V = 9100cm₃
r₁ = 10cm
r₂ = 30cm
Substitute
9100 = (1/3) * (3.14) * h * (10² + 30² + (10* 30))
9100 = 1/2(3.14)*h*(100+900+300)
9100 = 1.57*h*(1300)
9100 = 2,041h
h = 9100/2,041
h = 4.46cm
Hence the height of the cap is 4.46cm
If r = .15, this indicates
Answer:
Then D=.30
Step-by-step explanation:
Diameter is two times the radius
I think this is correct I'm not to sure
hope this helps :)
What fraction is less than 1/2. 3/4,1/6,6/12,4/10,5/8,5/2
Answer:
1/6 and 4/10
Step-by-step explanation:
1/2 = 0.5 and 0.5 is greater than 1/6 which is 0.166666666667 and 4/10 which is 0.4.
Lol i dont know if im right but can someone explain it to me please and thanks man
Answer:
The correct answer would be A.
Step-by-step explanation:
You're right because the translation would make it so the circles have the same center. Because they have the same center it would be easier to see the correlation between them.
I hope this helps!!
An octagonal prism has...........lateral faces.
8
2
7
5
Answer:
an octagonal prism has 8 lateral faces
Answer:
8
Step-by-step explanation:
An octagonal prism has 8 lateral faces.
An octagonal prism has 10 faces – 8 lateral faces and 2 bases, 16 vertices, and 24 edges
Enter the value of 2 (4x + 3) when x = 3.
Answer:
30 is your answer
Step-by-step explanation:
2(12+3)
=30
Write an equation of the line that passes through (2, 1) and is parallel to the line y=2x+7.
Answer: y=2x-3
Step-by-step explanation:
Use the figure to find the measures of the numbered angles. ∠3 = ∘ ∠4 = ∘
Answer:
Step-by-step explanation:
∠3=95 (corresponding angle)
∠4=180-95
=85
Will give Brainly! Please help!
Answer:
The answer is option c.
Hope this helps!
Round 14.6837 to the nearest HUNDREDTHS
Answer:
it's 14.68
Step-by-step explanation:
Answer:
14.68
Step-by-step explanation:
1|4|.|6|8|3|7
1=tens
4=ones
.=decimal
6=tenths
8=hundreths
3=thousanths
7=ten thousandths
3 is less than 5 so 8 stays the same
35= h(b1+b2) solve for b2
Answer: look at the picture and I don’t know how to solve for b but I can do h
Step-by-step explanation: hope this help :)
Answer:
i dont know
Step-by-step explanation:
i dont know
Avery is buying string and beads to make bracelets for her family and friends. She plans to divide the string into 9-inch pieces to make at least 27 bracelets. What is the minimum amount of string she needs to buy?
Answer:
243 inches
Step-by-step explanation:
27 bracelets at 9inches each
9x27=243 inches or 20 feet and 1/4 inches of string. Depending on how the string is sold (by the foot, by the inch, yard, etc) will determine her minimum quantity, if you want to get specific.
Round to the nearest tenth.
x=
y=
Use properties of operations to determine whether or not the expressions (x + 10) + x + 9 and 2(x + 7) + 5 are
equivalent
Answer:
The expressions are equivalent.
Step-by-step explanation:
We can simplify each expression and compare the results.
(x + 10) + x + 9 = x + 10 + x + 9 = 2x + 19
2(x + 7) + 5 = 2x + 14 + 5 = 2x + 19
2x + 19 = 2x + 19
Answer: The expressions are equivalent.
Select the correct answer.
The surface area (SA) of a cube with a as the length of each of its sides is given by the formula SA = 6a2. If the surface area is known, how can
you rewrite the formula to find its side?
ОА va
OB. VSA
OC a = $
OD. =
Answer:
(A). [tex]\sqrt{\frac{SA}{6} }[/tex]
Step-by-step explanation:
Adult tickets to a play cost $22 tickets for kids cost $15. Tickets for a group of 11 cost a total of $228. How many children and how many adults went to the play?
Answer:Number of children = 2 and number of adults = 9 attended the play
Step-by-step explanation:
Step 1
Let the number of children be represented as x
and the number of adults in the group be represented as as y
such that the total number of the group that went to the play
= x+y=11--- equation 1
And the total cost paid for the play will be expressed as
15x+ 22y= 228------ equation 2
Step 2-- Solving
x+y=11--- equation 1
15x+ 22y= 228------ equation 2
B y elimination method, multiply equation 1 by 15 to give equation 3 and then subtract from equation 2
15x+ 22y= 228------ equation 2
15x+15Y= 165----- equation 3
7y=63
y= 63/7= 9
y= adults = 9
therefore x = number of children will be
x+y=11
x+ 9=11
x= 11-9= 2
In the group that attended the play, Number of children = 2 and number of adults = 9
Can someone help me with these 2 problems thank you
Answer:
For question 6 there are 3 steps, and for question 7 there are 2 steps
Step-by-step explanation:
Question 6:
step 1. 89 x 2=178
step 2. 89 x 3=267
step 3. 267 + 178=445
Question 7:
step 1. 35 x 3= 105
step 2. 25 x 5= 12
Your're welcome :)
what is the least common multiple (LCM) of 5 and 7 plz help need my grades up
Answer:
The least common multiple of 5 and 7 is 35
Step-by-step explanation:
Because 5 x 7 is 35
Answer:
The Least common multiple ( LCM) of 5 and 7 is 35
Step-by-step explanation:
We list the first few multiples of 5 and 7a and identify the common multiples .
The least among the common multiples is the LCM of 5 and 7.
LCM 5 and 7
Multiples of 5: 5,10,15,20,25,30,35,40,45
Multiples of 7: 7,14,21,28,35,42,49
The Least common multiple of 5 and 7 is 35 .
l hope it helps ❤❤
The main mast of s sailboat is supported by a rope that extends from the top of the mast to the deck. If the mast is 23 feet tall and the rope attaches to the deck 15 feet away from the base of the mast, how long is the rope?
Answer:
27.46
Step-by-step explanation:
please help me with this problem
Answer:
vitamin c is the independent variable
Step-by-step explanation:
the amount of vitaman c dose not change but the amount of oranges eaten can change
Which term has the definition "The value that describes the location of a digit within a number, such
as units, tens, hundreds, etc."?
O Repeating Decimal
O Rational Number
O Terminating Decimal
O Place Value
Answer:
place value is the answer
Answer:
The answer is 'PLACE VALUE'
Step-by-step explanation: