The area of the region that lies inside both curves is 11π/3 - 9√3/2 square units.
The area of the region that lies inside both curves first need to find the points of intersection.
The two equations equal to each other and solve for θ:
6sin(2θ) = 6sin(θ)
Dividing both sides by 6 get:
sin(2θ) = sin(θ)
The identity sin(2θ) = 2sin(θ)cos(θ) can rewrite this as:
2sin(θ)cos(θ) = sin(θ)
Dividing both sides by sin(θ) we get:
2cos(θ) = 1
Solving for θ we get:
θ = π/3, 5π/3
The area of the region by integrating the function r with respect to θ from θ = π/3 to θ = 5π/3:
A = ∫[π/3, 5π/3] 1/2 r² dθ
r = 6sin(2θ) when 0 ≤ θ ≤ π and r = 6sin(θ) when π ≤ θ ≤ 2π.
Substituting the appropriate values of r and integrating, we get:
A = ∫[π/3, π] 1/2 (6sin(2θ))² dθ + ∫[π, 5π/3] 1/2 (6sin(θ))² dθ
= ∫[π/3, π] 27sin²(2θ) dθ + ∫[π, 5π/3] 18sin²(θ) dθ
= [9θ - 3/4 sin(4θ)]π/3π + [6θ - 9/2 cos(2θ)]π/5π
= (π/3)[9π/2 - 3√3] + (2π/3)[5 - 9√3/2]
= 11π/3 - 9√3/2
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The w of a golden rectangle is 30cm. Find the lengths to the nearest centimeter
The length of the golden rectangle is 49 cm.
A rectangle is a quadrilateral (a polygon with four sides) in which each angle is a right angle (90 degrees). It is a type of parallelogram in which opposite sides are parallel and congruent (equal in length). Rectangles have four sides and four vertices (corners).
The length of a rectangle is the distance between its two longer sides, while the width is the distance between its two shorter sides. The perimeter of a rectangle is the sum of the lengths of all its sides, while the area is the product of its length and width.
A golden rectangle has sides in the proportion of the golden ratio, which is approximately 1:1.618. Therefore, if the width is 30cm, the length can be found by multiplying 30 by 1.618.
Length ≈ 48.54 cm
The length of the rectangle is 49 cm.
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janice wants to book a holiday
the holiday will cost £ 1754
janice will pay a deposit of £350
she will then pay the rest od the cost in 6 equal monthly payments
how much is each monthy paymwnt
Answer: £234
Step-by-step explanation:
First, we need to subtract the deposit (£350) from the total cost of the trip (£1754):
£1754 - £350 = £1404
Then we need to divide the remaining amount of money (£1404) by the number of months Janice will be on holiday (6 months):
£1404 ÷ 6 months = £234 each month
Hope this helps!
Bookwork code: K27
,Calculator
allowed
A pendulum of length 18 cm is swinging from a fixed point, as shown.
Calculate the distance that the end of the pendulum travels when it swings
through an angle of 87°.
Give your answer in centimetres (cm) to 1 d.p.
87°
18 cm
The distance that the end of the pendulum travels when it swings is given by the relation D = 27.3 cm
Given data ,
A pendulum of length 18 cm is swinging from a fixed point
Now , it swings through an angle of 87°
So , Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
Now , D = ( θ/360 ) x 2πr
On simplifying , we get
D = ( 87 / 360 ) x 2 ( 3.14 ) ( 18 )
D = ( 0.241667 ) ( 113.04 )
D = 27.3 cm
Hence , the pendulum travels a distance of 27.3 cm
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The parking lot at a mall has space for 318 cars. Eight percent of the parking spaces are for compact cars. About how many parking spaces are for compact cars? Explain.
pls answer me fast rapidly:
l want the steps.
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The first derivative of the parametric curve is:
dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]
How to solve1. To find the first derivative of the parametric curve x = 1/(t-1) and [tex]y = t^2/(t-1)[/tex], we can use the chain rule.
2. Let's differentiate each component separately.
3. Differentiating x with respect to t, we have:
dx/dt = [tex]-1/(t-1)^2[/tex]
4. Differentiating y with respect to t, we have:
dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2[/tex]
5. Therefore, the first derivative of the parametric curve is:
dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]
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3x° P (2x+45)° find the x value
Since angles M and P are complementary, if m∠M = 3x - 45 and m∠P = 2x + 15, the value of x is 24
and the value of M and P are 27° and 63° respectively.
Since M and P are complimentary, that means the sum of them is = 90°
So
3x - 45 + 2x + 15 = 90
Taking like terms
3x + 2x = 90 + 45 -15
5x = 120
x = 120/5
x = 24
to find M and P
since m∠M = 3x - 45
m = 3(24) -45
m = 27°
m∠P = 2x + 15
since x = 60
P = 2(24) + 15
P = 63°
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Angles M and P are complementary. If m∠M = 3x - 45 and m∠P = 2x + 15, what is the value of x? What is the measure of each angle?
find the perimeter of an equilateral triangle of edge of 4.24 cm
Answer:
perimeter = 12.72 cm
Step-by-step explanation:
an equilateral triangle has 3 congruent sides
the perimeter is the sum of the 3 sides , that is
perimeter = 4.24 + 4.24 + 4.24 = 12.72 cm
In Austin TX the cost of housing for a family of four is $1600 per month. How much more would the family need to bring home annually in order to cover the cost of increased housing
The family would need to bring home an additional $2400 annually to cover the increased cost of housing.
The family would need to bring home annually to cover the cost of increased housing need to calculate the total cost of housing for a year and subtract the current annual cost of housing.
The current monthly cost of housing is $1600 so the annual cost is:
$1600/month x 12 months = $19,200/year
Let's assume the family needs to cover an increased housing cost of $200 per month.
The new monthly cost of housing would be:
$1600/month + $200/month = $1800/month
The new annual cost of housing would be:
$1800/month x 12 months = $21,600/year
The family would need to bring home annually to cover this increased cost need to subtract the current annual cost of housing from the new annual cost of housing:
$21,600/year - $19,200/year = $2400/year
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Graph the function f(x) = -(1/5)^x+5 +7 on the axes below. You must Plot the asymptote and any two points with the integer coordinates
The graph of the function is added as an attachment
The asymptote: y = 7 and the points are (-5, 6) and (-7, -18)
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = -(1/5)ˣ ⁺ ⁵+ 7
The above function is an exponential function that has been transformed as follows
Reflected over the x-axisDecay factor of 1/5Shifted left by 5 unitsShifted up by 5 unitsNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment, where we have the following points
Asymptote: y = 7
(-5, 6) and (-7, -18)
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Please help asap I need to turn this in RIGHT NOW
The requried domain and range of the given graph are a set of all real values i.e. (-∞, ∞).
Consider the given figure,
The domain is said to be the values of the set of dependent variables, in the given case the value on the x-axis, represents the domain.
The domain is given as all real value i.e. (-∞, ∞)
Similarly, the range is represented by the y-axis and given as (-∞, ∞).
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a) On the occasion of Teej, the principal of a school organized a Teej program for her female staffs. She distributes 90 bangles and 108 sweets equally to the staffs including herself. If there are 20 male staffs in the school, find the maximum number of staffs of her school.
The maximum number of staff at the school, given the distribution of bangles and sweets, is 38 staff.
How to find the number of staff ?The principal has distributed 90 bangles and 108 sweets equally among her female staff includng herself. This means that the total number of female staff in the school is a number that can divide both 90 and 108 evenly, as each staff member must receve an integer number of bangles and sweets.
Find the greatest common divisor (GCD) of 90 and 108. The GCD of 90 and 108 is 18.
So, the princpal's school has 18 female staff including herself. In addition to the 20 male staff, this implies a maxmum of:
18 (female staff) + 20 (male staff) = 38 staff in total
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Give the coordinates of the point in the graph below.
-5
A
32
-3 -2
-1
-4
-3-
2-
0
-1-
--2-
-3-
-4
-5
-N-
2
3
4
5.
The coordinates of the point in the graph is (3, 2)
How to determine the coordinates of the point in the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following
The point is 3 units to the right of the x-axisThe point is 2 units above the y-axisRepresent the point with x
So, we have
X = (3, 2)
Hence, the coordinates of the point in the graph is (3, 2)
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.will give brainless
Step-by-step explanation:
OK, 'Brainless'.... the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...
42 + 20 > x then 12 , 20, 22, 32, 42, 50 will work here
42+x > 20 all of the possibles work here
20 + x > 42 32, 42, 50, 62 and 70 work here
so 32 and 42 are in all of the lists ....that is your answer
What is the solution of 3√x+8 = -4? X =√72 O x=-66 O x = 58 O no solution
Answer: add image
Step-by-step explanation:
A survey of the people who like the films made in Nepali, English or Hindi languages reported that 50 liked Nepali, 40 liked English, 30 liked Hindi, 24 liked Nepali and 11 English, 19 liked Nepali and Hindi, 13 liked Hindi and English, 6 liked all three and people were found not intended in any films.
To solve this problem, we can use the formula:
Total = n(A) + n(B) + n(C) - n(A and B) - n(A and C) - n(B and C) + n(A and B and C)
where:
n(A) = number of people who liked Nepali
n(B) = number of people who liked English
n(C) = number of people who liked Hindi
n(A and B) = number of people who liked both Nepali and English
n(A and C) = number of people who liked both Nepali and Hindi
n(B and C) = number of people who liked both English and Hindi
n(A and B and C) = number of people who liked all three languages
From the given information in the problem, we have:
n(A) = 50
n(B) = 40
n(C) = 30
n(A and B) = 11
n(A and C) = 19
n(B and C) = 13
n(A and B and C) = 6
We can now substitute these values into the formula:
Total = 50 + 40 + 30 - 11 - 19 - 13 + 6
Total = 73
ANSWER: Therefore, there were a total of 73 people who liked at least one of the three languages.
Given that events A and B are independent with P(A) = 0.68 and
P(A and B) = 0.544, determine the value of P(B), rounding to the nearest
thousandth, if necessary.
The value of P (B) = 0.8
The probability of event A, P (A) = 0.68
The probability of events A and B, P (A ∩ B) = 0.544
The probability of event B, P (B) = ?
We know that Independent events are those where the probability of A event occurring doesn't affect the probability of B event. In other words, they don't depend upon each other and are independent.
By formula;
P (A ∩ B) = P (A) . P (B)
By substituting the values to the above equation, we get;
0.544= 0.68 * P (B)
P (B) = 0.8
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Dividing by Binomials and Polynomials
ovement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
Match each expression on the left with its quotient on the right.
(x²-x-30) + (x-6)
(x³ - 2x² - 7x-4) + (x² + 2x + 1)
(x³ + 2x² - 1) + (x²-x + 1)
Clear
x+3 R2x-4
x+5
x-4
Click and hold an item in one column, then drag it to the matching item in the other column.
The target will highlight or the cursor will change. Need help? Watch this video.
The division expressions to the quotients and remainders are
(x² - x - 30) ÷ (x - 6) = x - 5(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1) = x - 4(x³ + 2x² - 1) ÷ (x² - x + 1) = x + 3 R 2x - 4Matching the division expressions to the quotient and remaindersExpression (a)
The expression is given as
(x² - x - 30) ÷ (x - 6)
The synthetic set up is
6 | 1 -1 30
|__________
Bring down the first coefficient, which is 1 and repeat the process
6 | 1 -1 30
|___6_-30_____
1 -5 0
This means that
Quotient = x - 5 with no remainder
Expression (b)
The expression is given as
(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1)
Using a graphing tool, we have
(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1) = x - 4 with no remainder
This means that
(x³ + 2x² - 1) ÷ (x² - x + 1) = x + 3 R 2x - 4
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Given: Isosceles trapezoid ABCD with diagonals BD and AC Identify the missing reason in the proof.
The statement thet complete the proof of the congruent triangles is (a) SAS criterion
How to determine the statement thet complete the proof of the congruent trianglesFrom the question, we have the following parameters that can be used in our computation:
The incomplete proof
In the proof, we have
AD ≅ BC --- side length
DC ≅ DC --- side length
∠ADC ≅ ∠BCD -- angle
This means that the triangles are congruent by the SAS theorem
The SAS theorem is defined by "If two sides in one triangle are congruent to two sides in another triangle and the included angle in both are congruent, then the two triangles are congruent"
This means that they are congruent by the SAS congruent
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Answer: A. SAS criterion.
Step-by-step explanation: Angle : ∠ADC ≅ ∠BCD Side length : AD ≅ BC Side length : DC ≅ DC
Because of this △ADC ≅ △BCD by SAS criterion.
How many faces dose a dodecahedron have
Answer:12 faces and 20 vertices
Step-by-step explanation:
Dodecahedron:- The three-dimensional geometric geometry of a dodecahedron comprises 20 vertices, 30 edges, and 12 flat faces.
Each face is a regular pentagon, with five equal-length sides and five equal-sized angles. One of the five Platonic solids, regular, convex polyhedrons with identical regular polygon faces and equal angles between them, the dodecahedron is one of these regular, convex polyhedrons. The dodecahedron is frequently utilised in architecture, design, and the arts because of its great degree of symmetry.
A dodecahedron has 12 faces.
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I’m not good at these
That's quadratic.
y=x^2
It's a very simple version of y=ax^2+bx+c. Just in this case, a = 1, b = 0 and c = 0.
rate of change between (-4,-12)and (2,4)
Answer: 2.667
Step-by-step explanation:
Answer:
Can you mark me brainiest.
Step-by-step explanation:
Instead of me telling you the answer I will make it easy for you go to M a th way its very easy.
Or 2.667
Using the MACRS rates from the following table, what is the book value of a $2,500 computer after 3 years? Ro Year MACRS Rate 1 2 3 4 5 20.0 % 32.0% 19.2% 11.52 % 11.52% book value = [?]
Using MACRS rates, the book value of the $2,500 computer after 3 years is $720.
What are MACRS rates?MACRS (Modified Accelerated Cost Recovery System) rates are prearranged percentages used for the purposes of tax.
They compute how much an asset depreciates each year based on its class and expected lifespan.
Using MACRS rates, we shall calculate the book value of a $2,500 computer after 3 years in this way.
First, we shall apply the respective depreciation rates to the initial cost and subtract the accumulated depreciation each year.
Year 1:
Depreciation = Year 1 MACRS Rate x Initial Cost
Depreciation = 20.0% × $2,500 = $500
Year 2:
Depreciation = Year 2 MACRS Rate x Initial Cost
Depreciation = 32.0% × $2,500 = $800
Year 3:
Depreciation = Year 3 MACRS Rate x Initial Cost
Depreciation = 19.2% × $2,500 = $480
Next, subtract the accumulated depreciation from the initial cost to have the book value for each year:
Year 1:
Book Value = Initial Cost - Depreciation
Book Value = $2,500 - $500 = $2,000
Year 2:
Book Value = Year 1 Book Value - Year 2 Depreciation
Book Value = $2,000 - $800 = $1,200
Year 3:
Book Value = Year 2 Book Value - Year 3 Depreciation
Book Value = $1,200 - $480 = $720
Therefore, the book value of the $2,500 computer after 3 years is $720.
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Find The perimeter of an equilateral triangle Of edge 4.24 cm
The required perimeter of the equilateral triangle is 12.72 cm.
An equilateral triangle has all three sides equal in length. Therefore, if the edge of an equilateral triangle is 4.24 cm, then all three sides are 4.24 cm.
To find the perimeter of the equilateral triangle, we need to add the length of all three sides together:
Perimeter = 4.24 cm + 4.24 cm + 4.24 cm
Perimeter = 12.72 cm
Therefore, the perimeter of the equilateral triangle is 12.72 cm.
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Find domain and range thank you for the help have a great afternoon
Step-by-step explanation:
Domain : (-5,4]
Range [-2,0)
BC is tangent to circle A at point B. DC=9 and BC=15. find the radius of the circle.
If $22,000 is invested in an account earning 4.5% interest compounded continuously,
determine how long it will take the money to quadruple. Round to the nearest year.
Use the model A = Pet where A represents the future value of P dollars invested at
an interest rate r compounded continuously for t years.
OA) 31 years
B) 36 years
OC) 3 years
D) 308 years
Answer:
31 years
Step-by-step explanation:
A = P(interest rate)^number of years (n)
if the money is to quadruple, A = 4 X 22,000 = 88,000.
P = investment amount = 22,000.
interest rate is 4.5%. so we have the whole (100%) + 4.5% = 1.045%.
n is number of years.
22,000 (1.045)^n = 88, 000
divide both sides by 22, 000:
(1.045)^n = 4
take logs for both sides:
log (1.045)^n = log 4
simplify using log laws (by bringing down the n):
n log (1.045) = log 4
divide both sides by log (1.045):
n = (log 4) / log (1.045)
= 31.49 (31 years to nearest year)
In ⊙C, DE≅FG. Select all the statements that must be true.
A. △DCE≅△FCE
B. arcDE arcFG
C. △FCE≅△FCG
D. ∠DCE≅∠GCF
E. EF≅ED
In a circle with congruent line segments DE and FG, statements A is true, B is false, C and D are false, and E may or may not be true.
In the given circle ⊙C, DE and FG are two line segments that are congruent. The following statements must be true:
A. △DCE≅△FCE: This statement is true because both triangles share the same side lengths of DE and FG and the common angle ∠DCE = ∠FCE.
B. arcDE = arcFG: This statement is false since congruent line segments do not necessarily correspond to congruent arcs in a circle.
C. △FCE≅△FCG: This statement is false since there is no given information to suggest that the line segment CG is congruent to CE.
D. ∠DCE≅∠GCF: This statement is false since there is no given information to suggest that ∠GCF is congruent to ∠DCE.
E. EF≅ED: This statement may or may not be true since we are not given any information about the length of either of these line segments.
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A 4-digit number has the digits 0,5,9 and 3.To the nearest thousand,it rounds to 10,000. What is the number? Explain.
Answer: 9530
Step-by-step explanation: It has to be 9 in the thousands place to start of. And for it to round to 10,000, it would have to be 5 since it would round up one more thousand. And I would just say 3 because its bigger. Then 0
Find the probability that a randomly
selected point within the square falls in the
red-shaded square.
1
1
3
P = [?]
3
Enter as a decimal rounded to the nearest hundredth.
The probability that a randomly selected point within the square falls in the red-shaded square is 0.11
Finding the probabilityFrom the question, we have the following parameters that can be used in our computation:
Red square of length 1White square of length 3The areas of the above shapes are
Red square = 1² = 1
White square = 3² = 9
The probability is then calculated as
P = Red square/White square
So, we have
P = 1/9
Evaluate
P = 0.11
Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.11
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