π/32 is the area enclosed by the curve r= sin(8θ)
The given curve is polar curve and hence the area of the polar curve is given by:
Let A be the area of the curve so,
A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex]
where a and b is the boundary at which r=0
so after equation r=0
sin(8θ) =0
=> sin(8θ) =0
=> 8θ = 0,π
=> θ = 0, π/8
so a=0 , b= π/8
now
A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex] ------(i)
so [tex]r^2[/tex] = (sin(8θ))^2
=> [tex]sin^2[/tex] ( 8θ )
ans we know that
cos(2α) = 1 - 2[tex]sin^2[/tex] α
so [tex]r^2[/tex] = (1- cos(16θ) )/2
putting the value of r in the equation (i) we get :-
A = [tex]\int\limits^a_b {\frac{1}{4} *(1-cos(16\alpha ) } \, d\alpha[/tex]
=> 1/4* [tex]\int\limits^a_b {(1-cos(16\alpha ) } \, d\alpha[/tex]
here a=0 and b=π/8
after putting the value and solving the integral
A = π/32
so A is the area enclosed by r=sin(8θ) is π/32
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a conditional probability p(b|a) is equal to its marginal probability p(b) if
A conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.
The likelihood that any two events will occur is equal to the sum of the probabilities of each event separately, less the probability that the two occurrences will meet. However, if two occurrences are incompatible with one another, then there is a zero probability of the two events intersecting, therefore the likelihood that either one or the other will occur is equal to the sum of the two individual probabilities.
To calculate conditional probability, use the following formula:
p( b | a ) = p( a ∩ b )/ p(a)
It is known that if two events A and B are independent, then p(a ∩ b) = p (a) . p(b)
So, p(b | a) = [p (a) . p(b)]/p(a) = p(b)
Thus, it is concluded that a conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.
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If vertical angles are congruent, then two lines cut by a transversal are parallel.a. Trueb. False
The vertical angles are congruent, then the two lines cut by a transversal are parallel is False.
Option B is the correct answer.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
Vertical angles are congruent.
Vertical angles are pairs of opposite angles made by intersecting lines.
Thus,
For vertical lines to be congruent, we do not need two parallel lines.
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Consider the figure shown below (not drawn to scale). Both of the triangles are RIGHT triangles. y X(0,13) Y(0,7) Z(0,3) (0,0) J The length of vertical segment XY is: W(3,13) P 0 T(9,9) S(9,3) -X
Both of the triangles are RIGHT triangles. y X(0,13) Y(0,7) Z(0,3) (0,0) J. the length of vertical segment XY is 6.
What is a vertical segment?Generally, A part of a line that is totally vertical is referred to as a vertical line segment. This means that the two vertices that make up the segment's ends have the same x- and y-coordinates but different z-coordinates than one another.
The length of vertical segment XY can be found by subtracting the y-coordinate of point X from the y-coordinate of point Y.
In this case, the y-coordinate of point X is 13 and the y-coordinate of point Y is 7, so the length of vertical segment XY is
13 - 7 = 6.
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Complete Question not found
Image not found
b(t)=1000 times e^.03t how long to reach $1500
Answer:
Below
Step-by-step explanation:
1500 = 1000 e^.03t
1.5 = e^.03t
take LN of both sides
.405465 = .03 t t =13.5 yrs
2[(x+2y)-4(6x+3y)+(4x+3y)]
Answer:
-38x - 14y
Step-by-step explanation:
2[x+2y - 24x - 12y + 4x + 3y]
2 [ -19x -7y]
- 38x - 14y
A function is graphed below. On which
interval of x is the average rate of change
of the function the smallest?
X
3
7
21
39
65
Y
3
18
28
36
40
Answer:
The x-axis interval of 39 to 65 has the smallest rate of change.
Step-by-step explanation:
See the attached worksheet. The interval of x that results in the least change in y can be visually seen by plotting the points and drawing a curve. The curve begins to flatten as x increases. So the smallest rate of change is between the last two points, x = 39 to 65.
This can also be calculated by finding the change in y per a change in x. The table in the graph confirms the earlier observation. Dx and Dy represent the "delta," or difference, D, between the x (Dx) and y(Dy) values. The rate of change is calculated as Dy/Dx, or the change in y divided by the change in x. The results confirm that the 39 to 65 segment is the smallest, at 0.15.
The ordered pair that is a solution of the equation y = | -6x + 2 |
The ordered pair that is a solution to the given equation, y = | -6x + 2 |, is (1, 4)
Determining the ordered pair that is a solution to an equationFrom the question, we are to determine the ordered pair that is a solution of the given equation
The given equation is
y = | -6x + 2 |
To determine the ordered pair that is a solution to the equation, we will pick a value for x and determine the value of y for the value
y = | -6x + 2 |
Put x = 1
y = | -6(1) + 2 |
y = | -6 + 2 |
y = | -4 |
y = 4
Hence, the ordered pair is (1, 4)
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Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.)
(a) (−7, 7, 7)
(√98, 7π /4,7) Incorrect:
(b) (−7, 7 3 , 1)
(14, π /3,1) Incorrect:
The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is (14, -π/3, 1).
We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)
A)(−7, 7, 7)
Given rectangular coordinates(x, y, z) =(−7, 7, 7)
The cylindrical coordinates are (r, θ, z)
As a result, we determine each value of r and θ separately.
r = √x²+y²
r = √(-7)²+(7)²
r = √49+49
r = √98
θ = tan⁻¹ (y/x)
θ =tan⁻¹ (7/-7)
θ =tan⁻¹ (-1)
θ = -π/4
So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)
B) (-7,7√3,1)
Given rectangular coordinates(x, y, z) = (-1,1,1)
The cylindrical coordinates are (r, θ, z)
As a result, we determine each value of r and θ separately.
r = √x²+y²
r = √(-7)²(7√3)²
r = √49+147
r = √196
r = 14
θ = (y/x)
θ = (7√3/-7)
θ = (-√3)
θ = -π/3
So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)
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What is the slope of the line that passes through the points (2, 3) and (0, 11)? Write
your answer in simplest form.
Answer:
The slope is -4.
Step-by-step explanation:
[tex]m = \frac{11 - 3}{0 - 2} = \frac{8}{ - 2} = - 4[/tex]
Whats the common denominator to find equivalent fractions for 2/3 and 1/6.
The common denominator of the fractions 2/3 and 1/6 will be 6.
What is the lowest common multiple?The lowest common multiple is the smallest multiple which is common between any two numbers.
It means we can divide both numbers by that and that is the smallest number by which both dived.
As per the given fractions 2/3 and 1/6.
Multiply 2 in numerator and denominator in 2/3.
2/3 x 2/2 = 4/6
Now denominator is the same thus common denominator is 6.
Hence "6 will be the common denominator for the fractions 2/3 and 1/6".
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PLEASE GIVE ME RIGHT ANSWERS HELP ME FAST I BEG YOU
17. Louis is offered an interest rate of 6.35%
for an investment with continuous
compounding. What is his equivalent rate
of interest with simple compounding?
[A] 1.23 or 12.3%
[B] 0.0593 or 5.93%
[C] 0.423 or 42.3%
ID] 0.0656 or 6.56%
[E] 0.0615 or 6.15%
The rate of interest for simple compounding if Louis is offered an interest rate of 6.35% for an investment with continuous compounding, is 0.0656 or 6.56%, so option D is correct.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
Louis is offered an interest rate of 6.35% for an investment with continuous compounding,
Here, P will be the same, the amount will be the same and the time period will be the same then,
The amount in simple compounding = The amount in continuous compounding
[tex]P(1 + r)^t = Pe^{rt}[/tex]
Here, r is the rate of interest for simple compounding,
[tex]1 + r = e^{0.0635}[/tex] (All same quantities get canceled)
r = 1.0656 - 1
r = 0.06556
r = 0.0656
r = 6.56%
Thus, the rate of interest for simple compounding is 6.56%.
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please help me answer this question
Answer:
The two equations are true for the same value because when you substitute 7 for x both of them are correct
Step-by-step explanation:
1) 3(7) - 5 = 16 3(7) = 21
27 - 5 = 16 21 = 21
16 = 16 True
True
points b , c and d lie on a straight line
AC is perpendicular to BD
BC=6cm and BD=22cm
triangle ABC has an area of 42
calculate the size of angle x
Step-by-step explanation:
To Find : size of angle x
Solution:
Area of ΔABC = (1/2) * BC * AC
=> (1/2) * BC * AC = 42
=> (1/2) * 6 * AC = 42
=> AC = 14 cm
BD = BC + CD
=> 22 = 6 + CD
=> CD = 16 cm
Tan x = AC /CD
=> Tan x = 14/16
=> Tanx = 7/8
=> x = Tan⁻¹(7/8)
=> x = 41.186°
The size of the angle is - 41. 186°
Points b,c, and d lie in a straight line. AC is perpendicular to BDBC = 6 cm, BD = 22 cm. Triangle ABC has an area of 42cm². the size of the angle = xarea of triangle ABC = 1/2 * BC * AC
or, 1/2 *BC * AC = 42
or, 1/2 * 6 * AC = 42
or, 3 * AC = 42
divide both sides by 3,
AC = 14 cm
BD = BC + CD
or, 22 = 6 + CD
or, CD = 16 cm
tan x = [tex]\frac{AC}{CD}[/tex]
or, tan x = [tex]\frac{14}{16}[/tex]
or, tan x = [tex]\frac{7}{8}[/tex]
or , x = 41. 186°
∴ The size of the angle is - 41. 186°.
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What is the quotient?
Answer:
11/50
Step-by-step explanation:
=5x2+1= 11/5
=1/10×11×5
=11/50
M. Jone wahed
2
5
of her laundry. Her on wahed
1
4
of it. Who wahed mot of the laundry? How much of the laundry till need to be wahed?
Solve thi on paper. Then check your work on Zearn. Who wahed mot of the laundry?
i greater than
o wahed mot of the laundry
Ms. Jones washed most of the laundry and the remaining laundry need to be washed is 7/20.
Converting the fraction to decimal to easily compare the amount of laundry washed.
Laundry washed by Ms. Jones = 2/5
Performing division
Laundry washed by Ms. Jones = 0.4
Laundry washed by her son = 1/4
Performing division
Laundry washed by her son = 0.25
0.4 is greater than 0.25, hence, Ms. Jones washed more laundry.
They washed the laundry in fractions. So, the total laundry can be taken as 1.
Total laundry washed = 0.4 + 0.25
Total laundry washed = 0.65
Remaining laundry = 1 - 0.65
Performing subtraction
Remaining laundry = 0.35
Converting into fraction = 35/100
Remaining laundry in fraction = 7/20
Thus, Ms. Jones washed more laundry and 7/20 is remaining.
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The complete question is -
Ms. Jones washed 2/5 of her laundry. Her son washed 1/4 of it. How much of the laundry still needs to be washed?
high school has 36 players on the football team. the summary of the players' weights is given in the box plot. how many players weigh between 169 and 194 pounds?
There are 8 players who weigh between 169 and 194 pounds.
To answer this question, we can look at the box plot to understand the distribution of weights on the football team. The box plot shows us the minimum, maximum, median, and quartiles of the team's weights. The left quartile is 169 pounds, and the right quartile is 194 pounds. This means that 25% of the team's players weigh between 169 and 194 pounds. Since the team has 36 players, 25% of 36 is 9. However, since we are looking at the number of players between 169 and 194 pounds, we need to subtract 1 since the right quartile of 194 pounds is included in the number of players. Thus, there are 8 players who weigh between 169 and 194 pounds.
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if f(x) + x2[f(x)]5 = 34 and f(1) = 2, find f '(1).
if f(x) +[tex]x^{2}[/tex] [tex][ f(x) ]^{5}[/tex] = 34 and f(1) = 2, then f '(1) = - [tex]\frac{64}{81}[/tex]
f ′(x )'s indicates that it is derived from f (x). The second notation is dydx. The instantaneous rate at which y changes in relation to x is shown by this notation.
f(x) + [tex]x^{2}[/tex] [tex][ f(x) ]^{5}[/tex] = 34
differentiate with respect to x :
f' (x) + [tex]x^{2}[/tex] . 5 [tex][ f(x) ]^{4}[/tex] f'(x) + [tex][ f(x) ]^{5}[/tex] 2x = 0
putting x = 1
f' (1) + [tex]1^{2}[/tex] . 5 [tex]f(1)^{4}[/tex] f'(1) + [tex]f(1)^{5}[/tex] 2(1) = 0
f' (1) + 1.5 [tex](2)^{4}[/tex] f'(1) + [tex](2)^{5}[/tex] . 2 = 0
f' (1) + 80 f' (1) = - 64
81 f' (1) = - 64
f' (1) = - [tex]\frac{64}{81}[/tex]
thus , the f ' (1) is found.
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make a box-and-whisker plot of data 21,27,22,22,25,14,16,10
The minimum value, Q1, Median, Q3 and maximum value of the data are 10,15,21.5, 23.5 and 27 respectively. The box-and-whisker plot of data is attached
How to make a box-and-whisker plot of data?Given: 21,27,22,22,25,14,16,10
Arrange the data in ascending or descending order:
10,14,16,21,22,22,25,27
The minimum value = 10. The maximum value = 27
Find the median. The median is the value in the middle. The median values are 21 and 22. Thus:
10,14,16,21,22,22,25,27
Median (Q2) = (21+22)/2 = 21.5
Consider the values to the left of the median with one of the median numbers included (since we have two numbers in the middle): 10,14,16,21
Median = (14+16)/2 = 15
Thus, Q1 = 15
Also, consider the values to the right of the median with one of the median numbers included: 22,22,25,27
Meadian = (22+25)/2 = 23.5
Thus, Q3 = 23.5
To create a box and whiskers plot use Minimum value, Maximum value, Q1, Median(Q2) and Q3 (Check the attached image)
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Daliyah is given one point on a line as (3,−1) and the slope of the line as −5. What is the y-intercept of the line?
Answer: The y-intercept is 14
Step-by-step explanation:
The slope intercept is y=mx+b
since we already have the slope, we can write this as
y=-5x+b
substitute the points of (3,-1) into the equation and solve for b
-1=-5(3)+b
-1=-15+b
b=14
The y-intercept is 14
The y-intercept of the line is 14.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Slope = -5
The line passes through the point (3, -1).
The equation of the line is y = mx + c.
y = -5x + c
(3, -1) = (x, y)
-1 = -5 x 3 + c
-1 = -15 + c
-1 + 15 = c
c = 14
Thus,
The y-intercept is 14.
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The gift hop at the Harbor Lighthoue ordered a hipment of 45 hirt with a pecial whale print. The hirt come in 5 different ize, and there are the ame number of hirt in each ize. How many hirt did the tore order in each ize? Write a diviion equation with that model the tory
equation will be the number of shirts ordered in each size. division equation with that model the theory 45 ÷ 5 = 9
The Harbor Lighthouse gift shop ordered a shipment of 45 shirts with a special whale print. This means that we need to divide 45 by 5, in order to find out how many shirts were ordered in each size. To do this, we can use a division equation.
In this equation, 45 represents the total number of shirts and 5 represents the number of sizes. The answer to this equation will be the number of shirts ordered in each size. When we divide 45 by 5, we get 9 as our answer. Therefore, the store ordered 9 shirts in each size.
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Question 2
Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an'hour babysitting. What is the solution of the
inequality that determines how many hours she will need to babysit to buy the dress?
Let x represent the number of hours Matilda babysits.
Answer: x ≥ 8
Step-by-step explanation:
We know that our inequality must be greater than or equal to $112 because she needs at least $112 to buy the new dress. This is the first part of our inequality.
Next, we see that she already has $40 and will earn $9 an hour babysitting, if x is the number of hours. $9 an hour can become 9x, then we will add the $40 she already has for 9x + 40 as the second part of our inequality.
This complete inequality is:
9x + 40 ≥ 112
Now, we can solve by isolating the variable x with inverse operations.
9x + 40 ≥ 112
9x ≥ 72
x ≥ 8
Matilda needs to babysit at least 8 hours to afford the new dress.
PLEASE HELP n is m% of what
Answer:
100n/m
Step-by-step explanation:
n = m% of x
n = mx/100
x = 100n/m
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-3,-5) and (5,0)
Maon bought 64 pack of candy for $2 each. He old all of thee pack to hi friend for $4
each. Which equation can be ued to find p, the total profit that Maon earned?
The equation representing the total profit earned by Maon is Profit = 256 - 128.
Profit is calculated by the formula -
Profit = Cost price - Selling price
Cost price = 64×2
Performing multiplication to find the cost price
Cost price = $128
Selling price = 64×4
Performing multiplication to find the selling price
Selling price = $256
Keep the values in equation to find the profit
Profit = 256 - 128
Performing subtraction on Right Hand Side of the equation to find the profit
Profit = 128
Thus, the profit earned is $128.
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Use synthetic division to find the result when x4 - 11x³ +26x² + 10x + 28 is
divided by x - 7.
Answer: x³-4x²-2x-4
Tips:
Bring down top values, then multiply by the outside value, then put it under the next value, add, and repeat
slope: 3; y-intercept: -8
I need help with question one, who would you find the missing side length
similar triangles have a ratio and in this case the ratio is 1:2 i hope you understand
What is 1/4 − (−1 1/2)? Write the answer as a mixed number in simplest form.
plsssssss help ill give 20 pnts
The answer as a mixed number in simplest form will be 1 3/4.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The expression is,
⇒ 1/4 - (- 1 1/2)
Now,
Since, The expression is,
⇒ 1/4 - (- 1 1/2)
Hence, Solve the expression as;
⇒ 1/4 - (- 1 1/2) = 1/4 + 3/2
= 1/4 + 6/4
= 7/4
= 1 3/4
Thus, The answer as a mixed number in simplest form will be 1 3/4.
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Find the equation of the line pictured.
Answer: y=-1/2x+4
Step-by-step explanation:
find the slope of the line given which would be-2/4 which simlifys down to 1/2 then add your b (y intercept) and that wold be 4.