The area of the region enclosed by one loop of the curve r = sin(12θ) is π/48.
We have to find the area of the region enclosed by one loop of the curve.
The given curve is:
r = sin(12θ)
Consider the region r = sin(12θ)
The area of region bounded by the curve r = f(θ) in the sector a ≤ θ ≤ b is
A =
Now to find the area of the region enclosed by one loop of the curve, we have to find the limit by setting r=0.
sin(12θ) = 0
sin(12θ) = sin0 or sin(12θ) = sinπ
So θ = 0 or θ = π/12
Hence, the limit of θ is 0 ≤ θ ≤ π/12.
Now the area of the required region is
A = [tex]\int ^{\pi/12}_{0} \frac{1}{2}(\sin12\theta)^2d\theta[/tex]
A = [tex]\frac{1}{2}\int ^{\pi/12}_{0}\sin^212\thetad\theta[/tex]
A = [tex]\frac{1}{2}\int ^{\pi/12}_{0}\frac{1-\cos24\theta}{2}d\theta[/tex]
A = [tex]\frac{1}{4}\int ^{\pi/12}_{0}(1-\cos24\theta)d\theta[/tex]
A = [tex]\frac{1}{4}\left[(\theta-\frac{1}{24}\sin24\theta)\right]^{\pi/12}_{0}[/tex]
A = [tex]\frac{1}{4}\left[(\frac{\pi}{12}-\frac{1}{24}\sin24\frac{\pi}{12})-(0-\frac{1}{24}\sin24\cdot 0)\right][/tex]
A = [tex]\frac{1}{4}\left[(\frac{\pi}{12}-\frac{1}{24}\sin2\pi)-(0-\frac{1}{24}\sin0)\right][/tex]
A = 1/4[(π/12-0)-(0-0)]
A = 1/4(π/12)
A = π/48
Hence, the area of the region enclosed by one loop of the curve r = sin(12θ) is π/48.
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What is a written description of x − 14?
Answer: The written description of x - 14 is given as the difference of variable x and integer 14 gives x -14.
Step-by-step explanation:
Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Let x be a variable,
And 14 is an integer.
By using mathematical operations,
The difference of x and 14 can be given as,
x - 14.
A rectangular yard measuring 40ft by 53ft is bordered (and surrounded) by a fence. Inside, a walk that is 4ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer. helpppppp plssss for my final
Area of the walk that goea around the rectangular yard is 680 sq. ft.
What is a Rectangle ?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.
The rectangle's characteristics are listed below:
There are four vertices and four sides.Every vertex has an angle of 90 degrees.Equal and parallel sides are on the opposing sides.Intersect each other diagonallyThe perimeter is equal to double the length plus width of the object.the product of its length and width determines its area.It has four right angles and is a parallelogram.All inner angles added together equal 360 degrees.Dimension of the yard is
width = 40 ft
length = 53ft
Dimension of the yard without the walkway is
Width =40 - 4*2 = 40 - 8 = 32 ft
Length = 53 - 4*2 = 53 - 8 = 45 ft
Area of the yard = Width * Length = 40 * 53 = 2120 sq. ft
Area of the yard wtihout the walk = 32 * 45 = 1440 sq. ft
Therefore the area of the walk is = Area of yard - Area of yard without walk = 2120 = 1440 = 680 sq. ft.
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Write an equation that represents the line. Use exact numbers. hurry please!!
Answer:
y=3/4x-9/2
Step-by-step explanation:
y=mx+c
m=dy/dx
=-3/-4
=3/4
-3=(3/4*2)+c
-3=3/2+c
-9/2=c
PLS HELP
What is the range of f(x) = |x| + 7?
−7 ≤ y < ∞
−∞ < y ≤ −7
0 ≤ y < ∞
7 ≤ y < ∞
The range of the function f(x) = |x| + 7 is given by the option presented as follows:
7 ≤ y < ∞.
How to obtain the range of a function?The range is composed by the set containing all the values assumed by the output of the function, that is, all the numeric values assumed by the function.
In the context of this problem, the function is defined as follows:
f(x) = |x| + 7.
The parent function is the absolute value function g(x) = |x|, which gives the distance of a point x from the origin, assuming real values of at least 0, as a distance cannot be negative.
The addition by 7 means that the parent function was translated up seven units, meaning that the minimum value assumed by the range is seven, and the range of the function is given by the last option given as follows:
7 ≤ y < ∞.
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PLEASE HURRY!
Write and solve the inequality that represents negative one eighth is less than the product of negative two thirds and a number.
A: negative one eighth is less than negative two thirds y where y is less than three sixteenths
B: negative one eighth is less than or equal to negative two thirds y where y is greater than negative three sixteenths
C: negative two thirds is less than negative one eighth y where y is less than one twelfth
D: negative two thirds is greater than negative one eighth y where y is greater than negative one twelfth
The solution to the inequality statement is x < 3/16
How to determine the solution to the inequality?From the question, we have the following parameters that can be used in our computation:
negative one eighth is less than the product of negative two thirds and a number.
Express as numbers and operators
So, we have
-1/8 < -2/3x
Divide both sides by -2/3
So, we have the following representation
1/8* 3/2 > x
Evaluate the produdts
3/16 > x
Rewrite as
x < 3/16
Hence, the solution is x < 3/16
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A company makes a loss of 2 million dollars in its first year of trading. In the following two years it makes a profit of $625 000 per year. What is the average profit or loss per year made by the company over the three years?
Answer: They lose $250000 per year over the three years!
Step-by-step explanation:
First, find the total profit for the two following years
Take $625000 times 2 = $1250000
Next, find the total they made in 3 years
Take -$2000000 of the first year + $1250000 = - $750000
Now we find their average profit per year
Take -$750000 divided by 3 = -$250000
They lose $250000 per year over the three years
What is the product of 5x(x - 8) ?
Answer:
5x^2 - 40x
Step-by-step explanation:
5x (x-8)
5x^2 - 40x
Quadrilateral ABCD with vertices A (-3,3), B (8,8), C (6,2), and D (0,0) is shown. You want to reflect quadrilateral ABCD in the vertical
line that passes through the midpoint of CD. Graph the line of reflection and the image after the reflection.
Polygon
here to search
Line
14
13-
12-
11-
10-
9
7
6
5
Undo
Redo
x Reset
13
calculate
gra
The line of reflection and the image of after reflection graph is attached below
What is line of reflection ?
The picture is consistent with the preimage when reflecting a figure in a line or a point. Every point on a figure is translated into an image by a reflection across a set line. The term "line of reflection" refers to the fixed line.
The line of reflection is a line across which an image will reflect. Every point in a figure is said to reflect the other figure if and only if it is equally spaced from every corresponding point in the other figure. The image that is reflected should be identical in size and shape but face the opposite way.
Graph the quadrilateral. By inspection, you can tell where the midpoint is. (see attachment 1)
Now, I'll draw a line through it. (see attachment 2)
To reflect across a line, think about the points traveling across the line the same number of spaces the point is from the line. For example, point A is three away from the line. So, A' will be 3 away from the other side. The coordinates will be at (-3,2). (see attachment 3).
Do the same for the other points, and you'll have your image.
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someone with great knowledge of this please help its due asap please help.
Answer: x = 2 hours y= 7 hours = 9 hours a week, 80$ a week
Step-by-step explanation:
5$x2=10$ 10$x7=70$ 70$ + 10$ = 80 $.
hopefully, maybe that helps for the first question.
Paul pent $72 on 4 day-lilie and 7 geranium. Megan pent $128 on 10 day-lilie and 11 geranium. Find the cot of one day-lily and the cot of one geranium
The cost of one day-Lilly is found to be $4 and the cost of one geranium is found to be $8. Therefore, Paul spent about $16 for day-Lilly and $56 for geranium. And Megan spent about $40 for day-Lilly and $88 for geranium.
Two or more algebraic equations that have a common variable and are solved simultaneously are referred to as simultaneous equations. We can find the answers to both unknowns if we have two separate equations with the same two unknowns in each. Here, we'll employ the addition-and-subtraction or elimination method.
Let's consider the cost of day-Lilly as x and the cost of geranium as y. The cost spent by Paul is written as 4x+7y=$72 and Megan is written as 10x+11y=$128.
Solving these two equations for x and y,
[tex]\begin{aligned}40x+70y = \$720\\\underline{40x+44y=\$512}\\26y=\$208\\y=\$8 \end{aligned}[/tex]
Substitute the value of y in equation 4x+7y=$72 to get the value of x,
[tex]\begin{aligned}4x+7(8)&=\$72\\4x&=\$16\\x&=\$4\end{aligned}[/tex]
The answers are $4 and $8.
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Is anyone good at this math
Answer:
x = 3
Step-by-step explanation:
4 + x = 7 Subtract 4 from both sides of the equation
4 - 4 - x = 7 - 4 Simplify
x = 3 X equals 3
Answer:
x = 3
Step-by-step explanation:
4 + x = 7
x + 4 - 4 = 7-4 = 3
x = 3
To solve for x, subtract 4 from both side of the equation. This leaves x by itself on the left side of the equation. Next subtract 4 from 7 to get the solution, x = 3.
If this trapezoid is moved through the translation (x+3,y-2), what will the coordinates of B be?
The coordinate of the vertex B after the transformation of the given trapezoid is (-2, 2).
How to transform a graph of the function?The graph of a function can be transformed by either shifting it in the right, left, up or down.
When the transformation is rightwards, the function becomes as f(x - a).
For left shifting it is f(x + a).
As per the given graph, the coordinate of vertex B is (-5, 4).
After the translation (x, y) → (x + 3, y - 2), the new coordinate can be obtained as,
(-5, 4) → (-5 + 3, 4 - 2)
⇒ (-2, 2)
Hence, the coordinate of B after the transformation is (-2, 2).
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Draw a line PQ and take a point A outide it. Uing ruler and compa , draw a line through A parallel to PQ
Using a ruler and compass, draw a line through point A parallel to line PQ by first drawing a line segment from A to any point on PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. Finally, use the ruler to draw a line through the arc, parallel to PQ.
Drawing a line parallel to an existing line can be done using a ruler and compass. First, draw a line segment from point A to any point on line PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. This arc should intersect with the first line segment. Finally, use the ruler to draw a line through the arc, parallel to PQ. This line will be parallel to PQ since it is the same distance from each point on the original line. The use of the compass ensures that the resulting line is the same distance away from the original line throughout, thus resulting in a line parallel to PQ.
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10. dice when a pair of dice is rolled, what is the probability tha tthe sum of the dice is 5, given that exactly one of the dice shows a 3?
The probability sum of the dice is 2/11.
Let A be the event that the sum of dots is 5, then
A={(1,4), (2,3), (3,2), (4,1)}
n(A)=4
And, B is the event that one die shows a "one"
B={(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (3,1), (4,1), (5,1), (6,1)}
n(B)=11
The Event that some of the dots are five and one of the die shows "one".
A intersection B = {(1,4), (4,1)}
Since n(A) = 36 (thirty-six possible samples of two dice)
P(A)=4/36
P(B)=11/36
P(A intersection B)=2/36
So, the required probability is
P(A|B)=P(A intersection B)/P(B) =2/11
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Joe asked a bank teller to cash a $570 check using $20 bills and $50 bills, If the teller gave him a total of 15 bills, how many of each type of bill did he receiver
Answer:
9 $50 bills and 6 $20 bills
Step-by-step explanation:
Let f = number of $50 bills.
Let t = number of $20 bills.
f + t = 15
50f + 20t = 570
f = 15 - t
50(15 - t) + 20t = 570
750 - 50t + 20t = 570
-30t = -180
t = 6
f + t = 15
f + 6 = 15
f = 9
Answer: 9 $50 bills and 6 $20 bills
A group of students is asked if they travel
Students travelling Students not by car
travelling by car 14 to school by car. Here
are the results. 11 a) What percentage of
these students do not travel to school by
car? % No of students b) 14 of these
students travel by car. Number of cars in
one car Some of these travel in the same
car. Fill the missing frequency in the table.
c) Work out the mean number of students
in each car
The percentage of those that don't travel by car will be 44%.
How to calculate the percentage?It's important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, 14 students travel by car and 11 don't travel by car. The total number of students will be:
= 11 + 14.
= 25
Therefore, the percentage of those that don't travel by car will be:
= 11 / 25 × 100
= 44%
The percentage is 44%.
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What D
Evaluate each expression for the giver
3x² when x is 10
Answer:
3x²
= 3(10)²
= 3(100)
= 300
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-What is the answer to this question
Answer:
Step-by-step explanation:
a because if you divide everything under the fraction number you get answer a
The solution for the given expression is x = 4³/₅. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is x - 17⁴/₅ = -13¹/₅. The given expression will be solved as,
x - 17⁴/₅ = -13¹/₅
x = 17⁴/₅ -13¹/₅
x = 89 / 5 - 66 / 5
x = 23 / 5
x = 4³/₅
The expression will be equivalent to x = 4³/₅.
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you round_trip drive to work is 4 3/10 miles how many miles do you drive to and from work in 3 days?
Answer:
12.9 or 12 9/10
Step-by-step explanation:
4 3/10 or 4.3 x 3
12.9 or 12 9/10
How many lines of symmetry does the figure have?
0
1
2
3
Answer:
1
Step-by-step explanation:
because you can only cut it in a certain way that both pieces are the same measurements
an agriculturalist working with australian pine trees wanted to investigate the relationship between the age and the height of the australian pine. a random sample of australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the australian pine based on the age, in years, of the tree. Predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?
The height increases by 0.48 meters each year.
The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
The height increases, an average, by 0.48 m per year.
Because co-efficient of slope variable indicate the positive sign and we increase 1 year in age then automatically height increased is 0.48 m.
The height increases, on average, by 0.48 meter each year.
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The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
Three years ago Joseph was three times older than Agnes in 2 years times the sum of their ages will be 75 years. Determine their present ages
Answer:
Hey, answer is attached.
Step-by-step explanation:
Hope this helps.
Pls help I’ll put in a picture
Answer:
2 < x < 26
Step-by-step explanation:
The length of the side of a triangle must be less than the sum of the lengths of the other two sides of a triangle.
Therefore:
12+14>x
x<26
However, the following must also be true:
x+12>14 (The sum of x and 14 will always be greater than 12 because 14>12, so we don’t need to include that in the inequality)
So, x>2.
This means that the answer is 2<x<26
You buy the following from Walmart:
1 puzzle for $8, 1 TV for $350, 1 cutting board for $9, and 1 blender for $25
What is the Subtotal: $
You have a 10% off coupon, how much do you save: $
What is the new Subtotal: $
Sales tax is 5%: $
What is the total: $
4
Answer:
You buy the following from Walmart:
1 puzzle for $8, 1 TV for $350, 1 cutting board for $9, and 1 blender for $25
$8 + $350 + $9 + $25What is the Subtotal: $392You have a 10% off coupon,
392 * 0.1 = $39.2How much do you save: $39.2What is the new Subtotal:
$392 - $39.2 = $352.8$352.8Sales tax is 5%: $
352.8 * 0.05 = $17.64$17.64What is the total:
$352.8 + $17.64 = $370.44$370.44Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-What i the equation of the line that pae through the point (-1,5)(−1,5) and ha a lope of -3
The equation of the line is y = -3x + 2.
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by Δy and Δx, respectively.
As a result, m = change in y/change in x = Δy/Δx is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
Given that, the line passes through the point (-1,5) with slope of -3.
The equation of line passes through (x₁, y₁) with slope m is
y - y₁ = m(x - x₁)
Putting x₁ = -1, y₁ = 5 and m = -3.
y - 5 = -3(x - (-1))
y - 5 = -3x - 3
y = -3x + 2
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which of the three methods of assigning probabilities is used when we are dealing with sampling (as a method of determining probabilities)? no need to explain.
Random sampling methods of assigning probabilities is used when we are dealing with sampling.
Random sampling is a method of assigning probabilities used when dealing with samples of a population. It involves randomly selecting a sample from the population and then using that sample to estimate the probabilities of different outcomes. This is done by calculating the proportion of the sample that falls into each category. For example, if you are trying to determine the probability of a certain outcome, you would randomly select a sample from the population and then count how many of the individuals in the sample fall into that category. The probability of the outcome would then be calculated by dividing the number of individuals in that category by the total number of individuals in the sample.
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If f(x)=|x−5| 2, find f(3). responses 10 10 6 6 4 4 0
If the function f(x) = |x-5| + 2, then the value of f(3) is 4
The function
f(x) = |x-5| + 2
The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators
Here the function consist of the absolute value symbol.
|-a| = a
The absolute value of the positive and the negative number will be always positive.
The function is f(x) = |x-5| + 2
Then,
f(3) = |3-5| + 2
= |-2| + 2
= 2 + 2
= 4
Therefore, the value of f(3) is 4
I have answered the question in general, as the given question is incomplete
The complete question is:
If f(x)=|x−5| + 2, find the value of f(3).
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Solve the inequality 3(x-2) + 1 ≥x + 2(x + 2).
O A. x≤ 4
OB. x ≥-5
OC. no solution
OD. all real numbers
Answer: no solution
Step-by-step explanation:
1. distribute through both sides to get 3x-6+1 ≥ x+2x+4
2. then combine like terms to get 3x-5 ≥ 3x+4
3. then make sure like terms are together on either side -> 3x -3x ≥ 4+5 ->
4. since the 3x-3x = 0, there are no solutions
According to the american dental association, 8% of adults have never had a cavity. A dental graduate student contacts an srs of 1000 adults and calculates the proportion p in this sample who have never had a cavity
The proportion of people who never had a cavity is 0.92.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, 8% of adults have never had a cavity. A dental graduate student contacts an srs of 1000 adults.
8% of 1000 is,
= (8/100)×1000.
= 80.
Now, The proportion of people who never had a cavity is (1000 - 80)/100.
= 920/1000.
= 92/100.
= 0.92 proportion of people never had a cavity.
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Graph the image of this figure after a dilation with a scale factor of 3 centered at
(−7, −6). Use the polygon tool to graph the dilated figure. *picture Below*
Answer:
See the picture below
Step-by-step explanation:
You start from the center given (-7,-6), then count how many spaces from the center to that point. Take that number and triple it to find the new point. I drew lines so that you could see the path of two of the points.
The path that I did not draw was from the point (-3,-2). If you start at (-7,-6) you will have to move 4 spaces to the right and 4 spaces up to get to (-3,-2) Now triple that. You will move 12 spaces to the right and 12 spaces up for the new point of (5,6)