a) No, it is not possible. A Type I error is rejecting the null hypothesis when it is in fact true.
b)Yes, it is possible. A Type II error is not rejecting the null hypothesis when it is in fact false.
A false positive conclusion in statistics is known as a Type I error, and a false negative conclusion is known as a Type II error.
The significance level, or alpha, determines the likelihood of a Type I error, whereas beta determines the likelihood of a Type II error. These dangers can be reduced by carefully designing the layout of your study.
If your results show statistical significance, that means they are very unlikely to occur if the null hypothesis is true. In this case, you would reject your null hypothesis. But sometimes, this may actually be a Type I error.
If your findings do not show statistical significance, they have a high chance of occurring if the null hypothesis is true. Therefore, you fail to reject your null hypothesis. But sometimes, this may be a Type II error.
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In the diagram below of triangle ABC, D is a midpoint of AB and E is a midpoint of BC. If DE =9x-20, and AC =5x+12, what is the measure of AC?
Applying the triangle midsegment theorem, the measure of AC is: 32 units.
How to Apply the Triangle Midsegment Theorem?Since DE is a midsegment of triangle ABC, the triangle midsegment theorem therefore states that the length of DE is half of the length of the third side of the triangle, AC.
Given the following:
DE = 9x - 20
AC = 5x + 12
Find the value of x by creating an equation to solve:
DE = 1/2(AC) [based on the triangle midsegment theorem]
Substitute:
9x - 20 = 1/2(5x + 12)
Solve for x:
2(9x - 20) = 5x + 12
18x - 40 = 5x + 12
18x - 5x = 40 + 12
13x = 52
Divide both sides by 13
13x/13 = 52/13 [division property of equality]
x = 4
AC = 5x + 12
Plug in the value of x
AC = 5(4) + 12
AC = 32 units.
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I need help with this please help me
The sequence of transformations that maps ∆ABC to ∆A'B'C' include the following: D. (T(0, -4) о r(90°, 0)(∆ABC)
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of triangle ABC (∆ABC), the coordinates of the vertices of the image (∆A′B′C′) are as follows:
(x, y) → (-y, x)
Ordered pair A = (5, 5) → Ordered pair A' = (-5, 5)
Ordered pair B = (1, 3) → Ordered pair B' = (-3, 1)
Ordered pair C = (2, 1) → Ordered pair C' = (-1, 2)
Next, we would translate the vertices of the image (∆A′B′C′) 0 units to the right and 4 units downward as follows;
Ordered pair A' = (-5, 5) → (-5 + 0, 5 - 4) = (-5, 1)
Ordered pair B' = (-3, 1) → (-3 + 0, 1 - 4) = (-3, -3)
Ordered pair C' = (-1, 2) → (-1 + 0, 2 - 4) = (-1, -2)
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The marketing department of a large chain of automobile tire retail stores would like to pursue consumers interested in all-terrain tires. They wish to investigate the extent to which the amount of money spent on TV advertising (ADV) on Sundays is related to the sales revenue (REV) for the week- from this type of tire. They begin by selecting a random sample of 50 stores in various cities. The analyst looks at the data and notices that 9 of the stores are located in cities with warm climater year-round, and there are no off-road driving possibilities anywhere near these locations. She suggests eliminating these cities from the sample as she feels that money spent advertising these tires will have little, if any, effect on sales. Using the remaining cities, a simple regression model is determined. Regression Analysis 7² 0.862 #41 > 0.929 5, 915.247 Dep. Var. REV Regression output variables std. error Intercept
If a store decides to spend $1500 on Sunday TV ads for all-terrain tires, we can predict that 95% of the values for the revenue in those weeks from the sale of these will be between $21863.59 and $25617.41.
A company can use regression analysis to determine statistical relationships between the total sales of its products and the costs associated with promotions and advertising. The outcomes of these analyses can then be used to determine how best to allocate spending funds among, say, various products or sales regions.
n = 41
df = n - 2
df = 41 - 2 = 39
SSₓₓ = (n - 1)S²ₓ
SSₓₓ = (41 - 1) * (400)²
SSₓₓ = 6400000
y = 15531.3086 + 5.4728 * x
If, x = 1500 then:
y = 15531.3086 + 5.4728 * 1500
y = 23740.51
Prediction range of y at 95% = [tex]y + t_{\frac{0.05}{2},39 } * S_{e} * \sqrt{1 + \frac{1}{n} + \frac{(x - x_{1} )^{2}}{SS_{xx} } }[/tex]
Prediction range of y at 95% = [tex]23740.51 + 2.022691 * 915.247 * \sqrt{1 + \frac{1}{41} + \frac{(1500 - 1700)^{2} }{6400000}[/tex]
Prediction range of y at 95% = (2186.1 , 25619.92)
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Rosa makes candles to sell.
Each candle is in the shape of a cuboid of height 8 cm.
The base of each candle is a square of perimeter 20 cm.
Rosa needs to know the volume of one candle.
Work out the volume of one candle.
Remember to give units with your answer
describe the transformation of f(x) = sin x to g(x) = sin (x - pi/3)
Answer:
gh(b)
Step-by-step explanation:
Answer:
shifted to the right
Step-by-step explanation:
A square has a side length of x- 9 units. What is its perimeter in terms of x?
16
O A. x-9
16
OB.X - 36
OC. x + 36
OD. x - 36
The perimeter of the given square is 4x-36 units which have a side length of x- 9 units.
What is the perimeter of the square?The perimeter of a square is defined as the addition of the lengths of the square.
The perimeter of a square is the sum of all its sides.
Since a square has four sides of equal length, the perimeter is four times the length of one side.
Therefore, the perimeter of a square with a side length of x-9 units is :
⇒ 4(x-9) units.
This can be simplified to 4x-36 units.
Hence, the perimeter of the given square is 4x-36 units.
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10. In a class, % of the students are girls. % of the boys and % of the girls can swim.
(a) What percentage of students are boys? (b)What fraction of the students in the class can
swim
Please I'm in hurry help me
Answer:
I cant see numbers sorry. post question again
The question is unclear.
A customer is buying bath towels and hand towels and can spend no more than $100. Each bath towel costs $8, and each hand towel costs $5. The inequality 8x+5y ≤100 represents all possible combinations of x, the number of bath towels, and y, the number of hand towels the customer can buy.
Which graph best represents the solution set for this inequality?
There is an attachment that includes the graph for the inequality 8x + 5y 100.
How do you calculate the scenario's graph?
The parameters are as follows, taken from the query:
The customer's purchase must not exceed $100.
Each bath towel costs $8.
Each hand towel costs $5.
Inequality among the available combinations is another factor that we have.
8x + 5y ≤ 100
like that
x is the quantity of bath towels, while y is the quantity of hand towels.
Plotting the inequality's graph is the following step.
A graphing tool can be used for this.
In order to attach the graph, we enter the inequality in the graphing tool.
Keep in mind that the inequality is provided as
8x + 5y ≤ 100
See the inequality graph in the attached. 8x + 5y ≤ 100
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Any help would greatly be appreciated.
The point of intersection is (0, -4).
What is the point of intersection?
In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.
Here, we have
Given: f(x) = -x -4, g(x) -5x -4
The lines intersect where f(x) = g(x)
f(x) = g(x)
- x - 4 = -5x - 4
-x +5x = -4 +4
4x = 0
x = 0
Now, we put the value of x in f(x) and we get
f(0) = - 0 - 4
f(0) = -4
Hence, the point of intersection is (0, -4).
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Which best describes the graph of
f(x) = log₂(x + 3) + 2 as a transformation of the
graph of g(x) = log₂x?
A translation 3 units left and 2 units up best describes the graph of f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x
How to solve this problem?
f(x) = log2(x + 3) + 2 (given)
g(x) = log2x (given)
We need to describe the best statement for the graph
The graph is shown in the image
The following steps are shown to describe the graph.
The general equation of f(x) = log2(x-h)+k
When h > 0 (positive)
The graph of the base of the function shift to the right
When h < 0 (Negative)
The graph of the base function shifts to the left.
When k > 0 (Positive)
The graph of the base function shifts upward.
When k < 0 (Negative)
The graph of the base function shifts downward
Here h = 3 , k = 2
Hence , a translation 3 units left and 2 units up describes the graph.
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What is the scale factor from the drawing to the actual billboard?
The scale factor is ?
10 inches is the scale factor from the drawing to the actual billboard
What is a Scale Factor?A scale factor is a ratio of change from a drawing to real life. Typically, a scale factor is unit-less; a scale factor of 48 (or 1:48) is saying that for one unit on the page, it represents 48 of the same units in real life.
A scale factor is the ratio between corresponding measurements of an object and a representation of that object.
How to do scale drawing?Scale drawings show an image either reduced or enlarged in size. The change between the original and the scaled drawing is generally represented by two numbers separated by a colon, like 10:1 (read as “ten to one”).
The difference between the ratio numbers represents the factor by which the scaled image is enlarged or reduced. So for a 10:1 scale ratio, a 1 inch (2.5 cm) drawing will be 10 inches (25 cm) in real life.
Methods are as follows :
Adjusting Image Size by Hand- Measure the object you’ll be scaling.Choose a ratio for your scaled drawing.Convert the actual measurements with the ratio.Start drawing the perimeter with a straight segment when possible. - Refer to the original drawing frequently.Use a piece of string to check the scaled lengths of irregular images.Add details after finishing the perimeter.Changing Scale Digitally-
Scan the image or snap a pic of it with your phone.
Insert the image into a suitable program or app.
Navigate to the image layout options.
Adjust the height and width under the “Scale” heading.
Save the scaled image and you’re done.
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WEIGHT A bag of apples claims to have a weight of 6 pounds. However, the actual weight is
6.241 lbs. Determine the approximate error of weight.
The approximate error of weight is
lbs.
Answer:
The approximate error of weight is 6.241 - 6 = 0.241 lbs
The approximate error of the given weight is 0.241 lbs
How to find the approximate error of weight?The approximate error of weight is the difference between the claimed weight and the actual weight, which is:
Approximate error = Actual weight - Claimed weight
As per the question, we have
Actual weight = 6.241 lbs
Claimed weight = 6 lbs
Substitute the values in the formula and we get:
Approximate error = 6.241 lbs - 6 lbs
Approximate error = 0.241 lbs
Therefore, the approximate error of weight is 0.241 lbs.
This means that the claimed weight is off by 0.241 lbs, which could be significant depending on the context.
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10. A test consisting of 25 multiple-choice questions with 5 answer choices for each question is administered For each question; there is only | correct answer Let X be the number of correct answers if a student guesses randomly from the 5 choices for each of the 25 questions What is the probability distribution of X? This test, like many multiple-choice tests, is scored using penalty for guessing: The test score is determined by awarding point for each question answered correctly, deducting 0.25 point for each question answered incorrectly, and ignoring any question that is omitted. That is, the test score is calculated using the following formula Score = number of correct answers) (0.25 number of incorrect answers) + (0 number of omits) For example, the score for a student who answers 17 questions correctly, answers 3 questions incorrectly, and omits 5 questions is Score 17) - (0.25 * 3) + (0 x 5) = 16.25 Suppose student knows the correct answers for 18 questions, answers those 18 questions correctly, and chooses randomly from the 5 choices for each of the other 7 questions. Show that the expected value of the student'$ score is 18 when using the scoring formula above
Using the given formula, we have been able to prove that; the expected value of the students' score is 18 correct responses
How to solve binomial probability distribution problems?1) Let X denote the number of correct guesses, assuming that a student guesses randomly among the five options of all 25 questions. Then X has a binomial probability distribution with;
n = 25
p = 1/5 = 0.2
2) Let Y denote the number of correct responses on the seven questions for which the student guesses randomly from among the five options. Then Y has a binomial probability distribution with n = 7 and p = 0.20. Then the expected value of Y is;
E(Y) = np = 7(0.2) = 1.4
Using the scoring formula given, we have;
Score = (18 + Y) - 0.25(7 - Y) + 0(0)
= 16.25 + 12Y
The expected value of the students' score is;
E(16.25 + 12Y) = 16.25 + 12(1.4)
= 18 correct responses.
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Which number line represents the solution set of the inequality -2x + 0.25 > 6.25?
The linear inequality x < - 3 is represented on the number line below
Graph of Linear InequalityAn Inequality represents the mathematical expression that shows both sides are not equal. When the relationship makes a non-equal comparison between two expressions or two numbers, then it is known as inequality. In this case, the equal sign in the expression is represented by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).
The inequality given is;
-2x + 0.25 > 6.25
-2x > 6.25 - 0.25
-2x > 6.0
Divide both sides by coefficient of x
x < -3
Placing this on a number line, we would have;
Kindly find the attached graph below
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Sydney went to the store and bought candy that was priced according to the weight in pounds. She purchased 2 1/4 pounds of black licorice, 1 7/8 pounds of red licorice, and 1 1/2 pounds of butterscotch candy. if the candy costs $ 4.00 per pound, how much did Sydney spend on candy?
Answer:
$22.50
Step-by-step explanation:
Consider the equation below. − 5 n + 31 = − 14 n − 5 Select the equation that has the same solution. − 1 − 22 n = − 20 n − 9 1 = 0.75 n + 3.25 3 − 6 n + 3 n = − 3 + 4 − 4 n
Answer: The equation that has the same solution as the given equation is −1 − 22 n = −20 n − 9. This can be seen by solving both equations for n.
To solve the given equation − 5 n + 31 = − 14 n − 5 for n, we can start by adding 5n to both sides to obtain 31 = − 9 n − 5. Then, we can add 9n and 5 to both sides to obtain n = −1.
To solve the equation −1 − 22 n = −20 n − 9 for n, we can start by adding 22n to both sides to obtain −1 = −20 n − 9. Then, we can add 20n and 9 to both sides to obtain n = −1.
Since both equations have the same solution for n (namely, n = −1), they have the same solution. Note that the other equations listed in the question do not have the same solution as the given equation. For example, the equation 1 = 0.75 n + 3.25 has the solution n = −4, while the equation 3 − 6 n + 3 n = − 3 + 4 − 4 n has the solution n = 1/5. These solutions are different from the solution n = −1 of the given equation, so these equations do not have the same solution as the given equation.
Answer:
11/4n+2=-3+ 3/2n
Step-by-step explanation:
9. Divide the polynomials using synthetic division.
(2y² + 10y + 17) ÷ (y + 3)
The polynomials using synthetic division is [tex]2 y+4+\frac{5}{y+3}[/tex].
What is polynomials?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x^2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
[tex]\frac{\left(2 y^2+10 y+17\right)}{(y+3)}$$[/tex]
[tex]$$\begin{aligned}& \text { Divide } \frac{2 y^2+10 y+17}{y+3}: \frac{2 y^2+10 y+17}{y+3}=2 y+\frac{4 y+17}{y+3} \\& =2 y+\frac{4 y+17}{y+3}\end{aligned}$$[/tex]
Divide [tex]$\frac{4 y+17}{y+3}: \quad \frac{4 y+17}{y+3}=4+\frac{5}{y+3}$[/tex]
[tex]=2 y+4+\frac{5}{y+3}[/tex]
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How many bags of marshmallows and boxes of toothpicks will each kit have? (Image below for context)
Each kit will have 3 bags of marshmallows and 4 boxes of toothpicks
How to determine the number of bags of marshmallows and boxes of toothpicksFrom the question, we have the following parameters that can be used in our computation:
Bags of marshmallows = 36Boxes of toothpicks = 48Greatest number of identical kits = 12The number of bags of marshmallows in each kit is calculated as
Bags = Bags of marshmallows/Greatest number of identical kits
Bags = 36/12
Bags = 3
The number of boxes of toothpicks in each kit is calculated as
Boxes = boxes of toothpicks/Greatest number of identical kits
Boxes = 48/12
Boxes = 4
hence, the bags are 3 and the boxes are 4
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Which polynomial represents the difference below?
8x³ + 5x+6-(2x² + 3x)
OA. 10x¹0 + 8x² +6
OB. -2x7 + 8x³ + 8x+6
O C. 6x¹0+2x+6
OD. -2x7 + 8x³ + 2x+6
The difference of the given polynomials 8x³+5x+6 and 2x²+3x is 8x³-2x²+2x+6. So, the correct answer is D.
What is the subtraction of polynomials?To subtract polynomials from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Given that, 8x³+5x+6-(2x²+3x)
Group the like terms are perform the addition or subtraction
= 8x³+5x+6-2x²-3x
= 8x³+(5x-3x)-2x²+6 (Here, like terms are 5x and 3x)
= 8x³+2x-2x²+6
= 8x³-2x²+2x+6
So, the standard form of obtained polynomial is 8x³-2x²+2x+6.
The polynomials difference is 8x³-2x²+2x+6. Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which polynomial represents the difference below?
8x³ + 5x+6-(2x² + 3x)
A. 10x+ 8x² +6
B. -2x² + 8x³ + 8x+6
C. 6x¹⁰+2x+6
D. -2x²+ 8x³+2x+6
Write the equation of the line that has the slope of 7/3
and goes through the point (7,-9) in standard form.
****
The equation of the line that has the slope of 7/3 is: y = (7/3) x - 27/49
What is equation of the line?Finding the slope and y-intercept is necessary to express the equation of a graphed line in y-intercept (y=mx+c) form, which can then be used to get the equation of the line. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.
Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.
Given that,
slope (m) = 7/3
Putting (7,-9) into the equation: y =mx+c
or, -9 = (7/3) × (7) + c
or, -9 = 49 /3 + c
or, c = (-9) × (3/49)
or, c = -27/49
Thus, the equation becomes:
or, y = (7/3) x + -27/49
or, y = (7/3) x - 27/49
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The supply function and the demand function for a product are linear and are determined by the tables that follow.
Supply Function
Price ($) Quantity
75 125
150 150
300 200
Demand Function
Price ($) Quantity
45 355
120 330
270 280
(a) Write an equation for the supply function's price p as a function of q.
p =
Write an equation for the demand function's price p as a function of q.
p =
(b)Find the quantity and price that give market equilibrium.
Market equilibrium is achieved with a product quantity of units at a price of $ per unit.
The required supply function is p = 3q - 300 and the required demand function is p = -3q + 1110. The equilibrium quantity is 235 and the equilibrium price is $405.
a) Find an equation for the supply function's price p as a function of q as follows.
Let p = mq + b be the required linear supply function.
From the given information, the supply function passes through points (125, 75) and (150,150).
Find the slope m using the points (125, 75) and (150,150) as shown below.
m = (p2-p1)/(q2-q1)
m = (150-75)/ (150-125) = 75/25 = 3
Now find the value of b using the point (125, 75) and slope m = 3 as follows.
p = mq + b
75 = 3(125) + b
b = - 375 + 75 = -300
Therefore, the required supply function is p = 3q - 300.
b) Find an equation for the demand function's price p as a function of q as follows.
Let p = mq + b be the required linear supply function.
From the given information, the demand function passes through points (355, 45) and (330,120).
Find the slope m using the points (355, 45) and (330,120) as shown below.
m = (p2-p1)/(q2-q1)
m = (120-45)/ (330-355) = 75/-25 = -3
Now find the value of b using the point (355, 45) and slope m = -3 as follows.
p = mq + b
45 = -3(355) + b
b = 1065 + 45 = 1110
Therefore, the required demand function is p = -3q + 1110.
Find the equilibrium quantity and equilibrium price as follows.
In order to find the equilibrium quantity, equate the demand function and supply function and solve the equation solve for q as shown below as p is common.
3q - 300 = -3q + 1110
=> 6q = 1410
=> q = 235
Thus, the equilibrium quantity is 235.
Find the equilibrium price by substituting q = 235 in p = 3q -300.
p = 3 x 235 - 300
p = 705 -300 = 405
Hence, the equilibrium price is $405.
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(a) You have a 10 inch by 15 inch piece of tin which you plan to form into a box (without a top) by cutting a square from each corner and folding up the sides. How much should you cut from each corner so the resulting box has the greatest volume? (b) If the piece of tin is A inches by B inches, how much should you cut from each corner so the resulting box has the greatest volume?
Resulting box has the greatest volume for the values (25 ± 5√7)/6 .
This is a problem that can be solved using derivatives , maxima & minima and common logic.
Hence , going by logic :
Creating a flap of 'a' inches in width, the base of the box will be
(10 - 2a) by (15 - 2a)
and the depth of the box will be the width of the fold-up flap: a.
Then the volume of the box is
v = [tex]a(10 -2a)(15 -2a) = 150a -50a^2 +4a^3[/tex]
Using the derivative of the volume will be zero at the maximum volume.
0 = [tex]dv/da = 150 -100a +12a^2[/tex]
This has roots at
a = (100 ±√(100² - 4(12)(150)))/(2·12)
a = (100 ± √2800)/24 = (25 ± 5√7)/6
Only the smaller of these solutions gives a maximum volume.
You should cut (5/6)(5-√7) ≈ 1.962 inches to obtain the greatest volume.
Similarly , replacing the values of 10 by A and 15 by B , a generalized solution can be formed .
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one seventh plus nine fourteenths equals blank
Answer: 11/14 (eleven over fourteen)
Step-by-step explanation:
Your school is planning a fundraising dinner. The expense for this event must not exceed $2,475.00. The team organizing the event has calculated that the cost per adult guest will be $18.00 and the cost per child guest will be $9.00. The venue can hold no more than 150 guests.
The two inequalities that describe the total cost and no. of guests are
18a + 9c ≤ 2475 and
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let 'a' be the no. of adults and 'c' be the no. of children.
The expense for this event must not exceed $2,475.00.
Therefore, 18a + 9c ≤ 2475...(i)
The venue can hold no more than 150 guests.
Therefore, a + c ≤ 150...(ii)
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Solve for x. Triangle stuff
Answer:
x=9
Step-by-step explanation:
these 2 angles are supplementary angles meaning added together they will equal 180 degrees
so we can add them together and set it equal to 180
(8x-3)+(16x-33)=180
combine like terms
(8x+16x)+(-3-33)=180
24x-36=180
+36. +36
24x=216
/24. /24
x=9
hopes this helps
The vertices of quadrilateral PQRS are listed.
P(3,7). Q(6,-2), R(0,-4), S(-3,5)
Which of the following is the strongest classification that identifies quadrilateral PQRS?
O A.
Quadrilateral PQRS IS a parallelogram.
O B.
Quadrilateral PQRS is a rectangle.
• c.
Quadrilateral PQRS is a square.
• D.
Quadrilateral PQRS is a trapezoid.
Answer: O B. Quadrilateral PQRS is a rectangle.
Step-by-step explanation: The image should help you picture my answer. Good luck with your end of semester test!
Have a great day! :)
help thank youuu, very much
The results of division of integers are
1. -5 2. -14 3. -6 4. 4
What is an integer?
A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8
1. -30/6
6 five times = 30
So, -30/6 = -5
2. 14/ -1
Denominator is -1, numerator remains same with sign
So, 14/ -1 = -14
3. -42/7
7 six times = 42
So, -42/7 = -6
4. -48/-12
Same signs cancel out. 12 four times = 48
So , -48/-12 = 4
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find the area of the surface formed by revolving the polar equation over the given interval about the given line. polar equation interval axis of revolution r
The area of the surface formed by revolving the polar equation over the given interval about the given line , r = 4cosθ is 16π .
What is Polar co-ordinate System ?Polar coordinate system is a two dimensional coordinates system like Cartesian system with the variables r, θ ( polar coordinates) and axis called polar axis . Consider the polar equation
r = 4cosθ --(1) ; 0≤θ ≤π/2
The axis of a rotation is in polar axis.
We know that, the surface area about θ = π/2 is
S = 2π ∫(r sinθ√(r² + (dr/dθ)²) dθ with limits
so, differenatiate equation (1) with respect to θ we get , dr/dθ = - 4 sinθ
Now, S =2π₀∫ˣ [4cosθsinθ√(4²cos²θ + (-4 sinθ)²)]dθ where x = π/2
S = 2π ₀∫ˣ[ 4cosθsinθ√(4²cos²θ + 4²sin²θ)]dθ
S = 2π₀∫ˣ [ 4cosθsinθ√4²(cos²θ+sin²θ)]dθ
S = 2π ₀∫ˣ [ 16cosθsinθ√(cos²θ+sin²θ)]dθ
S = 32π ₀∫ˣ [cosθ sinθ √1 ]dθ
S = (32π/2) ₀∫ˣ 2cosθsinθdθ
S = (16π) ₀∫ˣ sin2θdθ
S = 16π ₀[- cos2θ/2]ˣ
putting the upper limit θ = x = π/2 and lower limit θ = 0
S = (- 16π/2) [ cos2 (π/2) - cos2(0)]
S = (- 8π )[ cosπ - cos0° ] = - 8π[ - 1 - 1]
S = 16π
Hence, surface area is 16π .
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Complete question :
Find the area of the surface formed by revolving the polar equation over the given interval about the given line_ Polar Equation r = 2 cosQ
Interval 0 < Q <π/ 2 Axis of Revolution Polar axis.
Please help will mark Brainly
Answer:
A
Step-by-step explanation:
Blue = River Y
Red = River Z
River Y equation: y = 18
River Z equation: y = 10 + 2x
Graph A represents this system of equations.
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Find the slope of the line graphed below.
Answer:
-2
Step-by-step explanation:
The line appears to cross through (2,3) and (4,-1)
You can subtract the x values and y values to determine the difference:
[tex]2 - 4= - 2 \\ 3 - ( - 1) = 4[/tex]
These can be used as the y and x values in y over x to find the slope:
[tex] \frac{4}{ - 2} = - 2[/tex]
The slope is -2
