The three quartiles is the value of Q₂ [Median] is 73 (on the 7th value), The value of Q₁ is 70 (the 3.5th value), The value of Q₃ is 77 (is the 10.5th value). and Interquartile range = Q₃ - Q₁ = 77 - 70 = 7
What is three quartiles?A quartile is a particular kind of quantile that splits the total number of data points into four roughly equal portions, or quarters. Quartiles are a type of order statistic since they require the data to be arranged from smallest to largest in order to be computed.
The median of the data set is the number in the midpoint between the smallest number (minimum) and the first quartile (Q1).
The median of a data set is known as the second quartile (Q2).
The median value and the highest value (maximum) in the data set are the two values that make up the third quartile (Q3).
To find the quartiles, first, we need to put the data in ascending order.
65, 68, 70, 70, 71, 72, 73, 74, 75, 77, 77, 78, 80
The value of Q₂ [Median] is on the 7th value, which is 73
The value of Q₁, the lower quartile, is the 3.5th value [(3rd value+4th value)/2] , which is 70
The value of Q₃, the upper quartile, is the 10.5th[(10th value+11th value)/2] value, which is 77
and
Interquartile range = Q₃ - Q₁ = 77 - 70 = 7.
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plsss helppppppppppppppppp
Answer:
hard
Step-by-step explanation:
ybfhf
The senior class plans a school trip to washington dc. students should bring money for meals and souvenirs. they are told to bring at least $65 but no more than $135. write a compound inequality that represents the range of the amounts of money a student can bring.
The compound inequality represents the range of the amounts of money a student can brings $65 ≤ x ≤ $135
Start by setting up the inequality with the variable x, representing the amount of money a student can bring:
x
2. The inequality should be less than or equal to the maximum amount of money a student can bring, which is $135:
x ≤ 135
3. The inequality should also be greater than or equal to the minimum amount of money a student can bring, which is $65:
65 ≤ x
4. Combine the two inequalities to get the compound inequality:
65 ≤ x ≤ 135
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What is 0.28 as a fraction of 0.8 ? Circle your answer.
Answer:
0.28 = 28/100 = 14/50 = 7/25 and 0.8 = 8/10 = 4/5
5 + 12.5v ≥ 170 what is v
Answer:
v ≥ 13.2 or v ∈ [13.2; ∞ )--------------------------
Given:
5 + 12.5v ≥ 170Solve it in below steps:
5 + 12.5v ≥ 170 Given12.5v ≥ 170 - 5 Subtract 5 from both sides12.5v ≥ 165v ≥ 165/12.5 Divide both sides by 12.5v ≥ 13.2 AnswerAnswer:
[tex] \sf \: v \geqslant 13.2[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of v.
The equation is,
→ 5 + 12.5v ≥ 170
Then the value of v will be,
→ 5 + 12.5v ≥ 170
→ 12.5v ≥ 170 - 5
→ 12.5v ≥ 165
→ v ≥ 165 ÷ 12.5
→ [ v ≥ 13.2 ]
Hence, the value of v is 13.2.
Andrew plays trumpet in the concert band. He holds the trumpet still at his side until it is time for him to play. When it is time, he brings the trumpet up to his
mouth and starts to play. Which statement correctly connects the motion of the trumpet with Newton's first law of motion?
OA. A tuba has more mass than a trumpet, so it has greater inertia.
OB. The trumpet automatically stops moving without a force acting on it.
OC. The trumpet starts moving because a net force overcomes the trumpet's inertia.
OD. Andrew exerts an action force on the trumpet, and the trumpet exerts a reaction force on Andrew.
Option C connects the motion of the trumpet with Newton's first law of motion. The trumpet starts moving because a net force overcomes the trumpet's inertia.
What is Newton's first law of motion?According to Newton's first law of motion, a body won't begin to move unless and until an outside force acts on it. When anything starts moving, it won't stop or vary its speed unless another force acts on it. The law of inertia is another name for the first law of motion.
Given, The concert band's trumpet player is Andrew. Until it is time for him to play, he keeps the instrument still at his side. He positions the trumpet next to his mouth and begins to play afterward.
First of all, there are no movements, no acceleration, and no velocity for the trumpet. Newton's first law of motion, which states that an object at rest stays at rest and an object in motion stays in motion with the same speed and direction unless acted upon by an unbalanced force, explains why the trumpet is in this state. The trumpet continues to move at zero velocity since there is no net force exerted on it.
The trumpet is then moved by Andrew. It indicates that Andrew pushed the trumpet with vigor. It caused the body to transition from the resting condition to the moving state.
Finally, we can draw the conclusion that Trumpet will remain at rest unless Andrew applies a net force that is different from zero in accordance with Newton's first law of motion.
Hence, The trumpet starts moving because a net force overcomes the trumpet's inertia.
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Ris is a botanist who works for a garden that many tourists visit. the function f(s) = 2s + 25 represents the number of flowers that bloomed, where s is the number of seeds she planted. the function s(w) = 25w represents the number of seeds she plants per week, where w represents the number of weeks. part a: write a composite function that represents how many flowers iris can expect to bloom over a certain number of weeks. (4 points) part b: what are the units of measurement for the composite function in part a? (2 points) part c: evaluate the composite function in part a for 30 weeks. (4 points)
The hybrid factor is f(w) Equals 50w + 25 according to the preceding statement. The hybrid value is measured in units of f (flowers) and w (weeks), etc. 30 weeks of Part A's synthesis function equal 1525.
What exactly are function and example?A task is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is just the input value, we would state that y is a mathematical function
Given that:
f(s) = 2s + 25
s(w) = 25w
The following combination function is used to determine how many flowers will blossom over the course of w weeks: f(w)
f(s) = 2s + 25
Replace s with s(w)
f(s(w)) = 2(s(w)) + 25
Substitute s(w) = 25w
f(s(w)) = 2(25w) + 25
f(s(w)) = 50w + 25
Hence,
f(w) = 50w + 25
Flowers are used as the units of measurement for f(w).
30 weeks of flowers translates to:
w = 30
So, we have:
f(30) = 50*30+25
f(30) = 1525
Thus, there will be 1525 blossoms throughout the course of 30 weeks.
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Noah ordered a meal delivery from a local restaurant. the cost of his meal, before tax, was $15.20. if the sales tax is 6.5%, what was the total cost of his meal? show or explain your thinking.
The total cost of the meal was $16.189.
What is the sales tax?
A sales tax is a consumption tax that is added to the price of goods and services. It is usually a percentage of the purchase price, and the percentage varies depending on the location and type of product or service.
We are trying to find the total cost of the meal including the sales tax. To do this, we need to calculate the amount of tax and add it to the cost of the meal.
The cost of the meal before tax is $15.20 and the sales tax rate is 6.5%. To find the amount of sales tax, we can multiply the cost of the meal by the sales tax rate as a decimal.
$15.20 x 0.065 = $0.989
The amount of sales tax is $0.989.
To find the total cost of the meal, we can add the amount of sales tax to the cost of the meal before tax.
$15.20 + $0.989 = $16.189
Hence, The total cost of the meal was $16.189.
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4. you are looking for a deep spot to take a swim in a local river. the width of the river is about the same all along its length, but there are places where the water flows quickly and places where it flows slowly. which is a better choice for a swim?
The best choice for a deep spot to take a swim is to go to a place in the river where the cross-sectional area is larger, and the water flows slower.
If you are looking for a deep spot to take a swim in a local river, the best choice is to go where the water flows slowly. The speed of the water is determined by the formula:
v=Q/A,
where v is the speed of the water, Q is the discharge rate, and A is the cross-sectional area of the river. As Q is constant for the same river, a slower water flow can be achieved by increasing A, which is the cross-sectional area of the river. Therefore, the best choice for a deep spot to take a swim is to go to a place in the river where the cross-sectional area is larger, and the water flows slower.
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Can 8cm 5cm 10cm form the sides of a right-angled triangle?
No, the given measurement of the sides of a triangle does not forms a right angled triangle.
As given in the question,
For the given triangle,
Length of the sides of the triangle is given by :
8cm , 5 cm , and 10cm
In the given triangle longest side is equal to 10cm
Condition for a right angled triangle:
Longest side is the hypotenuse of the right angled triangle.
By Pythagoras theorem we have,
( Hypotenuse )² = ( Side1)² + ( Side 2)²
R.H.S. ( Right hand side )
= ( 8 )² + (5 )²
= 64 + 25
= 89
≠ 10²
Here given length side of a triangle does not satisfies the Pythagoras theorem .
Therefore, the given sides of a triangle is not representing a right angled triangle.
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If the ratio of areas of two similar hexagons are to each other as 5: 2, and one side of the first hexagon is 25, what is the corresponding side in the other hexagon? (Round your answer to two decimal places.)
A. 3.16
B. 10.00
C. 15.81
D. 250.00
The corresponding side in the other Hexagon will be 15.81.
What is Hexagon?
In geometry, a hexagon is a six-sided polygon. Each internal angle and the side length of a regular hexagon are both 120 degrees. The formula used to determine the area of a regular hexagon is:
Area = 3 [tex]\sqrt{3}[/tex]/2 * [tex]side^{2}[/tex]
Each internal angle in an irregular hexagon can be greater than or less than 120 degrees, and the sides are uneven in length.
In our question it is given that the ratio of the area of two similar hexagons is 5:2. This indicates that the sides' square ratio is 5: 2.
Let x represent the corresponding side in the opposite hexagon.
Then, [tex]25^{2}[/tex] : [tex]x^{2}[/tex] = 5:2
= 625/[tex]x^{2}[/tex] = 5/2
= [tex]x^{2}[/tex] = (625 *2)/5
= [tex]x^{2}[/tex] = 250
= x = [tex]\sqrt{250}[/tex]
= x = 15.81 approx
Therefore, the corresponding side in the other hexagon will be 15.81.
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Which of the following is equivalent to the quadratic equation below after completing the square?
x² +6x-3=12
A. (x+6)² = 12
B. (x+3)² = 24
C. (x+6)² =9
D. (x+3)² = 9
William invested $550 in an account paying an interest rate of 2% compounded monthly. Violet invested $550 in an account paying an interest rate of 2% compounded continuously. To the nearest hundredth of a year, how much longer would it take for William's money to triple than for Violet's money to triple?
Answer:
We can use the formula A = P(1 + r/n)^(nt) to find out how long it takes for William's money to triple, where A is the final amount, P is the principal, r is the interest rate, t is the time in years and n is the number of times the interest is compounded per year.
A = P(1 + r/n)^(nt) = 550(1 + 0.02/12)^(12*t) = 3P
Solving for t we get
t = (ln(3)/ln(1+0.02/12))/12 = 49.41
For Violet's account, using the formula A=Pe^(rt) where A is the final amount, P is the principal, r is the interest rate, t is the time in years, we get:
t = ln(3) / (2 * e^-2) = 49.41
Therefore, it will take approximately 49.41 years for William's money to triple, and 49.41 years for Violet's money to triple.
So the difference in time is 0.
Write your answer as a whole number or decimal.The volume of a cylinder with a base of area B and a height h is Bh. Bryce is using a cylinder-shaped can to hold his pencils. The can has a 5.4-square-inch base and a height of 8 inches.
Step-by-step explanation:
that means we have to calculate the volume of that cylinder ?
as the decryption says : the volume is
base area × height
or
Bh
base area = 5.4 in²
height = 8 in
the volume is
5.4 × 8 = 43.2 in³
60 POINTS BEING AWARDED!!!!!!!! PRECISION Find the values of x and y in the trapezoid. Justify your answer.
The values of x and y in the trapezoid are x = 15 and y = 3
What is a trapezoid?You should understand that a trapezoid or trapezium is a quadrilateral having two parallel sides and two non-parallel sides
If the trapezoid is isosceles, angles A and C are supplementary, so ...
(4x+4) +(7x+11) = 180
This implies that
11x +15 = 180
Collecting terms we have
11x = 165 . . . . . . . . . subtract 15
x = 15 . . . . . . . . . . . . divide by the coefficient of x
And angles C and E are congruent.
4·15 +4 = 21y +1
63 = 21y . . . . . subtract 1
3 = y . . . . . . . . divide by the coefficient of y
In conclusion x and y are 15 and 3
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Maddox has 21 to spend on souverniers as gift for his friends. He wants to buy each friend a keychain and a pin. The equation 3f + 4f =21 can be used to find f, the number of friends for which he can buy souvenirs
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{3f + 4f = 21}[/tex]
[tex]\textbf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{(3f + 4f) = 21}[/tex]
[tex]\mathsf{3f + 4f = 21}[/tex]
[tex]\mathsf{7f = 21}[/tex]
[tex]\textbf{DIVIDE 7 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{7f}{7} = \dfrac{21}{7}}[/tex]
[tex]\textbf{SIMPLIFY it!}[/tex]
[tex]\mathsf{f = \dfrac{21}{7}}[/tex]
[tex]\mathsf{f = 3}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{f = 3}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
3(2x-7)= 3
What are the solutions
One-fourth of total candidates failed in an examination if passing marks are
(A) 2 less than average marks of total number of candidates,
(B) 11 less than average marks of candidates who passed,
(C) twice the average marks of failed students,
then find the passing marks.
Answer:
Let the number of the passed candidates = x.Then the number of the failed candidates = 120 - x.Now the total of the marks obtained by 120 candidates = 120
Step-by-step explanation:
The correct option is B 100Here, total marks obtained by 120 students = 120 × 35 = 4200 Let the number of passed candidates = Then, total marks obtained
Given the recursive formula below, find the first five terms.
Answer:
3, 5, 7, 9, 11
Step-by-step explanation:
the recursive formula allows a term to be found by adding 2 to the previous term, that is
u₁ = 3
u₂ = u₁ + 2 = 3 + 2 = 5
u₃ = u₂ + 2 = 5 + 2 = 7
u₄ = u₃ + 2 = 7 + 2 = 9
u₅ = u₄ + 2 = 9 + 2 = 11
the first 5 terms are 3, 5, 7, 9, 11
Imagine you have a classmate who has never had an introduction to statistics in a math course. Explain to that person how the probability of selecting a red tile is determined. Use complete sentences.
The probability of selecting a red tile is determined by the formula number of red tiles/total number of tiles.
Probability is used to determine the chances of events.
To calculate the probability of selecting a red tile, we start by:
Get the number of red tiles
The total number of tiles
Then we need to divide the number of red tiles by the total number of tiles.
According to the question, there are 15 red tiles in a total of 60 tiles, then the probability of selecting a red tile is:
P(red) = 15/60
Divide 15 by 60
P(red) = 0.25
Thus, the probability of selecting a red tile for the given values is 0.25.
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QuestionReflect (4,5) in the x-axis followed by the y-axis. QuestionReflect (4,5) in the x-axis followed by the y-axis
The resulting reflection will be (4,-5) and will be followed by (-4,-5).
What is coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. A series of data indicating a precise position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is 12 units long and 5 units high.
Here,
given coordinates=(4,5)
Firstly, reflecting across x axis, point (x,y) turns to (x, -y).
=(4,-5)
Secondly, reflecting (x,-y) across y-axis, point (x,-y) turns to (-x,-y).
=(-4,-5)
The resultant reflection will lead (4,-5) followed by (-4,-5).
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a piece of wire 10m long is cut into 2 pieces. one piece is bent into a square and the other into a circle. how much of the wire should be used for the square if you want to minimize the total enclosed area? please give an exact simplified answer.
Bend 4.4 m of the wire into a circle and bend 5.6 m of the wire into a square in order to minimize the total area.
Let x = length of the portion that is bent into a circle
Then, 10-x = length bent into a square
Each side of the square has length (10-x)/4
So, area of square = (10-x)2/16
x = circumference of circle = 2πr So, r = x/(2π)
Therefore, Area of circle = πr2 = x2/(4π)
T = total area = (10-x)2/16 + x2/(4π)
= [(10-x)2π + 4x2 ]/(16π)
= [(100-20x+x2)π + 4x2]/(16π)
= [(4+π)x2 -(20π)x+100π]/(16π)
= [(4+π)/(16π)]x2 - (5/4)x + (25/4)
The graph of T is a parabola opening upward. The minimum of T occurs at the vertex of the parabola.
The x coordinate of the parabola is (5/4)/[(4+π)/(8π)] = (10π)/(4+π) ≈ 4.4
Thus, Bend 4.4 m of the wire into a circle and bend 5.6 m of the wire into a square in order to minimize the total area.
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Review the table forecasting a company’s profit based on the number of units sold.
Which statement is the best interpretation of the value 29,864 in the quadratic regression equation?
The company has an initial loss of about $29,864.
The company has an initial profit of about $29,864.
The company needs to sell about 29,864 units to break even.
The company needs to sell about 29,864 units to maximize its profit.
The statement that best interprets the value 29,864 in the quadratic regression equation (y = -0.004·x² + 34.637·x - 29,864) for the data in the table forecasting the company's profit based on the number of units sold is the option;
The company has an initial loss of about $29,864What is a regression equation?A regression equation is an equation that aims at discovering the relationship between a dependent or output variable and the input or independent variable.
The possible data in the question, obtained from a similar question, posted online, is presented as follows;
Number of Units[tex]{}[/tex] Profits ($)
500 [tex]{}[/tex] -10,000
1200 [tex]{}[/tex] 3000
2500 [tex]{}[/tex] 27000
3200 [tex]{}[/tex] 40000
3600 [tex]{}[/tex] 45000
4300 [tex]{}[/tex] 47000
5000 [tex]{}[/tex] 45000
6750 [tex]{}[/tex] 20000
Based on the above data, using the Polynomial trendline option of Order 2, in MS Excel, the quadratic regression equation, obtained using the Display Equation on chart option is; y = -0.004·x² + 34.637·x -29,864
The function, f(x) = -0.004·x² + 34.637·x -29,864, indicates that at x = 0, which is the point where 0 units have produced, we get;
Initial Profits = f(0) = -0.004 × 0² + 34.637 × 0 -29,864 = -29,864
The value, -29,864 indicates a loss of $29,864, therefore;
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Answer:
Step-by-step explanation:
The company has an initial loss of about $29,864
The label on a \frac{1}{3}
3
1
-pound bag of seeds states that it will cover an area of 5656 square feet. How many square feet do the seeds cover per pound?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, mixed numbers, or whole numbers.
To enter a mixed number on the double number line, use a space and the slash key. For example: 3 1/2
Answer: The bag of seeds covers 5656 square feet and is 1/3 pound. To find how many square feet the seeds cover per pound, we can divide the total coverage by the weight of the bag.
Formula: Coverage per pound = Total coverage/weight of the bag
5656 / (1/3) = 5656*3 = 16,968 square feet per pound.
Step-by-step explanation:
Is 1.5 in the same as one and a half in?
Yes 1.5 is the same as one and a half
Answer: Yes
Step-by-step explanation:
1/2 = a half 1/2 also = 0.5 1 + 0.5 = 1.5 or 1 and 1/2
Which best describes the offspring of protists?
always genetically identical to one parent
always genetically identical to both parents
never genetically identical to one parent
sometimes genetically different than both parents
The best description of the offspring of Protists is D. sometimes genetically different than both parents
How do Protists reproduce ?Asexual reproduction in protists includes methods such as binary fission, budding and fragmentation, in these methods the offspring are always genetically identical to one parent.
Sexual reproduction in protists can be through conjugation, meiosis, or syngamy, in this case the offspring are not always genetically identical to one or both parents. It is possible for the offspring to be genetically different from both parents due to the genetic recombination that occurs during sexual reproduction.
So, the statement that best describes the offspring of protists is "sometimes genetically different than both parents" as it depends on the type of reproduction method used.
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The given equation had a solution r in the interval -2≤r≤-1. Approximate the solution correct to two decimal places.
8x^3+3x^2-7x+6=0
r≈ ?
The approximate solution of the polynomial in the interval -2≤ x ≤-1 is given as follows:
x = -1.5.
What is the rational zero theorem?The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant divided by the factors of the leading coefficient.
The polynomial for this problem is given as follows:
8x³ + 3x² - 7x + 6.
Hence the leading coefficient and the constant are given as follows:
Leading coefficient: 8.Constant: 6.The factors of the leading coefficient and of the constant are given as follows:
Leading coefficient: {1, 2, 4, 8}.Constant: {1, 2, 3, 6}.Hence the possible roots are given as follows:
±1, ±2, ±3, ±6, ±0.5, ±1.5, ±0.25, ±0.75, ±0.125, ± 0.375.
The only possible root between -2 and -1 is given as follows:
x = -1.5.
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if your answer is not an integer, leave it in simplest form
The value of the x is option b. 9√3.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given figure is a right angled triangle because it is marked in the figure.
For right angled triangle, we have the Pythagoras theorem,
Hypotenuse² = Base² + Altitude²
Given,
Length of hypotenuse = 18
Length of base = 9
Substituting in the Pythagoras theorem,
18² = 9² + x²
x² = 18² - 9²
x² = 243
x² = 81 × 3
x = √(81 × 3)
x = 9√3
Hence the value of the unknown side is 9√3.
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. An integer a is said to be a type 0 integer if there exists an integer n such that a3n. An integer a is said to be a type 1 integer if there exists an integer n such that a-3n 1. An integer a is said to be a type 2 integer if there exists an integer m such that a - 3m + 2. * (a) Give examples of at least four different integers that are type 1 integers (b) Give examples of at least four different integers that are type 2 integers (c) By multiplying pairs of integers from the list in Exercise (9a), does it appear that the following statement is true or false? If a and b are both type 1 integers, then a b is a type 1 integer.
When n is known to be an integer, the formula for m also produces an integer. The assumption is confirmed once the necessary integer m was located.
what is integer ?Positive, negative, and zero are all examples of integers. As a result, integers include numbers like 0, 1, 2, 3, as well as -1, -2, and 3. There are no additional parts, such as fractions or decimals, in integers. As a result, fractional values like 3 1/2 and decimal numbers like -7.5 are NOT integers. All positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity are included in the category of integers. The fundamental arithmetic operations are included in integer operations (addition, subtraction, multiplication and division). In mathematics, integers are any numbers that are either positive, negative, or zero, with the exception of fractions. As a result, operations on integers are simple.
given
Any whole number that is a multiple of 3 is a type 0 integer. Examples are 3, 6, 9, and 12.
n=1: 3(1)=3
n=2: 3(2)=6
n=3: 3(3)=9
n=4: 3(4)=12
When n is known to be an integer, the formula for m also produces an integer.
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Can somebody help me translate these expressions.
A integer, a constant, or a mix of both, combined with specific operation symbols, make up an expression 3r+ 37.5 is the equation.
Describe expression.A number, a constant, or a mix of both, combined with specific operation symbols, make up an expression. An expression can only be an exponential function if it contains both an operators and a variable. Any unknown term can be used as a factor, together with the operator + and -. Examples of such terms include x, y, and z. Since 5 isn't an exponential function, it can be claimed that it.
Here,
Given :
It is reasonable to assume that r = n rides. Since each ride costs $3 ($3xr), the total cost is $3.
In addition, we know that FIVE people, including Tory and every one of her friends, will be at the fair. The entrance fee is $7.50, therefore we can increase it by five to reach $37.5.
That is $3r plus $37.5.
Therefore, the equation is $37.5 + $3r, where r seems to be the total of rides taken by Tory and his friends.
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During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed in a horizontal circle as shown. Knowing that the speed of the hammer is 2.5 m/s and θ = 60°, determine (a) the tension in wire BC, (b) the radius of the circle, rho.
(a) The value of the tension in wire BC will be = 80.4 N
(b) The value of the speed of the hammer’s head will be = 2.30 m/s
Mass of the head of the hammer = 7.1 Kg.
The speed at which it is revolving = v
value of ρ=0.93 m
The value of the angle θ=60°
Tension is described as the force transferred through a rope, string, or wire when pushed by opposing forces. The tension force is directed along the length of the wire and draws energy evenly on the bodies at the ends.
(a) Now, we will first calculate the value of the tension in wire BC,
First, we will note
[tex]$$a_A=a_n=\frac{v_A^2}{\rho}$$[/tex]
(a)
[tex]$+\Sigma F_y=0: T_{B C} \sin 60^{\circ}-W_A=0$[/tex]
or we can write it as:
[tex]$$\begin{aligned}T_{B C} & =\frac{7.1 \mathrm{~kg} \times 9.81 \mathrm{~m} / \mathrm{s}^2}{\sin 60^{\circ}} \\\end{aligned}$$[/tex]
=> =80.426 N
=>= 80.4 N (approx)
(b) Now calculate the speed of the hammer’s head.
[tex]$\quad+\Sigma F_x=m_A a_A: T_{B C} \cos 60^{\circ}=m_A \frac{v_A^2}{\rho}$[/tex]
or
[tex]$$v_A^2=\frac{(80.426 \mathrm{~N}) \cos 60^{\circ} \times 0.93 \mathrm{~m}}{7.1 \mathrm{~kg}}$$[/tex] = 2.30 m/s
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Note: The correct question may be like this:
During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed v in a horizontal circle as shown. If ρ=0.93m and ,θ=60° determine (a) the tension in wire BC, (b) the speed of the hammer’s head.
The needed diagram is attached below
