The accurate scale diagram shows a telephone mast and a box.
Find an estimate for the real height, in metres, of the telephone mast.
telephone mast
5.5
+2.5 m
box
+
Total marks: 2
Using proportions, the real height of the telephone mast is estimated to be 9 meters.
What exactly is a proportion?A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.
The following proportional relationship is established as a result:
x / 1.5 cm = 10.8 cm / 1.8 cm.
The relationship's left side can be simplified as follows:
6 = x / 1.5 cm.
The estimate is then calculated using cross multiplication, as shown below:
6 x 1.5 cm = 9.5 cm².
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Question 2 Which is NOT the method that can be used to show congruency of two triangles? a) SSS b) ASA c) SAS d) SSA 0) None of the above Review Question3 ASATABFE by the HL method mZ AST 48 and m FEB 3x Find x.
Answer:
NO.2- SSA is not the method to show the congruency of two triangles.
a) Explain the concept of a greedy algorithm. b) Provide an example of a greedy algorithm that produces an optimal solution and explain why it produces an optimal solution. c) Provide an example of a greedy algorithm that does not always produce an optimal solution and explain why it fails to do so.
a) A greedy algorithm is an approach to problem-solving that makes the locally optimal choice at each step with the hope of finding a globally optimal solution.
This means that at each step, the algorithm chooses the best available option without considering the future consequences of that decision.
(b) An example of a greedy algorithm that produces an optimal solution is the activity selection problem.
Given a set of activities with their start and end times, the goal is to select the maximum number of non-overlapping activities. The greedy algorithm sorts the activities by their end times and selects the first non-overlapping activity.
It then repeats this process with the remaining non-overlapping activities until all activities have been selected. This algorithm produces an optimal solution because selecting the activity with the earliest end time leaves the maximum amount of time available for the remaining activities.
(c) An example of a greedy algorithm that does not always produce an optimal solution is the knapsack problem.
Given a set of items with their weights and values, the goal is to maximize the value of items that can be carried in a knapsack of a given weight capacity. The greedy algorithm selects items based on their value-to-weight ratio until the knapsack is full.
However, this algorithm can fail to produce an optimal solution if there are items with high value but large weight, which cannot fit in the knapsack after the algorithm selects several low-value items with small weight. In such cases, a more sophisticated algorithm is required to find the optimal solution.
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The zero product property, says that if a product of two real numbers is 0, then one of the numbers must be 0.
a. Write this property formally using quantifiers and variables.
b. Write the contrapositive of your answer to part (a).
c. Write an informal version (without quantifier symbols or variables) for your answer to part (b).
The contrapositive of the zero product property is that if neither of the two real numbers is 0, then the product of the two numbers will not be 0. In plain language, this means that if neither of the two numbers are 0, then the product of the two numbers cannot be 0.
In an informal version, this can be stated as "if neither number is 0, then their product cannot be 0". This can be understood as "if neither number is 0, the result of multiplying them together cannot be 0". In other words, the product of two real numbers will not be 0 if neither of them is 0.
Each of the following is not a vector space. For each of them, determine at least one part of the vector space definition that fails. (a) A={ax2+1:a∈R}with vector addition and scalar multiplication defined as forPn. (b) B=R2 with scalar multiplication defined as usual for Rn but with vector addition defined as below: [\begin{array}{c}a1\\b1\end{array}\right] + [\begin{array}{c}a2\\b2\end{array}\right] = [\begin{array}{cc}a1-a1\\b1-b2\end{array}\right]
The definition of vector space that fails is part A and B because it does not satisfy the any property of vector space.
The following statement can be determined if at-least one part of vector space definition that fails as:
(a) A is not a vector space because it does not contain the zero vector.
The zero vector is the unique vector that satisfies the property that when it is added to any other vector in the space, the result is the original vector.
However, in this case, the [a1, b1] + [a2, b2] = [a1 - a2, b1 - b2] is 0x² + 1, which is not an element of A. Therefore, A fails to satisfy the requirement of having a zero vector, and it is not a vector space.
(b) B is not a vector space because it does not satisfy the distributive property of scalar multiplication over vector addition.
In general, scalar multiplication must distribute over vector addition, meaning that for any scalar a and any vectors u and v in the space, a(u+v) = au + av.
However, in B, the scalar multiplication is defined as usual for R², but the vector addition is defined differently. In particular,[a1, b1] + [a2, b2] = [a1 - a2, b1 - b2].
The vector space definition fails because the vector addition is not associative, and it is also not commutative, which are the first two conditions for vector spaces. Therefore, the first and second conditions of the definition are not met.
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C = {[1 2 3], ['cell '; 'array'], 24; [3; 6; 9], [22, 44; 66, 88], 'matrix'} what is the result of c{2, 1}?
'cell '. The element in the second row and first column of the cell array C is accessed using the phrase c(2,1). The first element in the second row of C is the string "cell," which is that element.
The element in the second row and first column of the cell array C is accessible by the equation c(2,1). The first element in the second row of C is the string "cell," which makes up that element. The string "cell" is the result of c(2,1).
The curly braces in MATLAB are used to retrieve the contents of a cell array. "Access the contents of the cell in the second row and first column of C" is what the phrase C2,1 implies. The string in question is the outcome of the expression since it is present in the relevant cell.
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You ride your bike 1 3/4 miles to your friend's apartment and then another
1 3/10 miles to school. How many miles do you ride your bike in all?
Answer:3 1 /20
Step-by-step explanation:= 1+3/4+1+3/10
What is 25.71 rounded to 2 Decimal Place?
The rounded value of 25.71 to 2 decimal places is 25.71 itself.
How to find 25.71 rounded to 2 Decimal PlaceTo round 25.71 to 2 decimal places, we need to look at the third decimal place, which is 1.
If the third decimal place is 5 or greater, we round up the second decimal place. If the third decimal place is less than 5, we simply drop it and keep the second decimal place as is.
In this case, the third decimal place is 1, which is less than 5, so we simply drop it and keep the second decimal place as is. Therefore, 25.71 rounded to 2 decimal places is:
25.71 ≈ 25.71 (no rounding necessary)
So, the rounded value of 25.71 to 2 decimal places is 25.71 itself.
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An equilateral triangle as a side of 35 cm what is the distance around the triangle
Answer:
Step-by-step explanation:
To find the perimeter of an equilateral triangle is equalled to 3s.
35 x 3
105
the probability that deshawn palys basketball after school is 20% the probability that he talks to friends after school is 45% he says the p b or t is 65% explain dans error
Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
How do we find the error?Given:
Probability of Deshawn playing basketball after school = 20%Probability of Deshawn talking to friends after school = 45%Probability of Deshawn doing either basketball or talking to friends after school = 65%Let’s consider the probability of Deshawn not doing basketball after school:Probability of Deshawn not doing basketball after school = 100% - Probability of Deshawn doing basketball after school= 100% - 20% = 80%
Similarly, let’s consider the probability of Deshawn not talking to friends after school: Probability of Deshawn not talking to friends after school = 100% - Probability of Deshawn talking to friends after school= 100% - 45% = 55% Probability of Deshawn doing neither basketball nor talking to friends after school:Probability of Deshawn not doing basketball after school * Probability of Deshawn not talking to friends after school= 80% * 55% = 44%
The probability of Deshawn doing either basketball or talking to friends after school is 65%, and the probability of Deshawn doing neither basketball nor talking to friends after school is 44%, which is greater than 35% which is Dans mistake. Hence, Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
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what are the zeros of the function using factoring in f(x)=-x^2+8x-15
Answer: 0000
Step-by-step explanation:
Please help it’s for tmr, I only have 18 minutes left
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Leo might therefore have 36 or 48 toy soldiers, which is a choice between the two numbers.
What is the greatest number that is possible?The attempt to demonstrate that your integer is larger than anyone else's integer has persisted through the ages, despite their being more numbers than there are atoms in the universe. The largest number that is frequently used is a googolplex (10googol), which equals 101¹⁰⁰.
We'll name Leo's collection of toy soldiers "x" the amount. We are aware of:
We can infer x to be one of the following figures from the first condition: 28, 32, 36, 40, 44, 48, or 52.
To find out which of these integers meets the other two requirements, we can try each one individually:
x + 6 = 34 and x + 3 = 31, neither of which is a multiple of five, if x = 28.
X + 6 = 38 and X + 3 = 35, none of which is a multiple of 5, follow if x = 32.
When x = 36, x + 6 = 42, a multiple of 7, and x + 3 = 39, a multiple of 5, follow. This might be the answer.
x + 6 = 46 and x + 3 = 43, neither of which is a multiple of five, if x = 40.
x + 6 = 50 and x + 3 = 47, neither of which is a multiple of five, if x = 44.
When x = 48, x + 6 = 54, a multiple of 7, and x + 3 = 51, a multiple of 5, follow.
x + 6 = 58 and x + 3 = 55, neither of which is a multiple of five, if x = 52.
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if x < y < z and all three are consecutive non-zero integers, then which of the following must be a positive odd integer?
Option (A) x+1 is a positive odd integer.
Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.
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Helpppppppppp pleaseeee I really need itttttt
Answer: 96
Step-by-step explanation:
M = 180 - 84 = 96
m<k = 96
What is the next fraction in this sequence? Simplify your answer. 13/ 21 , 9/ 14 , 2/ 3 , 29 /42 ,
Answer:
5/7
Step-by-step explanation:
Make all the denominators 42.
26/42, 27/42, 28/42, 29/42
The pattern is the numerator increases by one each time.
30/42 = 5/7
Hope this helps!
in a lottery daily game, a player picks three numbers from 0 to 9 (without repetition). how many different choices does the player have a) if order matters? b) if order does not matter? 84
There are 720 different choices if order matters and there are 120 different choices if order does not matter.
Calculating the number of different choicesa) If order matters,
The player can choose the first number in 10 ways (any of the digits 0-9), the second number in 9 ways (since one digit has already been chosen), and the third number in 8 ways (since two digits have already been chosen).
So the total number of choices is:
10 x 9 x 8 = 720
Therefore, there are 720 different choices if order matters.
b) If order does not matter,
We need to divide the number of choices by the number of ways the three numbers can be arranged.
Since there are 3 numbers, they can be arranged in 3! = 6 ways.
So the number of choices when order does not matter is:
(10 x 9 x 8) / 6 = 120
Therefore, there are 120 different choices if order does not matter.
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a confidence interval for a population mean was reported to be to . if , what sample size was used in this study? (round your answer up to the next whole number.)
The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.
What is deviation?Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.
Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.
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The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.
What is deviation?Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.
Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.
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Complete Question:
A 95% confidence interval for a population mean was reported to be 152 to 160. If s 15, what sample size was used in this study?
Determine whether the set StartSet left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 0 3rd Row 1st Column negative 3 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 3 2nd Row 1st Column 1 3rd Row 1st Column 6 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column negative 1 3rd Row 1st Column 0 EndMatrix right bracket EndSet 1 0 −3 , −3 1 6 , 1 −1 0 is a basis for set of real numbers R cubedℝ3. If the set is not a basis, determine whether the set is linearly independent and whether the set spans set of real numbers R cubedℝ3. Which of the following describe the set?
The set [1 0 −3 , −3 1 6 , 1 −1 0] is not a basis for set of real numbers R cubed(ℝ3).
The reason why it is not a basis is because it is not linearly independent. However, the set does span set of real numbers R cubed(ℝ3).To determine if the given set is a basis for set of real numbers R cubed(ℝ3), we need to test for linear independence and for span.Linear independence
The given set is said to be linearly independent if and only if the only solution to the equation a[1 0 −3] + b[−3 1 6] + c[1 −1 0] = [0 0 0] is the trivial solution where a, b and c are constants.If the given set is linearly independent then it is a basis for R3; if it is not linearly independent, it is not a basis for R3.
SpanThe given set is said to span R3 if every vector in R3 can be written as a linear combination of vectors in the given set.
If the given set spans R3, then it can be considered a basis for R3.For us to test if the given set is linearly independent, we can form a matrix by placing the three given vectors into the columns of a 3 x 3 matrix as follows:[1 0 1] [−3 1 −1] [−3 6 0]
By expanding the determinant of the matrix above, we get: det(A) = 0 - 0 - (-3) = 3
Since the determinant is non-zero, we can say that the given set is linearly independent. Since the given set is linearly independent, we can then use it to span R3. Hence the given set does not form a basis for R3 but it is linearly independent and spans R3.
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A survey found that 34% of the students spend time with your family eating dinner. Oh the 500 student surveyed, about how many spend time with their family eating dinner?
Answer:
A survey found that 34% of the students spend time with your family eating dinner. Oh the 500 student surveyed, about how many spend time with their family eating dinner?
Step-by-step explanation:
If 34% of the students surveyed spend time with their family eating dinner, we can find the approximate number of students who do so by multiplying the percentage by the total number of students surveyed:
34% of 500 students = 0.34 x 500 = 170 students
Therefore, about 170 of the 500 students surveyed spend time with their family eating dinner.
If you can, give me brainliest please!
consider a completely randomized design with k treatments. assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. determine the total number of pairwise comparisons for k.
The total number of pairwise comparisons for k is (k*(k-1))/2.
There are (k*(k-1))/2 pairwise comparisons in a completely randomized design with k treatments. For example, if there are 4 treatments, there will be 6 pairwise comparisons (4C2 = 6). Here's the explanation:In a completely randomized design, the treatments are randomly assigned to the experimental units. The main objective of such a design is to determine whether the treatment means are different from each other or not.To compare the treatment means, we use the mean square between treatments (MST) and mean square error (MSE). The test statistic used to compare the means is F = MST/MSE.The ANOVA table for a completely randomized design has the following format:Source of variationSum of SquaresDegrees of freedomMean SquareF-testtreatmentSS(k-1)k-1MST=MSTrMSEResidualSSTn-kMSEReference: https://www.stat.yale.edu/Courses/1997-98/101/anovar.htmNow, we need to compare each pair of treatments using a multiple comparisons procedure. A pairwise comparison involves comparing the means of two treatments only.The total number of pairwise comparisons is given by the combination formula:$$ \frac{k!}{2!(k-2)!} = \frac{k(k-1)}{2} $$Therefore, the total number of pairwise comparisons for k is (k*(k-1))/2.
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Factorise fully - 4x² - 16x
Answer: 4x(x - 4)
Step-by-step explanation:
4x² - 16x = 4x(x - 4)
Now we can see that the expression inside the parentheses can also be factored:
x - 4 = (x - 4)
So the fully factorized expression is:
4x² - 16x = 4x(x - 4) = 4x(x - 4)
Answer:
ㅤ
- 4x( x + 4 )
ㅤ
Step-by-step explanation:
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[tex]\large{\pmb{\sf{ - 4x^{2} - 16x}}}[/tex]
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[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{4}} \: As \: Common:-}}}}[/tex]
ㅤ
[tex]\large{\pmb{\sf{\leadsto{- 4(x^{2} + 4x)}}}}[/tex]
ㅤ
[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{x}} \: As \: Common:-}}}}[/tex]
ㅤ
[tex]\large{\purple{\boxed{\pmb{\sf{\leadsto{- 4x(x + 4)}}}}}}[/tex]
━━━━━━━━━━━━━━━━━━━━━━
[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]
ㅤ
[tex]\large{\dashrightarrow}[/tex] Two positive always makes positive sign when multiplied.
ㅤ
[tex]\large{\dashrightarrow}[/tex] Two negatives always makes positive sign when multiplied.
ㅤ
[tex]\large{\dashrightarrow}[/tex] A positive and a negative always makes negative sign when multiplied.
ㅤ
[tex]\large{\dashrightarrow}[/tex] The sum of two positives is always positive with a positive sign.
ㅤ
[tex]\large{\dashrightarrow}[/tex] The sum of two negatives is always positive with a negative sign.
ㅤ
[tex]\large{\dashrightarrow}[/tex] The sum of a positive and a negative is always negative with the sign of whose number is greater.
10) Find the vertex form of the parabola.
Step-by-step explanation:
4x + y^2 + 2y = - 5
4x = - y^2 -2y - 5
4x = - (y^2 + 2y) - 5 'complete the square' for y
4x = - ( y +1)^2 + 1 - 5
x = - 1/4 ( y+1)^2 - 1 vertex is at -1, -1
-14x+2y^2-8y -20 = 0
14x = 2y^2 -8y-20
14x = 2 ( y^2 - 4y) - 20 complete the square for y
14x = 2(y-2)^2 -8 - 20
x = 1/7 ( y-2)^2 - 2 Vertex is at -2 , 2
The valume pf a right triangular prism is 72 cubic feet. The height of the prism is 9 feet. The triangular basevis an isosceles right triangle. What is the area of the base? 2,4,8,16 in square feet. What is the length of the edge of DF? 2,4,8,16 in feet
If the volume of a right triangular prism is 72 cubic feet, the area of the base is 2 square feet and the length of DF is approximately 2.83 feet.
To solve the problem, we can use the formula for the volume of a right triangular prism, which is:
Volume = (1/2) x base x height x length
where base is the area of the triangular base, height is the height of the prism, and length is the length of the prism.
We are given that the volume is 72 cubic feet and the height is 9 feet. Therefore, we can write:
72 = (1/2) x base x 9 x length
Simplifying this equation, we get:
base x length = 16
We are also given that the base is an isosceles right triangle. This means that the two legs of the triangle are equal, and the hypotenuse is equal to the length of one leg times the square root of 2.
Let's call the length of one leg of the triangle DF. Then, we can write:
base = (1/2) x DF x DF
Substituting this expression for base into the equation we derived earlier, we get:
(1/2) x DF x DF x length = 16
Simplifying this equation, we get:
DF x DF x length = 32
We know that the hypotenuse of the triangle is DF times the square root of 2. Since the hypotenuse is also one of the edges of the base of the prism, we can set it equal to the length of the prism:
DF x √(2) = length
Substituting this expression for length into the equation we derived earlier, we get:
DF x DF x DF x sqrt(2) = 32
Simplifying this equation, we get:
DF^3 = 16
Taking the cube root of both sides, we get:
DF = 2
Therefore, the area of the base is:
base = (1/2) x DF x DF = 2 square feet
And the length of DF is:
DF x √(2) = 2 x √(2) feet = approximately 2.83 feet.
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What is the next term of 24,30,36,42,48
Answer:
54
Step-by-step explanation:
Add six each time -> 24 + 6 = 30 + 6 = 36 etc
Answer needed ASAP!!
:)
The answer of the given question based on the finding the m∠QTS from a circle with the measure of minor arc the answer is the measure of angle ∠QTS is 60° degrees.
What is Arc?In geometry, arc is portion of a curve or circle. It is defined as the part of the curve that is contained between two points, called endpoints, on curve. The length of arc is fraction of the circumference of circle, determined by the measure of central angle that subtends it.
An arc is typically denoted by two endpoints, with small arc or arc symbol above the two letters. For example, an arc with endpoints A and B would be denoted as "⌒AB" or "AB".Arcs can be classified based on their measure or position of their endpoints.
An arc with measure less than 180 degrees is called minor arc, while an arc with measure greater than 180 degrees is called major arc. An arc with measure equal to 180 degrees is called semicircle.
Since arc QS is a minor arc, we know that angle ∠QTS is half the measure of arc QS. Therefore, we have:
m∠QTS = (1/2) m arc QS
m∠QTS = (1/2) (120°) [Substituting the given value of m arc QS]
m∠QTS = 60°
Therefore, the measure of angle ∠QTS is 60° degrees.
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Jenny wants to measure the height of a tree she sites the top of the tree using a mirror that is lying flat on the ground. The mirror is 20 feet from the tree, and Jenny is standing 8 feet from the mirror as shown in the figure, her eyes are 5 feet above the ground how tall is the tree?
The Height of tree is around 8.33 feet tall.
What is the connection among Height and distance?In science, we work out the Height of an item utilizing distance and points. Distance is the even distance between the items, and point is the point over the level of the article's top, which gives the item's level.
We can utilize the rule of comparable triangles.
The hypotenuse of this triangle would be the line associating Jenny's eyes to the highest point of the tree (we should refer to this distance as "h").
We can set up the accompanying extent between the two triangles:
h / 20 = (h + 5) / 8
To solve for "h", we can cross-multiply and simplify:
8h = 20(h + 5)
8h = 20h + 100
12h = 100
h = 8.33 feet
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A 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5 gram tennis ball is dropped from the same 3 meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9, determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls. (Balls meet at 0.5073 m above ground, final height of tennis ball = 12.6 m above the ground)
Given that a 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5-gram tennis ball is dropped from the same 3-meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9,
determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls.
The balls meet at a height of 0.5073 m above the ground. Hence the height that the tennis ball bounces above the ground is to be calculated.
Given that the coefficient of restitution between the ball and the ground is e = 0.87The coefficient of restitution between the tennis ball and the basketball is e = 0.9
The coefficient of restitution(e) is defined as the ratio of the relative velocity of separation and relative velocity of approach between two objects.
When a ball falls from height, it gains potential energy.
Potential energy (PE) = mghWhere, m = mass of the object, g = acceleration due to gravity, h = height
PE of Basketball = mgh= 0.625 kg * 9.81 m/s² * 3 m= 18.4 Joules
Initial kinetic energy (KE) = PE of Basketball
KE of Basketball = 18.4 J
Let the velocity of the basketball before collision be u1 and the velocity of the tennis ball before collision be u2. After the collision, let the velocity of the basketball be v1 and the velocity of the tennis ball be v2.
Using the coefficient of restitution (e) we can find the velocity of the balls after collision
v1 - v2 = -e(u1 - u2)
Initial momentum (P) = Final momentum (P)
before the collision P = m1u1 + m2u2
after collision P = m1v1 + m2v2P = (0.625 kg * u1) + (0.0585 kg * u2)P
= (0.625 kg * v1) + (0.0585 kg * v2)
Using the above two equations and the given coefficients of restitution, we can find the velocity of the balls after collisionv1 = (m1u1 + m2u2 + e * m2 * (u2 - u1)) / (m1 + m2)v2 = (m1u1 + m2u2 + e * m1 * (u1 - u2)) / (m1 + m2)
Here, m1 = mass of basketball
= 0.625 kg,
m2 = mass of tennis ball
= 0.0585 kg,
u1 = 0, u2 = 0P = m1v1 + m2v2 => v1 + v2 = P / (m1 + m2)
Also given that the time taken by the balls to meet is 0.15 seconds
Let h be the height to which the tennis ball bounces after the collision.
When the tennis ball bounces to height h, it gains potential energy.
KE + PE = Total energy
= Constant Using the principle of conservation of energy we can find the height to which the tennis ball bounces after collision(1/2) * m2 * v2² + (1/2) * m2 * g * h
= (1/2) * m2 * u2² + (1/2) * m2 * g * 0(1/2) * m2 * v2²
= (1/2) * m2 * u2² - (1/2) * m2 * g * h(1/2) * v2²
= (1/2) * u2² - g * h
Substituting the values of u1, u2, m1, m2, e, t and g, we get:
v1 = (0 + 0.0585 kg * 9.81 m/s² + 0.9 * 0.0585 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v1
= 1.96 m/sv2
= (0.625 kg * 0 + 0 + 0.9 * 0.625 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v2
= 5.5 m/s
Here, u1 = u2 = 0.
Using the above equation, we can find the height to which the tennis ball bounces after collision (1/2) * (0.0585 kg) * (5.5 m/s)² = (1/2) * (0.0585 kg) * (0 m/s)² - (0.0585 kg) * 9.81 m/s² * h12.83 J
= -0.286 J - 0.572 h0.572 h
= -12.83 J / 2h
= -12.83 J / (2 * 0.572)
= 11.2 m
Hence the height to which the tennis ball bounces above the ground after the collision is 11.2 m.
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17. The sum of the interior angles of a pentagon is6x + 6y. Find y in term of x
Answer:
We know that, the sum of interior angles of an n-sided polygon is (n−2)×180⁰
For a pentagon, n=5
so,
[tex] \implies \rm \: 6x + 6y = (n - 2)180[/tex]
[tex] \implies \rm \: 6(x + y) = (5 - 2)180[/tex]
[tex] \implies \rm \: 6(x + y )= 3 \times 180[/tex]
[tex] \implies \rm \: (x + y) = \dfrac{3 \times 180}{6} [/tex]
[tex] \implies \rm \: (x + y) = \dfrac{ 3 \times \cancel{180} \: \:30}{ \cancel6} [/tex]
[tex] \rm \implies \: x + y = 90[/tex]
[tex] \underline{\boxed{\implies \rm \: y= 90 - x}}[/tex]
Pentagon FormulasThere are many formulas related to a pentagon. A few basic ones are given below.
Diagonals of a pentagon: = n × (n − 3) ÷ 2 = 5 × (5 − 3) ÷ 2 = 5Sum of interior angles of a pentagon: = 180° × (n − 2) = 180° × (5 − 2) = 540°Each exterior angle of a regular pentagon: = 360° ÷ n = 360° ÷ 5 = 72°Each interior angle of regular pentagon: = 540° ÷ n = 540° ÷ 5 = 108°Area of a regular Pentagon = 1/2 × Perimeter × ApothemPerimeter of Pentagon = (side 1 + side 2 +side 3 + side 4 + side 5)If the weight of the package is multipled by 5/7 the result is 40. 5. How much does the package weigh
The weight of the package is 56 using arithmetic operations.
What is multiplication?Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the numbers.
let weight of package be= x
x*5/7=40
x=(40*7)/5
x=56
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7) Roy buys pizza for his friends. A whole pizza costs P 190. 00 and P 40. 00 for every
additional topping. If he spent P 1070 for pizza with 3 sets of additional toppings, how
many whole pizzas did he buy?
Roy purchased whole pizzas for P 190.00 each. To determine the number of whole pizzas he bought, we can divide the total cost of the pizzas by the cost of each pizza. Therefore, the calculation P 950.00 / P 190.00 results in 5, indicating that Roy bought five whole pizzas.
Roy spent a total of P 1070 for pizza with 3 sets of additional toppings. Since each set of additional toppings costs P 40.00, then the total cost of the toppings is 3 x P 40.00 = P 120.00. Subtracting this from the total amount spent gives us P 950.00, which is the cost of the pizzas alone.
Since each whole pizza costs P 190.00, we can divide the cost of the pizzas by the cost of each pizza to find the number of whole pizzas Roy bought. Therefore, P 950.00 / P 190.00 = 5.
Thus, Roy bought 5 whole pizzas.
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