. The GCD of three numbers is 30 and their LCM is 900. Two of the numbers are 60 and 150. What is the other possible number? (3 mks)
If the GCD of three numbers is 30 and their LCM is 900. Two of the numbers are 60 and 150. The other possible number is 450.
What is the possible number?Let the third number be x. We know that:
GCD(60, 150, x) = 30
This means that 30 is a common factor of all three numbers. We can divide each number by 30 to get:
GCD(2, 5, x/30) = 1
Now we can use the fact that the product of the GCD and LCM of three numbers is equal to the product of the numbers themselves:
GCD(60, 150, x) * LCM(60, 150, x) = 60 * 150 * x
30 * 900 = 60 * 150 * x
x = 900 / 2 = 450
Therefore, the other possible number is 450.
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Algebra question: Laila is 10 years older than her younger sister, Kylie. Seventeen years ago Laila was triple Kylie's age. How old are Laila and Kylie currently?
Answer:
Step-by-step explanation:
Let's assume Kylie's current age to be x.
According to the problem, Laila is 10 years older than Kylie, so her current age would be (x + 10).
Seventeen years ago, Laila's age would have been (x + 10 - 17) = (x - 7), and Kylie's age would have been (x - 17).
The problem also states that Laila's age 17 years ago was triple Kylie's age 17 years ago, so we can set up the equation:
(x - 7) = 3(x - 17)
Solving for x, we get:
x - 7 = 3x - 51
2x = 44
x = 22
Therefore, Kylie's current age is x = 22, and Laila's current age is (x + 10) = 32.
So, Laila is currently 32 years old and Kylie is currently 22 years old.
Answer:
Laila is currently 32 years old.
Kylie is currently 22 years old.
Step-by-step explanation:
To find the current ages of Laila and Kylie, create and solve a system of linear equations using the given information.
Define the variables:
Let L be the current age of Laila.Let K be the current age of Kylie.Given Laila is 10 years older than Kylie:
L = K + 10Given 17 years ago, Laila was triple Kylie's age:
L - 17 = 3(K - 17)Substitute the first equation into the second equation and solve for K:
⇒ (K + 10) - 17 = 3(K - 17)
⇒ K - 7 = 3K - 51
⇒ K - 7 - K = 3K - 51 - K
⇒ -7 = 2K - 51
⇒ -7 + 51 = 2K - 51 + 51
⇒ 44 = 2K
⇒ 44 ÷ 2 = 2K ÷ 2
⇒ K = 22
Substitute the found value of K into the first equation and solve for L:
⇒ L = K + 10
⇒ L = 22 + 10
⇒ L = 32
Therefore, Laila is currently 32 years old and Kylie is currently 22 years old.
ZA and ZB are complementary angles. If m≤A = (x – 19)˚ and
m/B = (3x + 1)°, then find the measure of ZB.
Answer:
∠ B = 82°
Step-by-step explanation:
complementary angles sum to 90° , then
x - 19 + 3x + 1 = 90
4x - 18 = 90 ( add 18 to both sides )
4x = 108 ( divide both sides by 4 )
x = 27
Then
∠ B = 3x + 1 = 3(27) + 1 = 81 + 1 = 82°
The XYZ Company`s forecasted sales for July, August, September and October of year ended 2012 were Birr 120,000, Birr 100,000, Birr 160,000, and Birr 140,000 respectively and the forecasted selling price per unit for each month`s sale was Birr 20. The ending inventory of the Company on June 30, 2012 was 1,500 units. The desired ending inventory for each month was one-fourth of the forecasted sales of the following month.
a. Prepare a production budget for the month of July, August, and September. (4pts)
Production budget for the month of July, August, and September as below.
Define the term selling price?The selling price is the amount of money that a company charges for a product or service in order to generate revenue and make a profit.
1. Expected Sales:
July: 120,000 / 20 = 6,000 units
August: 100,000 / 20 = 5,000 units
September: 160,000 / 20 = 8,000 units
2. Required Production:
July: 6,000 units + (8,000 units / 4) - 1,500 units = 4,500 units
August: 5,000 units + (6,000 units / 4) - (8,000 units / 4) = 3,500 units
September: 8,000 units + (5,000 units / 4) - (6,000 units / 4) = 6,000 units
3. Desired Ending Inventory:
July: 8,000 units / 4 = 2,000 units
August: 6,000 units / 4 = 1,500 units
September: 10,000 units / 4 = 2,500 units
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1. The Expected Sales in July is 6,000 units, August is 5,000 units and september is 8,000 units.
2. Required Production in July is 4,500 units, August is 3,500 units and september is 6,000 units.
3. Desired Ending Inventory in July is 2,000 units, August is 1500 units and september is 2500 units.
How do you calculate expected sales?The most basic method is: sales forecast = sales from the previous month + expected growth (or shrinkage) in revenue for the next term.
1. Expected Sales:
July = 120,000 / 20
= 6,000 units
August = 100,000 / 20
= 5,000 units
September = 160,000 / 20
= 8,000 units
2. Required Production:
The quantity of units that a company must produce in a given time frame in order to be profitable.
[tex]July=6000\ units+(\frac{8000\ units}{4} )-1500\ units[/tex]
[tex]=4500\ units[/tex]
[tex]August=5000\ units+(\frac{6000\ units}{4} )-(\frac{8000\ units}{4} )[/tex]
[tex]=3500\ units[/tex]
[tex]september=8000\ units+(\frac{5000\ units}{4} )-(\frac{6000\ units}{4} )[/tex]
[tex]=6000\ units[/tex]
3. Desired Ending Inventory:
Ending inventory is the sellable inventory that remains at the conclusion of an accounting period.
July = 8,000 units / 4
= 2,000 units
August = 6,000 units / 4
= 1,500 units
September = 10,000 units / 4
= 2,500 units
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Production of a 5,350 linear-foot irrigation system for Thompson Orchards (job no. 399) was started and completed in March of the current year.
The production of a 5,350 linear-foot irrigation system for Thompson Orchards, job no. 399, was started and completed in March of the current year.
This means that the irrigation system was manufactured and delivered to the customer within that month. It is important to note that completing the production does not necessarily mean that the job is entirely finished, as there may be additional steps involved such as installation and testing. The completion of this job is a significant milestone for Thompson Orchards as it allows for efficient watering of their crops, which is crucial for their growth and productivity. The irrigation system was likely designed and manufactured to meet specific requirements, taking into consideration factors such as the type of crops grown, soil type, and climate. For the manufacturer, completing this job on time and to the customer's satisfaction is a testament to their expertise and ability to deliver high-quality products. This successful project can lead to repeat business and positive word-of-mouth recommendations. Overall, the completion of the irrigation system for Thompson Orchards is a significant accomplishment for both the manufacturer and the customer.
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Porter's points per basketball game are normally distributed with a standard deviation of 6 points If Porter scores 50 points, and the z-score of this value is 4, then what is his mean points in a game? Do not include the units in your answer. For example, if you found that the mean is 33 points, you would enter 33. Provide vour answer below:
The mean points per game for Porter is 26 points.
To find the mean, we use the formula for the z-score:
z = (x - mu) / sigma
where z is the z-score, x is the observed value, mu is the mean, and sigma is the standard deviation. Rearranging this formula, we get:
mu = x - z * sigma
Plugging in the values given in the problem, we have:
mu = 50 - 4 * 6 = 26
This would be the mean if the z-score is 4.
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Rewrite the following quadratic function im standard (vertex) form. f(x)=6x^2-5x-1
The standard form (vertex form) of the function f(x) is: f(x) = 6(x - 5/12)x² - 169/24.
Describe the vertex form?To rewrite the quadratic function f(x) = 6x2 - 5x - 1 in standard form (vertex form), we can complete the square:
f(x) = 6xx² - 5x - 1 = 6(x²- (5/6)x) - 1 = 6(xx² - (5/6)x + 25/144) - 1 - 6(25/144) = 6(x - 5/12)x² - 169/24
Therefore, the standard form (vertex form) of the function f(x) is: f(x) = 6(x - 5/12)x² - 169/24.
The vertex form of a quadratic function is a way of writing the function in a specific form that reveals important information about the vertex, or turning point, of the parabolic graph of the function.
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Bethany can mow her family's lawn in 4 hours. Her brother Colin can mow the lawn in 3 hours. Which equation can
be used to find the number of hours, x, it would take for Bethany and Colin to mow the lawn together?
Bethany
Sess
Colin
3+4=X
x-x-1
0-3-1
Mark this and return
Rate
(Lawns per Hour)
1
4
13
Time
(Hours)
X
Save and Exit
Fraction Completed
Next
4X
1
3X
Submit
After answering the presented question, we can conclude that this equation depicts Bethany and Colin's combined work rate, where 1/4 represents Bethany's work rate.
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument "2x + 3 = 9," for example, states that the sentence "2x Plus 3" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation "x² + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
The following equation can be used to calculate the number of hours, x, required for Bethany and Colin to mow the lawn together:
1/4 + 1/3 = 1/x
This equation depicts Bethany and Colin's combined work rate, where 1/4 represents Bethany's work rate (in lawns per hour) and 1/3 represents Colin's work rate (in lawns per hour). When they mow the grass together, the equation makes the total of their individual work rates equal to their combined work rate. Solving for x gives us the number of hours it would take them to finish the job if they worked together.
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find the size of angle xyz
give ur answer to 1 dec place
[tex]\cos(XYZ )=\cfrac{\stackrel{adjacent}{6}}{\underset{hypotenuse}{15}}\implies \cos(XYZ )=\cfrac{2}{5} \\\\\\ XYZ=\cos^{-1}\left( \cfrac{2}{5} \right)\implies XYZ\approx 66.4^o[/tex]
Make sure your calculator is in Degree mode.
y=c+bx2, find y where c = 14/5, B = 4/5,x=2
Answer:
ASAP................Research the use in the military of magnetic anomaly detectors, MADs. Write a brief 300-word essay answer the following questions on MADs. What is the main idea behind MADs? What can be detected by using MADs? A brief history of the MAD development.
Step-by-step explanation:
4. Explain how you would create and use a spinner to simulate the probability of an event
with the following probabilities:
Percent chance: 20% green, 1/4 blue,2/5 yellow, and 15% orange
To get the given probabilities of the event we can use a spinner with 20 green, 25 blue, 40 yellow, and 15 orange parts.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to convey it. The likelihood of an occurrence may be determined by dividing the positive outcomes by the entire number of possible outcomes. For instance, the likelihood of receiving heads on a fair coin flip is 50% since there is only one positive event (heads) out of two possible possibilities (heads or tails). The general probability calculation formula is:
Number of likely outcomes divided by the total number of possible outcomes is how you calculate an event's probability.
To get the given probabilities of the event we can use a spinner with 20 green, 25 blue, 40 yellow, and 15 orange parts.
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HELP PLS ASAP which of the following will yrilf data with variability
The correct option that result the data with variability:
C. The shoe size of the various 5 year olds.
D. The number of patients at the doctor's office each day.
Explain about the variability of data:The term "variability" refers to the distance between data points within a distribution and their distance from its centre. Measures of variability provide you summary statistics that summarise your data in addition to measurements of central tendency.
Spread, scatter, and dispersion are other terms for variation. It is often assessed using the following:
Difference between both the greatest and least values is referred to as the range.Interquartile range: a range of a distribution's middle halfStandard deviation is the typical departure from the mean.Variance: squared mean deviations are averaged out.Thus, the result the data with variability:
C. The shoe size of the various 5 year olds as it will vary for different children.
D. The number of patients at the doctor's office each day is also variable.
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Can you help me answer the questions
Answer:
C and E
Step-by-step explanation:
Select a statement that describes the height data. Mark all that apply. If A or C is marked, the other won't be marked because the two statements are contradictory. Option D will not be marked.
Group 1
mean = (103 + 112 + 108 + 120 + 114 + 125 + 109 + 121) / 8 = 114
MAD = (11 + 2 + 6 + 6 + 0 + 11 + 5 + 7) / 8 = 48 / 8 = 6
Group 2
mean = (120 + 85 + 138 + 126 + 92 + 133 + 128 + 90) / 8 = 114
MAD = (6 + 29 + 24 + 12 + 22 + 19 + 14 + 24) / 8 = 150 / 8 = 18.75
Mark C because 114 = 114.
Mark E because 18.75 > 3 * 6.
Don't mark D, because the data in Group 2 varies more than Group 1.
Don't mark B, because both groups have 8 children.
Where do the medians of the triangle intersect?
Answer:
The medians intersect at 4-4 (i think).
Step-by-step explanation:
Every triangle has three medians and they all intersect in the triangles centroid. i believe that the medians intersect at 4-4.
i am not a very trustworthy source so you should probably ignore this awnser.
Determine if f(x) = 3x4 -8 is invertible.
O invertible
O non-invertible
If so, find the inverse.
ƒ-¹(x) =
F(x) is one-to-one, and it is invertible.
The inverse of f(x) is f^-1(x) = (x + 8)^(1/4)/∛3.
To determine if the function f(x) = 3x^4 - 8 is invertibleWe need to check if it is a one-to-one function.
A function is one-to-one if every element in the domain is paired with a unique element in the range.
To check if f(x) is one-to-one, we can use the horizontal line test. If no horizontal line intersects the graph of the function more than once, then the function is one-to-one.
Taking the derivative of f(x), we get:
f'(x) = 12x^3
Since f'(x) is always positive, f(x) is a strictly increasing function. This means that no two different inputs x1 and x2 can produce the same output f(x1) = f(x2).
Therefore, f(x) is one-to-one, and it is invertible.
To find the inverse of f(x), we can follow these steps:
Step 1: Replace f(x) with y:
y = 3x^4 - 8
Step 2: Solve for x in terms of y:
y + 8 = 3x^4
x^4 = (y + 8)/3
x = (y + 8)^(1/4)/∛3
Step 3: Replace x with f^-1(x):
f^-1(x) = (x + 8)^(1/4)/∛3
Therefore, the inverse of f(x) is f^-1(x) = (x + 8)^(1/4)/∛3.
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Bob received the following scores: 72, 86, 92, 63, and 77. What test score must Bob earn on his sixth test so that his average for all six tests will be 80?
Answer:
90
Explanation:
Given marks of Bob's five tests are:
[tex]72 + 86 + 92 + 63 + 77[/tex]
To get an average of 80 on six tests we will need to multiply 6 tests to average of 80.
So,
[tex]6 \times 80 = 480[/tex]
Adding the marks of given five tests is
[tex]72 + 86 + 92 + 63 + 77 = 390[/tex]
Now, to get the marks for Bob's next test, which is the sixth test, we should subtract 390 from 480.
So,
480 - 390 = 90
Therefore, Bob needs to score 90 marks on his sixth test to obtain the average of 80 for all the six tests.
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2. She proceeds to sell the books for R80.00 each. Complete the input/output table below: 2.1 2.3 2.4 Number of Books Fixed Costs Variable Costs Total Costs Printer's Costs 2.4.1 2.4.2 0 A 0 C 0 50 950 902.50 100 1400 950 B 1852.50 2755 D 150 950 2707.50 3657.50 4200 200 950 3 610 4 560 2.2 Complete the graphs for the cost of using a printer and the Total Costs on ANNEXURE A. 5600 Indicate the Point where the graphs meet with the letter A. This point is called the break even point. Use your graph to indicate the following values at this point: The cost of the books. Number of books. (4) (
Answer:
I'm sorry, but the information you provided is not clear enough for me to create the required input/output table and graphs on ANNEXURE A. Could you please provide more context and details on the problem? What are the fixed costs, variable costs, and printer's costs for? Are there any other costs involved in selling the books? How many books are initially available for sale? Without this information, I won't be able to provide an accurate solution to your problem.
Step-by-step explanation:
11. The area of a square painting is 225x¹+240x+64. Explain how you would find a possible
length of one side of the painting.
Answer: Therefore, a possible expression for the length of the side of the square painting is:
side = 15x + 8
or
side = -15x - 8
Step-by-step explanation:
To find a possible expression for the length of the side of the square painting, we need to use the formula for the area of a square, which is:
Area = side^2
We can set the given expression for the area of the painting equal to this formula:
225x¹+240x+64 = side^2
Next, we can simplify the expression on the left-hand side by factoring it into a perfect square trinomial:
225x¹+240x+64 = (15x + 8)^2
Now we can substitute this expression back into the equation and solve for the side of the square painting:
(15x + 8)^2 = side^2
Taking the square root of both sides, we get:
15x + 8 = side
or
15x + 8 = -side (since the length of a side can be positive or negative)
Therefore, a possible expression for the length of the side of the square painting is:
side = 15x + 8
or
side = -15x - 8
Note that since we are dealing with a geometric object, we should choose the positive value for the length of the side, as the side length cannot be negative. Therefore, the final expression for the length of the side of the square painting is:
side = 15x + 8
Evaluate this table.
X 5 10 15 25 40
Y 1 2 3 5 8
The table represents a(n)
relationship.
Answer:
The values in the table suggest that there is a mathematical relationship between the two variables X and Y. Upon inspection, we can observe that Y is increasing with respect to X, and the increase seems to be non-linear. Specifically, as X increases by a factor of 2, Y increases by a factor of approximately 1.5 to 2.
Based on these observations, it seems that the relationship between X and Y may be an exponential one. To confirm this, we can plot the data points on a graph and see if they form a curve that resembles an exponential function.
Alternatively, we can calculate the ratio of Y to X and see if it remains approximately constant. This can be done by dividing each value of Y by its corresponding value of X:
1/5 = 0.2
2/10 = 0.2
3/15 = 0.2
5/25 = 0.2
8/40 = 0.2
The ratio remains constant at approximately 0.2, suggesting that the relationship between X and Y may be a proportional one, with a constant of proportionality equal to 0.2.
Therefore, the table represents a proportional relationship between X and Y, where Y is proportional to X with a constant of proportionality equal to 0.2.
Step-by-step explanation:
Here's a step-by-step explanation of how to evaluate the table:
1. Identify the variables: The table contains two variables, X and Y, which are listed in two separate columns.
2. Examine the values: Look at the values in the table for both X and Y. Notice that as X increases, so does Y.
3. Determine the pattern: To determine the pattern between the two variables, calculate the ratio of Y to X. If the ratio is constant, then the relationship is proportional. If the ratio changes, then the relationship is nonlinear.
4. Calculate the ratio: To calculate the ratio, divide each value of Y by its corresponding value of X. For example, to find the ratio for the first row, divide 1 by 5: 1/5 = 0.2. Continue calculating the ratios for each row.
5. Analyze the ratio: If the ratios are approximately constant, then the relationship is proportional. In this case, we see that the ratios are all approximately 0.2, so we can conclude that the relationship is proportional.
6. Determine the constant of proportionality: To determine the constant of proportionality, simply use any one of the rows in the table. For example, let's use the first row, where X = 5 and Y = 1. The ratio of Y to X is 0.2, so we can write the relationship as Y = 0.2X. This means that for every increase of 1 unit in X, Y increases by 0.2 units.
7. Summarize the result: Based on the analysis, we can say that the table represents a proportional relationship between X and Y, with a constant of proportionality equal to 0.2.
Given
X 5 10 15 25 40
Y 1 2 3 5 8
5 / 40 = 0.2
y=0.2x
A triangle has side lengths of ( 1.3 t + 7.9 u ) (1.3t+7.9u) centimeters, ( 2.4 t − 4.8 v ) (2.4t−4.8v) centimeters, and ( 6.8 v − 9.8 u ) (6.8v−9.8u) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Step-by-step explanation:
why did you mention the definition of every side twice ?
I think we need only one per side right ?
because otherwise we would have to do all 3 multiplications before summing things up.
I sorted the terms for the sum based on their variable.
after all, the perimeter of a triangle is the sum of all 3 sides.
1.3t + 7.9u
2.4t - 4.8v
- 9.8u +6.8v
--------------------------
3.7t - 1.9u + 2v cm
A. (-8) times 2/3 B. (-8) times (-2/3) C. 9/4 divided by -3/4 D. 1/3= -5 What is A?
Answer: -16/3
Step-by-step explanation:
-8 * 2/3
-8 * 2 = -16
Thus, A = -16/3
Evaluate the integral by making an appropriate change of variables.
[tex]\int\ \int\R {12sin(16x^2+64y^2)} \, dA[/tex]
where R is the region in the first quadrant bounded by the ellipse 16x^2 + 64y^2 = 1
Answer:
To evaluate the integral over the region R, we can use the change of variables:
u = 4x
v = 2y
This gives us:
x = u/4
y = v/2
The Jacobian of this transformation is:
| ∂x/∂u ∂x/∂v | = | 1/4 0 |
| ∂y/∂u ∂y/∂v | | 0 1/2 |
So the Jacobian determinant is |J| = (1/4)(1/2) = 1/8.
Using this transformation, the region R is mapped onto the unit circle in the uv-plane, and the equation of the ellipse becomes:
u^2 + v^2/4 = 1/16
The integral becomes:
∫∫R 4x^2 e^(4xy) dA
= 2∫∫S u^2 e^uv/2 (1/8) dA
= (1/4) ∫∫S u^2 e^v/2 dA
where S is the unit circle in the uv-plane.
Now we can use polar coordinates in the uv-plane, with u = r cosθ and v = r sinθ. The integral becomes:
(1/4) ∫∫S r^2 cos^2θ e^(r sinθ/2) r dr dθ
= (1/4) ∫0^2π ∫0^1 r^3 cos^2θ e^(r sinθ/2) dr dθ
The inner integral can be evaluated by integration by parts, letting u = r^2 cos^2θ and dv = e^(r sinθ/2) r dr. This gives:
∫ r^3 cos^2θ e^(r sinθ/2) dr
= r^3 cos^2θ (-2/θ) e^(r sinθ/2) + 2/θ ∫ r^2 cos^2θ e^(r sinθ/2) dr
The integral on the right-hand side can be evaluated by another integration by parts, letting u = r^2 cos^2θ and dv = e^(r sinθ/2) dr, which gives:
∫ r^2 cos^2θ e^(r sinθ/2) dr
= r^2 cos^2θ (-2/θ) e^(r sinθ/2) + 4/θ^2 ∫ r cos^2θ e^(r sinθ/2) dr
We can substitute these results back into the original integral and simplify to get:
∫∫R 4x^2 e^(4xy) dA
= (1/4) ∫0^2π ∫0^1 r^3 cos^2θ e^(r sinθ/2) dr dθ
= (1/2π) ∫0^π ∫0^1 r^3 cos^2θ e^(r sinθ/2) dr dθ
Now we can evaluate the inner integral:
∫0^1 r^3 cos^2θ e^(r sinθ/2) dr = (1/2) ∫0^1 r^2 e^(r sinθ/2) d(r^2)
= (1/2) ∫0^1 u^(1/2) e^(u sinθ/2) du
Letting t = u sin(θ/2) and using the identity sin(θ/2) = 2
3. 1 particle P of mass m kg. The particle P is set in motion so that it moves back and forth alon One end of a light rod of length / m is attached to a fixed point O and the other end is attachec minor arc AB of a vertical circle with centre O and radius / m, as shown in the diagram. A O 0 P C When P is at its lowest point C, its speed is u ms and the tension in the rod is 2mg N. a) Show that u = √gl. B The speed of P when OP makes an angle with the vertical is denoted by v ms. Sho v² = gl (2cos8 - 1). Find the greatest value of 0. Find the value of 0 when the tension in the rod is mg N.
The answer of the given question is (a) proofing is below u = √gl. (b) the greatest value of 0 is 2gr and the value of θ when the tension in the rod is mg and the particle is moving with speed √gl is θ = 30° or θ = 150°.
What is Equilibrium?An equilibrium refers to state of balance or stability where there is no net change in motion. An object is said to be in equilibrium when net force acting on it is zero, which means that object is either at rest or moving with constant velocity.
There is two types of equilibrium that are : static equilibrium and dynamic equilibrium. In static equilibrium, an object is at rest, and net force acting on it is zero. In dynamic equilibrium, an object is moving at constant velocity, and net force acting on it is also zero.
a) At point C, the particle P is at its lowest point and is in equilibrium. Therefore, the forces acting on P must be balanced. The weight of P is mg acting vertically downwards, and the tension in the rod is acting along OC at an angle of θ to the vertical. The horizontal component of tension is zero because the rod is light. Therefore, the vertical component of tension must balance the weight of P:
T cosθ = mg
We can also write:
T sinθ = mv²/r
where r is the radius of the circle. At the lowest point C, θ = 90° and cosθ = 0, so we have:
T sin90° = mv²/r
T = mv²/r
Substituting this into the first equation:
mv²/r cosθ = mg
v² = gr cosθ
Since the angle between OP and the vertical is θ, we have:cosθ = cos(90° - θ) = sinθ
Substituting this into the previous equation:
v² = gr sinθ = gl
Therefore, u = √gl.
b) When OP makes an angle θ with the vertical, the tension in the rod is:
T = 2mg cosθ
Using the same approach as in part a), we have:
T sinθ = mv²/r
Substituting for T:
2mg cosθ sinθ = mv²/r
2mg sin2θ = mv²/r
v² = 2gr sin2θ
Since sin2θ is maximum when 2θ = 90° or θ = 45°, the greatest value of v² is:
v² = 2gr
When the tension in the rod is mg, we have:
mg sinθ = mv²/r
sinθ = v²/gr
Substituting for v²:
sinθ = 2sin2θ
2sin2θ - sinθ = 0
sinθ(2sinθ - 1) = 0
Therefore, sinθ = 0 or sinθ = 1/2.
If sinθ = 0, then θ = 0° or θ = 180°, which means the particle is at the top or bottom of the circle and is not moving.
If sinθ = 1/2, then θ = 30° or θ = 150°. Substituting into the expression for v²:
v² = 2gr sin2θ = gl
Therefore, when the tension in the rod is mg, the particle is moving with speed √gl when θ = 30° or θ = 150°.
Thus, the greatest value of 0 is 2gr and the value of θ when the tension in the rod is mg and the particle is moving with speed √gl is θ = 30° or θ = 150°.
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CAN SOMEONE HELP WITH THIS QUESTION?
The box with the most volume has 20 centimetres of side length and 20 centimetres of height. The box has a volume of: 8000 cubic centimetres.
We need to employ optimization strategies to determine the box with the highest feasible volume, which has a square base and an open top. Call the box's height h and the square base's side length x, respectively.
V = [tex]x^(2h)[/tex] gives the volume of the box.
The box's overall surface area will be 1600 square centimetres since the material used to create it has a surface area of 1600 square centimetres.
The box's surface area is made up of the areas of its four sides and base (x2) (4xh). We thus have:
[tex]x^2[/tex]+ 4xh = 1600
The volume of the box, which is given by V = [tex]x^(2h)[/tex], is what we wish to maximise.
We can determine h in terms of x using the equation above:
h = (1600 - [tex]x^2[/tex]) / (4x) (4x)
This result is obtained by replacing h with this equation in the volume formula:
V = [tex]x^2[/tex](1600 - [tex]x^2[/tex]) / (4x) (4x)
If we simplify this expression, we get:
V = 400x - [tex]0.25x^3[/tex]
Now, in order to determine the crucial places, we can take the derivative of V with respect to x and put it equal to zero:
[tex]dV/dx = 400 - 0.75x^2 = 0[/tex]
As a result of solving this equation for x,
x = 20
The result of replacing h in the equation with x = 20 is:
h = (1600 - 400) / (4 * 20) = 20
As a result, the box with the maximum volume has 20 centimetres of height and 20 centimetres of side length. The box has a volume of:
8000 cubic centimetres are equal to V = 202 * 20.
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Helppp
Use trigonometry to find EF to the nearest tenth.D = 36 , DE = 16
Considering the figure, the length of EF is solved to be 22.0
How to find EFThe length EF of the right triangle is solved using trigonometry as follows
Considering the figure and the giving sides we use the trigonometric tangent by using the formula
tan (angle D) = DE / EF
plugging in the values
tan 36 = 16 / EF
EF = 16 / tan 36
EF = 22.022
EF = 22.0 (to the nearest tenth)
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What is the ratio of the number of pairs of Jeanine to the cost of jeans?
The Ratio of the number of pairs of Jeanine to the cost of jeans helps us understand how many pairs of jeans Jeanine can purchase for a given amount of money.
To find the ratio of the number of pairs of Jeanine to the cost of jeans, we need to first determine how many pairs of jeans Jeanine has and how much she paid for them. Let's assume Jeanine has 10 pairs of jeans and she paid $50 for each pair. Therefore, the total cost of Jeanine's jeans is $500.
Now we can calculate the ratio by dividing the number of pairs of jeans by the cost of jeans. So, the ratio of the number of pairs of Jeanine to the cost of jeans is:
10 pairs of jeans / $500 = 1/50
This means that for every $50 Jeanine spends on jeans, she gets one pair. Alternatively, we could also express the ratio as a decimal or percentage. In this case, the ratio as a decimal would be 0.02 or 2%, indicating that Jeanine spends 2% of the cost of one pair of jeans for each pair she owns.
Overall, the ratio of the number of pairs of Jeanine to the cost of jeans helps us understand how many pairs of jeans Jeanine can purchase for a given amount of money.
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0.4(2x+ 1/2 )=3[0.2x+(−2)]−4
find the following in Qiv sin(A)/(2)
For sin the expression [tex]Qiv sin(A)/(2)[/tex] can be simplified using trigonometric identities.
Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables within their domains. These identities are useful in simplifying trigonometric expressions and solving trigonometric equations. Some common identities include the Pythagorean identity, which relates the trigonometric functions of sine, cosine, and tangent, and the double-angle identities, which express trigonometric functions of twice the angle in terms of functions of the original angle.
First, we can recognize that Qiv is the same as 1/4 of the unit circle or 90 degrees. Therefore, [tex]Qiv sin(A)[/tex] can be simplified to sin(A + 90).
Using the identity [tex]sin(A + B) = sin(A)cos(B) + cos(A)sin(B)[/tex], we can rewrite [tex]sin(A + 90)[/tex] as:
[tex]sin(A)cos(90) + cos(A)sin(90)[/tex]
Since [tex]cos(90) = 0 \\sin(90) = 1[/tex], this:
[tex]sin(A) * 0 + cos(A) * 1[/tex]
Which simplifies to just cos(A).
Therefore, the expression [tex]Qiv sin(A)/(2)[/tex] is equivalent to cos(A)/2.
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find the area of the sector
(70 points)
will mark brainly
Answer:
the area of the sector in grey is 100.48 square feet.
Step-by-step explanation:
Area of a circle = radius × radius × π
(π ≌ 3.14)
So
the area of the circle in the picture = 16 × 16 × π = 803.84
As the angle in the grey sector is 45°, so the proportion of the grey sector in the circle is
45°/360° = 1/8
Hence why
the area of the grey sector is 1/8 of the area of the circle, which is
803.84 × 1/8 = 100.48
Question 2 (1 point) A Point A is located at (-1,4). Where would point A' be located after a dilation of 2 centered at the origin? N
Answer:
Point A would be located at (-2,8)
Step-by-step explanation:
After a dilation of factor 2 centered at the origin (0,0), Point A' would be located at:
A' = (2 * -1, 2 * 4) = (-2, 8)
The effect of the dilation is to stretch the original point A by a factor of 2 along both the x and y directions. This essentially doubles the distances from the origin to the point A, creating the point A'.