Determine the area of the largest rectangle that can be inscribed in a circle of radius 4 cm.
3. (5 points) If R feet is the range of a projectile, then R(θ) = v^2sin(2θ)/θ 0≤θ phi/2, where v ft/s is the initial velocity, g ft/sec² is the acceleration due to gravity and θ is the radian measure of the angle of projectile. Find the value of θ that makes the range a maximum.
Answers
The area of the largest rectangle that can be inscribed in a circle of radius 4 cm is 32 square centimeters.
To find the area of the largest rectangle that can be inscribed in a circle, we need to determine the dimensions of the rectangle. In this case, the rectangle's diagonal will be the diameter of the circle, which is 2 times the radius (8 cm).
Let's assume the length of the rectangle is L and the width is W. Since the rectangle is inscribed in the circle, its diagonal (8 cm) will be the hypotenuse of a right triangle formed by the length, width, and diagonal.
Using the Pythagorean theorem, we have:
L^2 + W^2 = 8^2
L^2 + W^2 = 64
To maximize the area of the rectangle, we need to maximize L and W. However, since L and W are related by the equation above, we can solve for one variable in terms of the other and substitute it into the area formula.
Let's solve for L in terms of W:
L^2 = 64 - W^2
L = √(64 - W^2)
The area of the rectangle (A) is given by A = L * W. Substituting the expression for L, we have:
A = √(64 - W^2) * W
To find the maximum area, we can differentiate the area formula with respect to W, set it equal to zero, and solve for W. However, for simplicity, we can recognize that the maximum area occurs when the rectangle is a square (L = W). Therefore, to maximize the area, we need to make the rectangle a square.
Since the diameter of the circle is 8 cm, the side length of the square (L = W) will be 8 cm divided by √2 (the diagonal of a square is √2 times the side length).
So, the side length of the square is 8 cm / √2 = 8√2 / 2 = 4√2 cm.
The area of the square (and the largest rectangle) is then (4√2 cm)^2 = 32 square centimeters.
To find the value of θ that makes the range (R) of a projectile a maximum, we can start by understanding the given equation: R(θ) = v^2sin(2θ)/(gθ), where R represents the range, v is the initial velocity in feet per second, g is the acceleration due to gravity in feet per second squared, and θ is the radian measure of the angle of the projectile.
To find the maximum range, we need to find the value of θ that maximizes R. We can do this by finding the critical points of the function R(θ) and determining whether they correspond to a maximum or minimum.
Differentiating R(θ) with respect to θ, we get:
dR(θ)/dθ = (2v^2cos(2θ)/(gθ)) - (v^2sin(2θ)/(gθ^2))
Setting this derivative equal to zero and solving for θ will give us the critical points. However, the algebraic manipulations required to solve this equation analytically can be quite involved.
Alternatively, we can use numerical methods or optimization techniques to find the value of θ that maximizes R(θ). These methods involve iteratively refining an initial estimate of the maximum until a satisfactory solution is obtained. Numerical optimization algorithms like gradient descent or Newton's method can be applied to solve this problem.
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Related Questions
Identify the sampling technique used for the following study. 00:24:26 For budget purposes, a financial advisor needs to know the average length of tenure of instructors at their college. Answer 2 Points i Keypad > Keyboard Shortcuts Next O Census Simple Random Sampling Stratified Sampling O Cluster Sampling Systematic Sampling O Convenience Sampling
Answers
The correct answer is option c. Stratified Sampling is a type of sampling method used when the population is divided into homogeneous subgroups or strata.
With this sampling method, the population is segmented into a number of smaller groups depending on traits like gender, age, or location.
The financial advisor has to know the typical tenure of instructors at their college for the specified study.
As a result, strata can be created within the population according to how long the instructors have been teaching, and samples can be drawn from each of the strata.
In this manner, it will be possible to calculate the sample data's correct estimation of the average tenure of the college's instructors.
Complete Question:
Identify the sampling technique used for the following study
For budget purposes, a financial advisor needs to know the average length of tenure of instructors at their college.
a. Census Simple
b. Random Sampling
c. Stratified Sampling
d. Cluster Sampling
e. Systematic Sampling
f. Convenience Sampling
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BRAINLIEST IF YOU CAN ANSWER!!
Answers
The Area of the given figure is 22 unit square.
What is Area?The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.
Given:
We have given the figure.
Then, we will count the boxes the area will be
= 2 x (1/2 + 2/3 + 1/3 + 1/2 + 1 + 2/3 + 1 + 1 + 1 + 1 + 1 + 1/2 + 1/2 + 1/3)
= 2 x (4/2 + 6/3 + 6)
= 2 x (2 + 3 + 6)
= 2 x (11)
= 22 unit square.
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Answer:
the answer is b
Step-by-step explanation:
Help me pls. Brainy reward.
Answers
Increasing the sample size by a factor of 4 causes what kind of change to the distribution of sample means?
a. Decreases the standard error of the sample mean by a factor of 2
b. Decreases the standard error of the sample mean by a factor of 4
c. Decreases the mean of the sample mean by a factor of 4
d. Decreases the mean of the sample mean by a factor of 2
Answers
Increasing the sample size by a factor of 4 b) decreases the standard error of the sample mean by a factor of 2
The standard error of the sample mean is calculated as the standard deviation of the population divided by the square root of the sample size. When the sample size is increased by a factor of 4, the denominator of the equation (i.e., the square root of the sample size) becomes twice as large.
This causes the standard error to decrease by a factor of 2 (i.e., the standard error is halved). Therefore, option b is the correct answer. The mean of the sample mean is not affected by the sample size and remains the same.
Option c and d are incorrect. Option a is also incorrect as increasing the sample size actually decreases the standard error, not increases it.
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Write each polynomial in stndard form .What is the name of the polynomial based on its degree and number of terms a.3+5x-4x^2 ; b.8x+x+5+x^3
Answers
Answer:
a) 2nd degree Trinomial
b) 3rd degree Trinomial
Step-by-step explanation:
Write each polynomial in stndard form .What is the name of the polynomial based on its degree and number of terms
a.3+5x-4x^2
In standard form: -4x² + 5x + 3
Number of terms : 3
Degree of the polynomial : 2nd
Name of the polynomial : 2nd degree Trinomial
b.8x+x+5+x^3
x³ + 8x + x + 5
In standard form: x³ + 9x + 5
Number of terms : 3
Degree of the polynomial : 3rd
Name of the polynomial : 3rd degree Trinomial
The measure of A is 75°, and the measure of B is 105°. What is the relationship of angles A and B?
Answers
Answer:
Supplementary Angles
Step-by-step explanation:
Its what they are, 2 angles that add up to 180°
Answer:
They are supplementary angles.
Step-by-step explanation:
Supplementary angles are two angles that add up to 180°
105+75=180
someone please help!!
Answers
Answer: 1.distributive property, 2.subtraction property of equality, 3. i dont know 4. division property of equality and 5. i dont know
Step-by-step explanation:
what plus 4726 equals 5064?
Answers
Answer:
338
Step-by-step explanation:
B/c if you subtract 4726 from 5064 it would get you 338.
Hope this helps!
Answer:338
Step-by-step explanation: 5064 - 4726 = 338
4726 + 338 = 5064
Jennifer installs solar panels. Today it takes her 8
hours to install 2 solar panels. She plans to install
solar panels for 40 hours next week.
Answers
10 solar panels according to me is the answer
Answer: 10
Step-by-step explanation:
40 hours/8 hours = 5 hours
5 hours *2 solar panels = 10 solar panels
Since it takes her 8 hours to install 2 solar panels, we need to multiply 5 with 2.
determine whether the set s is linearly independent or linearly dependent.s = {(−2, 2, 4), (1, 9, −2), (2, 3, −3)}
Answers
To determine whether the set S is linearly independent or linearly dependent.The set is linearly independent. This is because the only way to make a linear combination of vectors equal to the zero vector is to have all the coefficients equal to zero.
A linear combination of vectors is the sum of a scalar multiple of each vector in the set. We must check if the equation a(-2,2,4) + b(1,9,-2) + c(2,3,-3) = (0,0,0) has only the trivial solution, i.e., a=b=c=0. This gives us the system of equations,-2a + b + 2c = 01a + 9b + 3c = 02a - 2b - 3c = 0We can solve the system of equations by using Gauss-Jordan elimination. The augmented matrix for the system is:[-2 1 2 0][1 9 3 0][2 -2 -3 0]Let's use elementary row operations to simplify the matrix.
We can swap the first and second rows since the first element in the second row is 1.[1 9 3 0][-2 1 2 0][2 -2 -3 0]We can then add twice the first row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][-2 1 2 0][0 16 3 0]We can then add nine times the first row to the second row to eliminate the leading coefficient in the second row.[1 9 3 0][0 17 15 0][0 16 3 0]We can then add -16/17 times the second row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][0 17 15 0][0 0 -117/17 0]We see that the only solution is a=0, b=0, and c=0. Therefore, the set S is linearly independent.
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Mean temperature: 78°
Standard deviation: 5°
Washington, DC
July 4: 1952 - 2011
Average Daily Temperature
Check all of the temperatures that are within one
standard deviation of the mean
o 72°
74°
799
84
Number of Years
C) ONO
DONE
Average Temperature
Answers
Answer:
74 and 79
Step-by-step explanation:
one standard deviation= 5°
range of one standard deviation: (78-5) to (78+5)
73° to 83°
Find the measures of the interior angles.
Answers
B = 88°
C = 44°
given this information, in order to use her 4 hours of time spent studying to get the highest possible test score, how many hours should she have spent solving multiple choice problems, and how many hours should she have spent reviewing lecture notes? 0 hours working on problems, 4 hours reading 2 hours working on problems, 2 hours reading 3 hours working on problems, 1 hour reading 4 hours working on problems, 0 hours reading
Answers
The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.
From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.
The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.
So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.
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Does (1,7),(1,6),(1,5),(1,4),(1,3) represent a function?
Answers
Answer:
No
Step-by-step explanation:
2,5,8,...
Find the 41st term.
Answers
Answer:
Step-by-step explanation:
hello :
this is the arithmetic -sequence because : 8-5=5-5=3 (comon dif)
An =A1+(n-1)r calculate......... (A1=2 and r=3 and n=41) continu...
Answer:
122
Step-by-step explanation:
!!!PLEASE ANSWER VERY QUICKLY I AM TIMED!!!
Suppose that 14 inches of wire costs 70 cents. At the same rate, how much (in cents) will 37 inches of wire cost?
Answers
Answer:
Step-by-step explanation:
2590
37x5=185
(Pls mark brainliest I’m trying to get next rank :)
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’, what will be the coordinate of D’?
Answers
According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)
Quadrilateral
Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.
Here we need to find the coordinate of D'.
In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.
While we looking into the graph, we have identify the point of
A (0,0), B(-4, 3), C(1,5) and D(2,3)
Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).
According to this rule, the new coordinates are written as,
A(0,0) = A'(0,0)
B'(-4,3) = B'(-3,-4)
C(1,5) = C'(5, -1)
D(2,3) = D' (3, -2)
Therefore, the new coordinate of D' is (3, -2).
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What is the length for both questions???
Answers
Answer:
1). 5.2 cm
2). 8.3 cm
step by step explanation
Answer:
5.4 and 8.6
Step-by-step explanation:
This is the right answer
A company’s profit is described by the equation P ( x ) = − 5 x 2 300 x 15 , 000 , where x is the price in dollars that the company charges for its product. What should the company charge for the product to generate the maximum profit?.
Answers
the company should charge a price of $30 for its product to generate the maximum profit.To find the price that will generate the maximum profit, we need to find the vertex of the quadratic function P(x) = -5x^2 + 300x - 15,000.
The vertex of a quadratic function in the form ax^2 + bx + c is given by the x-coordinate of the vertex, which is -b/2a. In this case, a = -5 and b = 300.
x = -b/2a = -300 / (2 * -5) = 300 / 10 = 30.
Therefore, the company should charge a price of $30 for its product to generate the maximum profit.
It's worth noting that the profit equation provided is a simplified model and may not accurately represent the real-world dynamics of the company's profit. Additionally, other factors such as demand, competition, and production costs should also be considered in determining the optimal price for maximizing profit.
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A flag pole is 20 ft high and cast a shadow of 5 ft. What is the distance from the top of the pole to the end of the shadow?
Answers
Answer:
100 ft high
Step-by-step explanation:
you multiply
Distance from the top of the pole to the end of the shadow is 20.62 ft.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Height of pole = 20ft
Length of the shadow = 5ft
Let distance from the top of the pole to the end of the shadow be x
then by Pythagoras theorem
Hypotenuse² = Base² + Perpendicular²
x² = 5² + 20²
x² = 25 + 400
x = √425
x = 20.62 ft
Hence, 20.62 feet is distance from the top of the pole to the end of shadow.
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Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5). Mark this and return
Answers
Answer:
(a) A two column table with five rows. ... The second column, y, has the entries, 2, 2, 2, 2
Step-by-step explanation:
You want to know which table shows a relation with zero slope.
Zero slopeWhen a graph has zero slope, it is a horizontal line. Every y-value is the same.
The table demonstrating zero slope will have all y-values the same:
The second column, y, has the entries, 2, 2, 2, 2
move 3 units and 1 units from the origin
Answers
Answer:
It depends on which why you are moving so let's say you have to move the 3 units to the right and 1 up, that would be the answer. I can't really give you the exact answer because you didn't say where they are supposed to go.
When we divide 1800 birr to three brothers in the ratio 2:3:1, what is the smallest share?
Answers
Answer:
300
Step-by-step explanation:
2+3+1=6
1800=6 parts
1 part=1800/6=300
The smallest share among the three brothers is 300 birrs.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, we divide 1800 birrs to three brothers in the ratio 2:3:1,
Let the amount they hold be 2x, 3x and x
Therefore, 2x+3x+x = 1800
6x = 1800
x = 300
Hence, The smallest share among the three brothers is 300 birrs.
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In computing the "pth" percentile if the index "i" is an integer the "pth" percentile is the
a. data value in position "i"
b. data value in position "i" + 1
c. average of data values in position "i" and "i" + 1
Answers
The index "i" is an integer, then the "pth" percentile is simply the data value in position "i".
How the answer depends on the specific definition?The answer depends on the specific definition used for computing percentiles. However, the most common convention is to use linear interpolation, in which the "pth" percentile is the weighted average of the data values in positions "i" and "i+1", where "i" is the integer part of the index of the "pth" percentile, with weights given by the fractional part of the index. In other words, if "d(i)" and "d(i+1)" are the data values in positions "i" and "i+1", respectively, and "f" is the fractional part of the index, then the "pth" percentile is given by:
(1-f) * d(i) + f * d(i+1)
If the index "i" is an integer, then the "pth" percentile is simply the data value in position "i".
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Solve each system by substitution. Check your answers.
4x+2y=7 , y = 5x
Answers
By substitution, the solution of the system of equations, 4x + 2y = 7 and y = 5x, is (1/2 , 5/2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
4x + 2y = 7 (equation 1)
y = 5x (equation 2)
Since the second equation is already expressed in y in terms of x, substitute the second equation to the first equation.
4x + 2y = 7 (equation 1)
4x + 2(5x) = 7
4x + 10x = 7
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
4x + 10x = 7
14x = 7
x = 1/2
Substitute the value of x in the second equation and solve for y.
y = 5x
y = 5(1/2)
y = 5/2
Hence, the solution of the given system of equations is (1/2 , 5/2).
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The sum of numbers is 28. the difference of two numbers is -2. find the numbers
Answers
Answer:
x=13 and y=15
Step-by-step explanation:
Let the 2 numbers be x and y
ATQ,
x+y = 28 ------ eqn.1
x-y=-2 -------- eqn.2
Adding both the equations:
x+y=28
+x-y=-2
_______
2x = 26
Therefore x=13
Now substituting the value of x in eqn. 1
x+y=28
13+y=28
Therefore y=28-13
=15
You are considering purchasing a consol that promises annual payments of $4. a. If the current interest rate is 3 percent, what is the price of the consol? Instructions: Round your answer to the nearest penny (2 decimal places). The price of the consol is $ b. You are concerned that the interest rate may rise to 4 percent. Compute the percentage change in the price of the consol and the percentage change in the interest rate. Compare them. Instructions: Round your answer for dollar amounts to the nearest penny (2 decimal places ) and answers for percentages to the nearest tenth (1 decimal place) The new price of the consol would be $ The price of the consol falls by 7% and the interest rises by 7% c. Your investment horizon is one year. You purchase the consol when the interest rate is 5 percent and sell it a year later, following a rise in the interest rate to 6 percent. What is your holding period return? Instructions: Round your answer to the nearest tenth (1 decimal place) Your holding period return is %
Answers
a. The price of the consol is approximately $133.33.
b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.
c. Your holding period return is approximately -49.99%.
a. The price of the consol can be calculated using the formula for the present value of a perpetuity:
Price = Annual Payment / Interest Rate
In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:
Price = $4 / 0.03 ≈ $133.33
Therefore, the price of the consol is approximately $133.33.
b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:
New Price = Annual Payment / New Interest Rate
Substituting the values, we get:
New Price = $4 / 0.04 = $100
The percentage change in the price of the consol can be calculated using the formula:
Percentage Change = (New Price - Old Price) / Old Price * 100
Substituting the values, we have:
Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%
The percentage change in the interest rate is simply the difference between the old and new interest rates:
Percentage Change in Interest Rate = (4% - 3%) = 1%
Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.
c. The holding period return can be calculated using the formula:
Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100
The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:
Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67
Substituting the values into the holding period return formula:
Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%
Therefore, the holding period return is approximately -49.99%.
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Please help not sure what to do
Answers
Answer:
3x12 theres 3 cirs and 6÷4 so 3x12
❗️5 points❗️
Find the slope of the line.
A. -4
B. -1/4
C. 4
D. 1/4
Answers
If you use the point (4,-3) and (0,-2) and count the boxes between them it’ll equal to four and since it’s pointing to the left the answer will be a negative.
EXPLAINTION:
FILL IN THE BLANK. The _______ method first quantizes the object space into a finite number of cells that form a _________ structure and then performs clustering on the ________ structure.
Answers
The grid-based method first quantizes the object space into a finite number of cells that form a grid structure and then performs clustering on the grid structure.
The grid-based methods are used in data mining and are based on a multi-resolution grid data structure. In the grid-based methods the space of instance is divided into a grid structure. Following the division, clustering techniques are employed using the cells of the grid as the base units instead of individual data points. The great advantage of grid-based clustering technique is its significant reduction of the computational complexity, especially for clustering very large data sets and improving the processing time.
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