The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)
Answers
The strength of the beam is proportional to the width and the square of the depth, so we can express it as Strength = k * width * depth²
where k is the proportionality constant.
In the given figures, the beam is cut from a cylindrical log of diameter d = 24 cm, which means the maximum width and depth of the beam are limited by this diameter. We can see from the figures that the width and depth of the beam change depending on the angle at which it is cut from the log.
In Figure 1, the width and depth of the beam are equal, so we can express the strength of the beam as:
Strength = k * width * depth² = k * x² * (d/2 - x)²
where x is the width and depth of the beam.
In Figure 2, the width and depth of the beam are not equal, so we need to express them separately. Let w be the width and d be the depth, then we can express the strength of the beam as:
Strength = k * width * depth² = k * w * d² = k * ((d/2)sinθ)² * ((d/2)cosθ)²
where θ is the angle at which the beam is cut from the log.
In Figure 3, the width and depth of the beam also vary with the angle θ. We can express the width and depth as follows:
w = d sinθ
d = (d/2)cosθ
Then we can express the strength of the beam as:
Strength = k * width * depth² = k * (d sinθ) * [(d/2)cosθ]²
Therefore, depending on the angle at which the beam is cut from the log, the strength of the beam can be expressed using different equations, but in all cases, the strength is proportional to the width and the square of the depth, with a proportionality constant k.
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Complete question is:
The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)
Related Questions
The decimal -2.97 is the solution to which subtraction problem?
Answers
The decimal - 2. 97 is the solution to the subtraction problem of D. - 6. 1 - ( - 3. 13 ).
How to find the solution ?When subtracting decimal numbers, the effective method is to align their decimal points and begin removing each corresponding digit from one another. You may extend any decimals with fewer digits by appending zeros on the right-hand side as required for parity.
= - 6. 1 - ( -3. 13 )
= - 6. 1 + 3. 13
= - 2. 97
The decimal 2.97 is the solution to the subtraction problem - 6. 61 - (- 3. 13).
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ANGELINA
Mr. Black's class sold highlighters and pens to raise money. Every highlighter cost the same amount. Every pen
cost the same amount.
. On day 1, the class made $120 and sold 80 highlighters and 20 pens.
. On day 2, the class made $200 and sold 120 highlighters and 40 pens.
What was the cost per highlighter?
$
1
4
7
0
2
5
8
per highlighter
3
6
9
Answers
The cost per highlighter is approximately $1.
To find the cost per highlighter, we can use a system of equations. Let's call the cost per highlighter "h" and the cost per pen "p". Then, we can set up two equations based on the information given;
80h + 20p = 120 (day 1)
120h + 40p = 200 (day 2)
We can simplify these equations by dividing both sides by 20;
4h + p = 6 (day 1)
6h + 2p = 10 (day 2)
Now we can use the first equation to solve for p in terms of h;
p = 6 - 4h
Substitute this expression for p into second equation;
6h + 2(6 - 4h) = 10
Simplify and solve for h;
6h + 12 - 8h = 10
-2h = -2
h = 1
Therefore, the cost per highlighter is $1.
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if you have the answer please reply im having trouble need the steps.
Answers
Over a given period of time, Seth sold more water bottles than Hayden.
To compare the number of water bottles sold by Seth and Hayden, we need to find out the equation for Seth's sales rate. Looking at the graph, we can see that Seth sold 10 bottles on day 1, 20 bottles on day 2, 30 bottles on day 3, and 40 bottles on day 4.
We can find the average daily sales rate for Seth by dividing the total bottles sold by the number of days:
Average daily sales rate for Seth = (10+20+30+40)/4 = 25
The equation given for Hayden's sales rate is y = 11x, where y represents the number of bottles sold and x represents the number of days. This equation shows that Hayden sells 11 bottles per day.
Comparing the two sales rates, we can see that Seth sold more water bottles. On average, Seth sold 25 bottles per day, while Hayden sold only 11 bottles per day. Therefore, over a given period of time, Seth sold more water bottles than Hayden.
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I need assistance please.
Your Assignment
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure A"B"C"D"E" using a series of two different transformations. They give two different answers.
Answer the questions to investigate ways to transform ABCDE.
1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this? (3 points)
2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E". (3 points)
3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not. (4 points)
Answers
Olivia could have used a combination of a rotation and a translation to move ABCDE onto A"B"C"D"E".
Angelica's transformed figure will not match A"B"C"D"E" because reflecting ABCDE over the y-axis will change the order of the letters in the figure.
No, Michael is not correct.
How to explain the transformationTranslating ABCDE diagonally by 8 units up and 10 units right will move each point in ABCDE the same distance horizontally and vertically, which will change the shape of the figure.
In order to match A"B"C"D"E", the transformation must preserve the order of the letters and the angles between the segments.
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Someone help i really need help with this
Answers
The percentage increase in the number of water bottles from February to April is 19%.
How to find the percentage increase?A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.
Therefore,
February: 4100 water bottlesMarch: 7% more water bottles than in FebruaryApril: 500 more water bottles than in marchTherefore,
Number of water bottles in march = 4100 + 7% of 4100
Number of water bottles in march =4100 + 7 / 100 × 4100
Number of water bottles in march = 4100 + 287
Number of water bottles in march = 4387
Hence,
Number of water bottles manufactured in April = 4387 + 500 = 4887
Therefore,
percentage increase from February to April = 4887 - 4100 / 4100 × 100
percentage increase from February to April = 787 / 4100 × 100
percentage increase from February to April = 78700 / 4100
percentage increase from February to April = 19.1951219512
percentage increase from February to April = 19%
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A local city government wants to display the ages of the city citizen. Would it be better to organize the data using a dot plot or a histogram, and why?
Answers
If local city government wants to display the ages of the city citizen, It would be better to organize the data using a histogram.
A histogram is a graph that shows the distribution of a set of continuous data. The ages of city citizens can be considered as continuous data, as there are many possible values for age within a certain range.
A dot plot, on the other hand, is a graph that shows the distribution of a set of discrete data. Discrete data are values that can only take on specific, isolated values, like shoe sizes or the number of siblings a person has.
A histogram would be more effective for displaying the distribution of the ages of city citizens because it can show the range of ages in a more continuous manner, and provide a more precise representation of the frequency of the different age groups.
A dot plot, on the other hand, would be less effective, as it could be difficult to represent every age value as a single dot, and the resulting graph may not provide a clear indication of the distribution of ages.
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The sum of two numbers is 998
The difference between them is 10
What are the two numbers?
Answers
Answer:
The two numbers are 494 and 504
Step-by-step explanation:
Let x = one of the numbers
Let y = the other number
x + y = 998
x - y = 10 or x = y + 10
Substitute y + 10 for x in the first equation and solve for y
x + y = 998
y + 10 + y = 998 Subtract 10 from both sides
y + y = 988 Combine like terms
2y = 988 Divide both sides by 2
y = 494
One of the numbers is 494.
x = y + 10 Substitute 494 for y
x = 494 + 10
x = 504
The other number is 504.
Check:
x + y = 998
504 + 494 = 998
998 = 998 checks
x - y = 10
504 - 494 = 10
10 = 10 checks
Helping in the name of Jesus.
Graph and solve y=1/2x-6 and y=1/2x+2
Answers
Answer:
No solution.
Step-by-step explanation:
To solve this problem, all you have to do is graph the lines and see where they intersect.
This is what you would do to solve a normal problem. However, these lines are parallel this means that the solution to these lines is no soultion
A yoga studio sells monthly memberships. The function f(x) = −x^2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.
Determine the zeros, and explain what these values mean in the context of the problem.
x = 6, x = 44; The zeros represent the number of monthly memberships that produces a maximum profit.
x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships that produces a maximum profit.
Answers
The zeros of the quadratic profit function are explained as:
x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made
How to find the zeros of a quadratic function?The quadratic function is given as:
f(x) = −x² + 50x − 264
The general form of expression of a quadratic function is:
f(x) = ax² + bx + c
The quadratic formula to find the zeros is:
x = [-b ± √(b² - 4ac)]/2a
Thus, we have the zeros as:
x = [-50 ± √((-50)² - 4(-1 * -264))]/2(-1)
x = 6 and x = 44
This represents number of monthly memberships where no profit is made.
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what is the solution to
-15x=90
Answers
Answer:
option c) x=-6
Step-by-step explanation:
-15x = 90
= x = 90/-15
= x = (-6)
i really don’t understand this so i would really appreciate help
Answers
Answer:
[tex]6\sqrt{2}+3\sqrt{10}[/tex]
Step-by-step explanation:
Use the Distributive Property. Remember that you can multiply the numbers under a square root whether or not they're the same. But you can ONLY add square roots when the square root part is the same.
[tex]\sqrt{3}(2\sqrt{6}+\sqrt{30})\\= \sqrt{3}(2\sqrt{6})+\sqrt{3}(\sqrt{30})\\=2\sqrt{18}+\sqrt{90}[/tex]
Simplify each square root part:
[tex]2\sqrt{18}+\sqrt{90}\\=2(3\sqrt{2})+3\sqrt{10}\\=6\sqrt{2}+3\sqrt{10}[/tex]
Since the square root parts are different, you cannot simplify any further.
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Answers
The most appropriate measure of variability to use in this case is the IQR (Interquartile Range) of 13.
How to determine which measure of variability should the charity use to accurately represent the dataThe reason for this is that the data appears to be skewed towards the higher values, with more donations in the higher range (from 40 to 59 dollars) and fewer in the lower range (from 10 to 39 dollars).
Using the range (which is the difference between the highest and lowest values) would not accurately represent the variability of the data, as it would be heavily influenced by the outliers. On the other hand, the IQR, which is the range of the middle 50% of the data, is a more robust measure of variability that is not influenced by outliers. Therefore, the IQR of 13 is the most appropriate measure of variability to use in this case.
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what could be the value of the point grafted only number line between 0.09 and 0.10
Answers
A list contains the names of six anthropology students, two sociology students, and four psychology students. If one name is selected at random to assist in the professor's new study, find the probability that the chosen student is
P(anthropology)=
Answers
The probability of selecting an anthropology student is the number of anthropology students divided by the total number of students:
P(anthropology) = 6/12 = 1/2
Therefore, the probability of selecting an anthropology student is 1/2 or 0.5, which can also be expressed as a percentage as 50%.
(PLEASE HELP! Im using a ton of points)
A new curved projection system for a small media room states the optimal viewing angle is
74° (m/ACB = 74°) when you sit 10 feet from the center of the TV (length of CD = 10 ft). The
depth of the curved screen is 2 feet (length of DE = 2 ft). Find the length of line segment AB, in feet, that corresponds to the width of the television. (Round your answer to the nearest foot)
(Thx for any help!)
Answers
The value of the length of line segment AB, in feet, that corresponds to the width of the television is,
⇒ 12 feet
We have to given that;
A new curved projection system for a small media room states the optimal viewing angle is 74° (m/ACB = 74°) when you sit 10 feet from the center of the TV (length of CD = 10 ft). The depth of the curved screen is 2 feet (length of DE = 2 ft).
Now, We can formulate;
CE = 10 - 2 = 8 feet
∠ACD = 74/2 = 37°
Hence, We can formulate;
tan 37° = AE / CE
0.75 = AE / 8
AE = 0.75 × 8
AE = 6
Hence, The value of the length of line segment AB, in feet, that corresponds to the width of the television is,
⇒ AB = 6 x 2
⇒ AB = 12 feet
Thus, The value of the length of line segment AB, in feet, that corresponds to the width of the television is,
⇒ 12 feet
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Write an inequality that matches the number line model. Then write
a situation that the inequality could represent.
-2.75 is greater than or equal to x
Answers
Answer:
x<=-2.75
Step-by-step explanation:
Express the following probability as a simplified fraction and as a decimal.
If one person is selected from the population described in the table, find the probability that the person
Answers
PLS HELP WILL GIVE BRAINLIEST
what will the coordinates be if Point A (-4,-5) of the trapezoid was reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction.
Answers
Answer:
If point A (-4,-5) of the trapezoid is reflected across the y-axis, the x-coordinate will change sign while the y-coordinate remains the same. This gives us the point A' (4, -5).
Next, if we shift the point A' by -6 units in the x-direction and 7 units in the y-direction, we get the new point A":
A" = (4 - 6, -5 + 7) = (-2, 2)
Therefore, the coordinates of point A after it is reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction are (-2, 2).
Step-by-step explanation:
Answer:
(-2, 2)
Step-by-step explanation:
I did the test
Hope this helps :)
Based on a survey of 100 households, a newspaper reports that the average number of vehicles per household is 1.8 with a margin of error of ±0.3. The population surveyed is 50,000 households.
How many vehicles are included in the margin of error? Enter your answer in the blank.
Answers
Answer:
Step-by-step explanation:
The margin of error is ±0.3. This means that the actual average number of vehicles per household in the population is expected to be between 1.5 (1.8 - 0.3) and 2.1 (1.8 + 0.3).
To calculate the range of the margin of error in terms of the number of vehicles, we can multiply the margin of error by the square root of the sample size (100) to get:
0.3 * sqrt(100) = 3
So the margin of error in terms of the number of vehicles is ±3.
Therefore, the number of vehicles included in the margin of error is between 1.5 * 50,000 = 75,000 and 2.1 * 50,000 = 105,000.
So the range of the margin of error in terms of the number of vehicles is 30,000, and the number of vehicles included in the margin of error is 30,000.
Part A: Is it possible to make a triangle that is both equilateral triangle and a right triangle? Explain
Part B: Is it possible to draw a triangle with side lengths of 15, 15 and 20? Explain.
Answers
Answer:
A. No, it is not possible. An equilateral triangle is also an equiangular triangle, meaning all of its angles measure 60°.
B. Yes, it is possible. By the Triangle Inequality Theorem:
15 + 15 > 20, and 20 + 15 > 15
Someone help i really need help with this
Answers
Step-by-step explanation:
we just need to find out how many percentage of the daily goal each day, so let's assume that $50 is 100% of the daily goal.
Find the areas of the trapezoids.
Answers
Answer:
Area = ½* height(a+b)
Where;
a=4units
b=8units
h=6units
Therefore Area= ½*6(4+8)
= ½*6*12
=36sq.un
Answer:
24sq²
Step-by-step explanation:
Area = ( b1 + b2) x h
---------------------
2
Area = (8 + 4) x 6
---------------------
2
Area = (12) x 6
---------------------
2
A = 72/2
A = 36
A = 1/2 * b * h
A = (1/2) * 4 * 6
A = (1/2) * 24
A = 12
36 - 12 = 24sq²
I hope this helps!
Find the principal needed now to get the given amount; that is, find the present value. To get $4000 after 2 1/4 years at 9% compounded daily The present value of $4000 is $? (Round to the nearest cent as needed.)
Answers
Step-by-step explanation:
Compounding formula
FV = PV ( 1 + i )^n FV = Future value (4000) PV = present value
i = decimal interest per PERIOD = .09/365
n = periods = 2 1/4 yrs * 365 days/yr = 821.25 periods
4000 = PV ( 1 + .09/365)^821.25
Solve for PV = $ 3266.83
Which of the points plotted is farther away from (−7, 8), and what is the distance?
Answers
Answer:
(10, -10)
Step-by-step explanation:
This are the farest the graph can go unless you want (100,-100)
Change the values from negative to positive and positive to negative to get the most farest results
Answer: D
Step-by-step explanation:
I graphed so you can see. Count how far each are away.
(5,8) is 12 away
(-7,-5) is 13 away
So you answer is D
Or
You can also think of it as, for, (5, 8) only the x changed so you only moved in the x direction. subtract the numbers 5-(-7)=12
For (-7,-5) you only moved in the y direction, so subtract those 8-(-5)=13
find - 4 - 2 1/2 expression on the number line by drawing an arrow
Answers
The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.
In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. Expressions can be simple or complex and are used to represent mathematical relationships and operations.
How to determine the expression?To find -4 - 2 1/2 expression on the number line by drawing an arrow, we need to start at -4 and then move left by 2 1/2 units.
To do this, we can draw an arrow starting at -4 and then mark off 2 1/2 units to the left. One way to represent 2 1/2 units is to divide the space between -4 and -5 into two equal parts, and then mark off one of those parts.
The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.
Here's an example of what the arrow would look like:
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Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2600. What was the rate charged per hour by each mechanic if the sum of the two rates was $155
per hour?
Answers
the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.
what is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,
In the given question,
Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.
From the problem, we know that:
The first mechanic worked for 20 hours, so he charged 20x dollars.
The second mechanic worked for 15 hours, so he charged 15y dollars.
Together, they charged a total of $2600, so we have:
20x + 15y = 2600
The sum of the two rates was $155 per hour, so we have:
x + y = 155
We can use these two equations to solve for x and y. First, we can rewrite the second equation as:
y = 155 - x
Then, we can substitute this expression for y into the first equation:
20x + 15(155 - x) = 2600
Simplifying and solving for x, we get:
20x + 2325 - 15x = 2600
5x = 275
x = 55
Now that we know x, we can use the second equation to find y:
y = 155 - x = 155 - 55 = 100
Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.
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I need help with this AP Stats question.
Answers
The probability that the team wins the debate is 0.6475
How to solve the probabilityP(win) = P(win | S)P(S) + P(win | J)P(J) + P(win | R)P(R)
= (0.25)(0.2) + (0.6)(0.35) + (0.85)(0.45)
= 0.6475
Therefore, the probability that the team wins the debate is 0.6475.
In order to simulate the probability that a Sophomore is never selected to give the closing argument in the next 5 debates, we can use the following steps:
Create a table of random digits with enough rows and columns to simulate the 5 debates. Each row represents a debate and each column represents a team member.
Assign the digits 0, 1, and 2 to represent the events that a sophomore, junior, and senior gives the closing argument, respectively.
Starting from the first row and first column, read the digits from the table and determine which team member gives the closing argument for the first debate.
If a sophomore is selected, record a 0 for that debate. Otherwise, record a 1.
Repeat steps 3 and 4 for the remaining debates, filling in the table as you go.
Calculate the proportion of simulations where a Sophomore is never selected to give the closing argument in the next 5 debates.
Repeat steps 1-6 many times (e.g., 10,000 times) to get a more accurate estimate of the probability.
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Find the distance from G to S.
Answers
Answer:
i think its b sorry if it's wrong
Step-by-step explanation:
Solve for x. −−9x+5<17 AND13x+25<−1
Answers
Answer: x<4/3
Step-by-step explanation: 17-5=12/9
box of chocolates contains five milk chocolates, five dark chocolates and five white chocolates. You randomly select and eat three chocolates. What is the probability that the first piece is a milk chocolate, the second is a dark chocolate and the third is a white chocolate?
Answers
Answer: 25/546 chance
Step-by-step explanation:
total is 15 chocolates.
Five are milk, so chance of getting milk is 1/3. second is dark, so 5/14 chance. Then white, so 5/13 chance
1/3*5/14*5/13=25/546