Find the measures of the interior angles that maximize the area of an isosceles trapezoid
where the length of the non-parallel sides are each 4 inches and the length the shorter of
the two bases is 6 inches.
Answers
The internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units.
How to determine the maximum possible area of an isosceles trapezoid
Quadrilaterals are figures formed by four line segments and whose sum of internal angles equals 360°. By geometry we know that the area of a trapezoid is the average of the length of the two bases (B, b), in inches, multiplied by the height of the quadrilateral.
A = 0.5 · (B + b) · h (1)
By trigonometry the measure of the longer base and the height of the isosceles trapezoid are, respectively:
B = b + 2 · l · cos θ (2)
h = l · sin θ (3)
Where θ is an internal angle, in degrees.
By (2) and (3) in (1):
A = 0.5 · (2 · b + 2 · l · cos θ) · (l · sin θ)
A = (b + l · cos θ) · (l · sin θ)
A = b · l · sin θ + l² · sin θ · cos θ
A = b · l · sin θ + 0.5 · l² · sin 2θ (4)
If we know that b = 6 in and l = 4 in, then the area of the isosceles trapezoid is represented by the following function:
A = 24 · sin θ + 8 · sin 2θ (5)
Now we determine the angle associated to the maximum area by graphic approach.
According to this approach, the internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units. [tex]\blacksquare[/tex]
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Related Questions
PLEASE HELP PLEASE HELP
Answers
Answer:
Option D - Line P
Step-by-step explanation:
Look at the coordinates in the (x, y) column of Max's table and see which line has the same points.
What is the difference between 8x^3-2x^2+5x-7 and 5x^3-3x^2-2x+4?
Answers
Answer:
B. 3x³ - 5x² + 3x - 3
Step-by-step explanation:
8x³ - 2x² + 5x - 7 - 5x³ - 3x² - 2x + 4 <== combine like terms
3x³ - 5x² + 3x - 3
Hope this helps!
Evaluate the following integral or state that it diverges.
*integral 0 to 1 (ln x)do
Answers
Answer:
-1
Step-by-step explanation:
so firstly we solve by integrating by parts.
lnX × X - the integral of x/x
so the integral is Xln(X) - X
so the value should converge at -1
Help picture below problem 15
Answers
Answer:
x = 25°
Step-by-step explanation:
→ Remember key fact
Angles in triangle add up to 180°
→ Set up equation
34 + 121 + x = 180
→ Simplify
155 + x = 180
→ Minus 155 from both sides
x = 25°
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundred. Radius is 4 height is 10
Answers
167.47 unit^3
[tex]\bold{EXPLANATIONS:}[/tex]
A fruit company guarantees that 94% of the pineapples it ships will ripen within four days of delivery. Find the probability that at least 10 pineapples in a case of 12 are ripe within four days.
Answers
The probability that at least 10 pineapples in a case of 12 are ripe within four days as described in the task content is; 0.783
Probability of PercentageFrom the task content;
It follows that 94% of the pineapples shipped will ripen within four days of delivery.On this note, the probability for ripening of each apple is; 0.94.
Ultimately, the probability that at least 10 pineapples in a case of 12 are ripe within four days is therefore; 0.94 × 10/12 = 0.783.
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Find the interquartile range. 44, 75, 62, 41, 59, 60, 79, 44, 49
Answers
Answer:
24.5 is our interquartile range
Step-by-step explanation:
First, you need to order the data set from least to greatest:
41, 44, 44, 49, 59, 60, 62, 75, 79
We have a total of 9 numbers in the data set.
**Note: Our minimum is 41 and our maximum is 79, this is important**
Next, we need to find the median in order to get the numbers divided into groups to find quartiles 1 and 3 easily.
Our median is the middle number which is 59.
**If you have an even set, find the 2 numbers in the middle add them, then divide by 2.**
Our data set without the median:
Data set 1: 41, 44, 44, 49
Data set 2: 60, 62, 75, 79
Now find the median of data sets 1 and 2.
Data set 1: 44+44/2 -> 88/2 =44
Data set 2: 62+75/2 -> 137/2 = 68.5
Now that we have quartiles 1 and 3, we need to take 68.5 and subtract it by 44.
68.5 - 44 = 24.5
24.5 is our interquartile range
how to find the area of a triangle with a base of 4 1/2 and a height of 2 2/3
Answers
Answer:
6
Step-by-step explanation:
The formula for the area of a triangle is 1/2(bh).
4 1/2=9/2, 2 2/3= 8/3
9/2x8/3=72/6,
12. However, you still have to divide by two, which gets you 6
Answer:
6
Step-by-step explanation:
The formula for the area of a triangle is 1/2(bh).
4 1/2=9/2, 2 2/3= 8/3
9/2x8/3=72/6,
Please help!!!
(07.02)
What is the value of y in the equation 3y - 8 = 22?
07.3
8
O 10
O 14
Answers
Answer:
The answer is 10 dude.
Step-by-step explanation:
You add 8 on both sides to get 3y by itself then divide 3 on both sides and that's it. If you really need to isolate a variable go on a website called microsoft math solver.
You invest $5000, add 50 each month, at 7.9% for 11 years.
Answers
Answer:
???
Step-by-step explanation:
What is your filed called when you open it in Photoshop?
A. PDF
B. MP3
C. JPEG
D. Doc
Answers
Answer:
B. MP3 idek if its right im just doing the 5 step thing
Find the square root of 2937.44 by the arithmetic method
Answers
The square root of 2937.44 by the arithmetic method is 54.20.
What is the square root of the number?
The square root of a number can be described as the value derived when a number is divided into two equal halves. The square root of 64 is 8. This is because 8 multiplied by 8 is equal to 64. The sign used to represent square root is √.
√2937.44 = 54.20
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for a standard distribution, which of the following variables always equals 0?
Answers
Historians have commonly believed that paint used before the year 1500 did not contain copper. However, lab techniques have shown that copper is present in the paint of both the Mona Lisa painted by Leonardo da Vinci (1452-1519), a widely-renowned and timeless piece that is one of the most valuable pieces in the Louvre today, and in that of another painting known as the Sine Nomine, also from the same time period, whose painter is unknown—but not found in the paint of any other Renaissance painting analyzed. This is strong evidence that the Sine Nomine was painted by da Vinci, as well as evidence that the presence of copper in the paint of a recently resurfaced map by Fra Mauro, ostensibly from the year 1450, cannot be used as an argument against the map's authenticity.
The reasoning in the passage is vulnerable to criticism on the grounds that:
A) both the Sine Nomine and the Fra Mauro Map are objects that can be appreciated on their own merits whether or not the precise date of their creation or the identity of the person who made them is known
B) it is unreasonable to suppose that determination of the date and location of an art piece’s painting or drawing can be made solely on the basis of the presence or absence of a single element in the paint used in the document
C) the results of the analysis are interpreted as indicating that the use of copper as an ingredient in fifteenth-century paint both was, and was not, extremely restricted
D) the discovery of copper in the paint of the Fra Mauro Map must have occurred before copper was discovered in the paint of the Sine Nomine and Mona Lisa
E)if the technology that makes it possible to detect copper in paint has only recently become available, it is unlikely that cartographers or artists in the fifteenth century would know whether their paint contained copper or not
Answers
The reasoning in this text is vulnerable to criticism because works such as Sine Nomine and the map can be appreciated on their own (option A).
What is the reasoning behind this text?The author of this text explains copper has been found in the Mona Lisa painting by Da Vinci that dates back to 1450. This evidence is used to conclude a similar painting known as the Sine Nomine belongs to the same painting and that a similar map belongs to the same period.
What is the problem with this reasoning?The reasoning fails at considering each artwork is unique and can be appreciated on its own without jumping to conclusions about the period and author of them.
Learn more about reasoning in: https://brainly.com/question/11478756
need help really please someone
Answers
Answer:
5/6 x 1 = 5/6 2/3 x 2= 4/6. 5/6 is greater than
2/3
Step-by-step explanation:
find a common denominator then see which one has more value
(3x10^-4)(5x10^8) in scientific notation
Answers
Answer:
[tex]15 \times {10}^{4} [/tex]
Step-by-step explanation:
[tex](3 \times {10}^{ - 4} )(5 \times {10}^{8} ) \\ \\ = 3 \times 5 \times {10}^{8 - 4} \\ \\ = 15 \times {10}^{4} [/tex]
2.
one day Jada and her cousin line up on the end of a swimming pier on the edge of a lake . At the same time , they start swimming and biking in opposite directions how far apart will they be after 15 mins
Answers
In 15 minutes, Jada would have covered about 2.5 miles, while the cousin would have covered 0.625 miles.
What is speed?Speed is the ratio of distance to time.
For Jada:
Speed = 2 miles / 12 minutes = 0.167 miles per minute
For Jada cousin:
Speed = 1 mile / 24 min = 0.0417 miles per minute.
Hence, in 15 minutes:
Jada distance = 15 min * 0.167 miles per minute = 2.5 miles
Jada cousin distance = 15 min * 0.167 miles per minute = 0.625 miles
In 15 minutes, Jada would have covered about 2.5 miles, while the cousin would have covered 0.625 miles.
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The graph shows two lines, A and
How many solutions are there for the pair of equations for lines A and B? Explain your answer. (5 points)
Answers
Answer:
there muse be at least 2 solution because we need it to draw lines at exact direction
Answer:
1 solution
Step-by-step explanation:
A solution to a system of lines in a graph is their intersection point. On the graph shown, there is only 1 point at which the lines intersect, therefore, 1 solution.
MATH. Someone please answer this for me :) 50 points
Image attached
Answers
Answer:
A=0.51
B=0.73
C=0.41
D=A student taking algebra II is dependent on whether they prefer it and a student being in 10th grade is dependent on their age
Step-by-step explanation:
These answers are all in fractions btw
A)5/255+20/245+65/225+90/725=0.514267 which rounds to 0.51
B)100+65=165
165/225=0.73
C)100/245=0.41
Hope it helps !
Write an equation of the line that passes through (3, 1) and (0,10) .
y=
Answers
Answer:
Step-by-step explanation:
hello :
y = -3x+10
Which of the following is the main
reason people buy auto insurance?
A. They want to be covered in case their home starts on
fire.
B. It is not expensive and easily affordable.
C. It is required by law in any state in America.
D. It is very expensive and hard to finance.
Haven't learned this yet.
Answers
Explanation:
Most states (but not all) require liability insurance at minimum. This covers injury and property damage to the person you accidently hit. It likely does not cover you personally so you'd need other insurance for that.
States like Iowa, New Hampshire, and Ohio offer exemptions from insurance if you can show you are responsible with money. Meaning that if you have a steady income and are smart with money, then you likely would be able to pay off any future accident without needing insurance. Though the damages might get wildly expensive, so a liability policy isn't always a bad thing.
I NEED HELP ASAP
Solve.
4x + 2(3x – 9) = x
A.
x = –2
B.
x = 1.8
C.
x = 2
D.
x = 18
Answers
Answer:
x=2
Step-by-step explanation:
[tex]4x+2(3x-9)=x\\\\\implies 4x +6x - 18 -x =0\\\\\implies 9x = 18\\\\\implies x = \dfrac{18}9 = 2[/tex]
If the probability of receiving a message on the internet today is 8/9, what is the probability of not receiving a message?
[Give the answer as a fraction in simplest form.]
Answers
Answer:
The probability is 1/9
Step-by-step explanation:
1 - 8/9 = 1/9
the ratio of the sides of a certain triangle is 2:7:8 if the longest side of the triangle is 40cm how long are the other two sides
Answers
The length of the other two sides is 10 and 35 respectively.
What is a ratio?A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.
From the given information:
The sides of the triangle = 2:7:8The total sides of the triangle = 2+7+8 = 17We are being told that the longest side is the triangle is equal to 40.
i.e.
[tex]\mathbf{\to\dfrac{8}{17}\times x = 40}[/tex]
[tex]\mathbf{x = 40 \div \dfrac{8}{17}}[/tex]
[tex]\mathbf{x = 40 \times \dfrac{17}{8}}[/tex]
x = 85
Now for the other two sides 2 and 7, their length is as follows.
[tex]\mathbf{\dfrac{2}{17}\times 85 = 10}[/tex]
[tex]\mathbf{\dfrac{7}{17}\times 85 = 35}[/tex]
Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.
Learn more about ratios here:
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A basketball player averaged 20 points a game over the course of six games. His
scores in five of those games were 23, 18, 16, 24, and 27. How many points did he score in the sixth game?
Answers
Average Points= 20
No. of games = 6
Total points= 20×6=120
So, Sum of Score of five games= 23+18+16+24+27= 108
Therefore, Score in 6th game= 120-108= 12
Hope this helps[tex]\sf\large \green{\underbrace{\red{Answer⋆}}}:[/tex]
To find :-
The sixth score of the game
Given :-
All five scores = 23, 18, 16, 24, and 27
The average of all six score = 20
Solution :-
We will use the average formula to find the sixth score.
[tex]average = \frac{total \: of \: all \: scores}{number \: of \: scores} [/tex]
And let the sixth score be x.
[tex]20 = \frac{23 + 18 + 16 + 24 + 27 + x}{6} [/tex]
Now we will cross multiply, the 6 which on L.H.S will come to R.H.S and multiply with 20.
[tex]20 \times 6 = 23 + 18 + 16 + 24 + 27 + x \\ 120 = 108 + x \\ 120 - 108 = x \\ 12 = x[/tex]
Result :-
The sixth score by the baseball player is 12.
From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?
Answers
=============================================================
Reason:
There are 20 ways to pick the first person, 19 for the next, and 18 for the last. We count down by one each time we fill up a slot since we cannot reselect any person more than once.
If order mattered, then we'd have 20*19*18 = 6840 permutations.
However, order does not matter because no member has a special seat or role. The individual members don't matter and instead it's all about the group.
Notice that for any group of 3 people, there are 3*2*1 = 6 ways to arrange such individuals. We have to divide by 6 to go from 6840 permutations to 6840/6 = 1140 combinations.
-------------------------
Here's a more formulaic approach using the nCr combination formula.
Plug in n = 20 and r = 3
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\20 C 3 = \frac{20!}{3!*(20-3)!}\\\\20 C 3 = \frac{20!}{3!*17!}\\\\20 C 3 = \frac{20*19*18*17!}{3!*17!}\\\\ 20 C 3 = \frac{20*19*18}{3!}\\\\ 20 C 3 = \frac{20*19*18}{3*2*1}\\\\ 20 C 3 = \frac{6840}{6}\\\\ 20 C 3 = 1140\\\\[/tex]
During a sale at the electronics store, movies sold for $3 and CDs sold for $2.50. Isla spent $24 and bought a total of 9 movies and CDs. How many of each did she buy?
Answers
3 Movies (3*3=$9)
What is the volume of the bird feeder? Round to the nearest tenth if nessacaryWhat is the volume of the bird feeder
Answers
how do i simplify this: (8 2/3)^4
Answers
Answer:
5641 55/81
Step-by-step explanation:
you can simplify the equation by removing the parenthesis.
this means that you also have to solve the ^4 part.
this would be
5641 55/81
I know that this is a large number but that is what happens when you do ^4.
Equivalent ratio for 3:7 is
Answers
3 : 7
to find:equivalent ratios for 3 : 7.
solution:6 : 14
9 : 21
12 : 28
15 : 35
18 : 42
( to find equivalent ratios just multiply or divide both the sides by the same number. )
Answer:
The answer is 6:14, 9:21, 12:28, 15: 35, and 18:42Step-by-step explanation:
What you need to do is take the ratio and you can turn it into a fraction!so take 3:7 and turn it into 3/7now from there you just need to multiply the numerator and the denominator by the same number and it will always equal the ratio of 3:7EXAMPLE-- 3/7 and multiply the numerator and denominator by 5 to get 15:35 THIS IS TRUE