Conversion of the given rectangular coordinates into polar coordinates gives: (8.06, -0.52)
How to convert rectangular coordinates into polar coordinates?To convert rectangular coordinates to polar coordinates, we will use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
where (r, θ) is the polar coordinates and (x, y) is the rectangular coordinates.
Using these formulas, we can convert (-7, 4) as follows:
r = √((-7)² + 4²)
r = √(49 + 16)
r = √65
r = 8.06
θ = tan⁻¹ (4/(-7)) = -0.52 radians
Therefore, the polar coordinates are (8.06, -0.52)
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Graph and write an inequality to
represent each situation.
6. No more than 180 people can be
seated in the auditorium.
Please help with this
Answer:
y=52 (or 90) - please read the explanation to understand what I mean
x=52
Edit: So basically what happened is that I thought that y was only that one angle, so I did that part of the problem wrong.
This is how it should be done:
We can look at the angles 38 and y. Together, the two angles form a straight angle. So, to find y, do 180-38.
180-38=142
Sorry for the mistake earlier! The diagram wasn't too clear and I thought the y was the one that wasn't the right angle...
Step-by-step explanation:
The measure of all the angles will always add to 360°. We can draw an imaginary circle around all the angles to visualize this. This also means that half a circle will add to 180°.
180 = 38+90+y
= 128+y
y=52
(By the way, if the y was the one with the right angle, it would be 90. You might want to try both, as the picture isn't too clear as to which one it is.)
Now to solve for x, we again see that half of our imaginary circle would add up to 180°. However, we need to choose a half that has more angles. Let's go with the half that has the 38° and the right angle, which equals 90°.
180=38+90+x
=128+x
x=52
I have attached a couple of screenshots so you can hopefully see what I mean by an imaginary circle.
Sorry for the bad handwriting - I'm on a computer right now so I can't really write well....
I hope this is correct and good luck on your homework!
The measure of angle x = 52 degree and angle y = 142 degree.
In the given figure;
The three intersecting lines are given
In which one inclination angle is 38 degree
And second is right angle.
To find value of y
from figure;
y + 38 = 180
⇒ y = 180-38 = 142 degree
To find value of y
⇒ x + 38 + 90 = 108
⇒ x = 52 degree
Hence, x = 52 degree and y = 142 degree.
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Find the volume of the oblique cylinder below. Round your answer to the nearest tenth if necessary.
The Volume of the oblique cylinder is approximately calculated as:
1,789.5 cubic units.
How to Find the Volume of an Oblique Cylinder?The formula for finding the volume of an oblique cylinder is the same as that used for finding the volume of a right cylinder. The formula is given as:
Volume (V) = πr²h, where r is the radius and h is the height of the oblique cylinder.
We are given the following:
Radius (r) = 8
Height (h) = √(12² - 8²) ≈ 8.9 units [Pythagorean Theorem]
Volume of the oblique cylinder (V) = π * 8² * 8.9
≈ 1,789.5 cubic units.
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please help me with this problem thank you and look at the picture
Answer:
819
Step-by-step explanation:
i multiplied each number
Diego’s skis are leaning at an angle against a fence railing and are parallel to each other. Find m∠1
and m∠3
if m∠2=158°
. Justify your answer.
The measure of the angles is 22°.
Given is figure with two parallel lines we need to find the measures of the asked angles,
∠1 + ∠2 = 180° [linear pair]
∠1 = 180° - 158°
∠1 = 22°
Now angles 1 and 3 are alternate exterior angles between parallel lines,
Hence are equal,
Therefore,
∠3 = 22°
Hence the measure of the angles is 22°.
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Determine the isoelectric point (pI) for aspartate.
pKC = 1.99, pKN = 9.90, and pKR = 3.90
Select one:
a. 1.99
b. 2.94
c. 3.90
d. 6.90
e. 9.90
The isoelectric point (pI) for aspartate is 2.94. The correct answer is option (b).
To determine the isoelectric point (pI) for aspartate, we need to consider the given pK values: pKC = 1.99, pKN = 9.90, and pKR = 3.90. The isoelectric point is the pH at which a molecule carries no net electrical charge, and for amino acids, this occurs between the pK values of the two ionizable groups that are involved in the formation of the zwitterion.
Aspartate is an acidic amino acid with a carboxyl side chain. Thus, we need to consider pKC (carboxyl group) and pKR (side chain group) for calculating the pI. We can use the formula:
pI = (pKC + pKR) / 2
Plugging in the given values:
pI = (1.99 + 3.90) / 2
pI = 5.89 / 2
pI = 2.94
So, the isoelectric point (pI) for aspartate is 2.94.
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Find the exact value of the trigonometric expression given that
sin u = − 8/17 and cos v = − 5/13. (Both u and v are in Quadrant III. )
cos(u − v)
The exact value of cos(u - v) is 80/221. To find the value of cos(u - v), we can use the trigonometric identity:
cos(u - v) = cos u * cos v + sin u * sin v
Given that sin u = -8/17 and cos v = -5/13, we can substitute these values into the formula:
cos(u - v) = (-8/17) * (-5/13) + (-8/17) * (-5/13)
Multiplying the numerators and denominators:
cos(u - v) = 40/221 + 40/221
Combining the fractions:
cos(u - v) = 80/221
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Find the value of a that makes AABC~ ADEF.
B.
6
When a =
21
4x-2
D
2x + 4
12
the triangles are similar.
Answer:
X= 5
Step-by-step explanation:
If 2 triangles are similar then their corresponding side ratio are proportional
∆ABC ~∆DEF
Then
AB/DE = BC/EF = AC/DF
AB/DE = BC/EF = AC/DF6/4 = 21/2x+4 = 4x-2/12 when we simplify them
3/2 = 21/2x+4 = 2x-1/6
3/2 = 21/2x+4 = 2x-1/63/2 = 21/2x+4 .............. criss cross
3(2x+4) = 42
3(2x+4) = 422x+4 = 14
3(2x+4) = 422x+4 = 142x=14 - 4 = 10
3(2x+4) = 422x+4 = 142x=14 - 4 = 102x/2 = 10/2
3(2x+4) = 422x+4 = 142x=14 - 4 = 102x/2 = 10/2x = 5 ........we solve the value of x
In order to take x = 5 we must check it by inserting to the other proportion
6/4 = 4x-2/12 ........ when we simplify it
3/2 = 2x-1/6 ........ then we will insert 5 in place of x
3/2 = 9/6....... when we simplify it by 3
3/2 = 3/2 ..... so the are proportional ( equal )
so the value of x is 5
Here are the approximate populations of three cities in the United States, expressed in scientific notation: San Jose: 1.1 * 106; Washington: 7 * 105 *; Atlanta: 4.8 * 105. 7.1 Lin says that about 6.2 * 105 more people live in San Jose than in Atlanta. Do you agree with her? Explain your reasoning.
A researcher who selects a sample of people of varying ages and studies them at one point in time is, by definition, using the ___________ method
The researcher in question is using a cross-sectional research method.
This method involves selecting a sample of individuals from a population and studying them at one point in time, usually in a single session. The purpose of the research is to gather information about the relationships between variables and to describe the population characteristics.
One of the primary advantages of the cross-sectional method is its efficiency. Researchers can gather a large amount of data in a relatively short amount of time, which can be helpful for studying large populations or for answering research questions that are time-sensitive.
However, there are also limitations to the cross-sectional method. For example, because it only captures data from one point in time, it cannot be used to study how variables change over time. Additionally, cross-sectional research cannot establish causality, as the data only shows correlations between variables, not their causal relationships.
Overall, the cross-sectional method is useful for gathering information about a population's characteristics and relationships between variables, but it should be used in conjunction with other research methods to gain a more comprehensive understanding of a phenomenon.
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Help with these two please!
The measure of angle DCB is 128°.
Measure of angle BEC and DEC are 54° and 126° respectively.
3) Given that,
∠ECB and ∠DCA are straight angles.
So,
∠ECA and ∠BCA = 180°
3x + 5 + x + 11 = 180
4x + 16 = 180
4x = 164
x = 41
Now, measure of ∠DCB = measure of ∠ECA [Since they are vertical angles]
m ∠DCB = 3x + 5 = (3 × 41) + 5 = 128°
4) AC and DB intersect at point E.
5x + 36 + 3x = 180
8x + 36 = 180
8x = 144
x = 18
m ∠BEC = m ∠AED [ Vertical Angles theorem]
m ∠BEC = 3x = 54°
Similarly,
m ∠DEC = m ∠AEB
m ∠DEC = 5x + 36 = (5 × 18) + 36 = 126°
Hence the measures of angles DCB, BEC and DEC are 128°, 54° and 126° respectively.
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A quadratic equation with opposite solutions can be found by multiplying
left parenthesis x minus r right parenthesis and left parenthesis parenthesis____
The equation will have ____
A quadratic equation with opposite solutions can be found when D > 0.
In a quadratic equation, the discriminant D describes the nature of the roots which is also called the solutions of the equation.
For a quadratic equation ax²+bx+c = 0, the discriminant D is given by =
D = [-b ± √(b² – 4ac)]/2a
Nature of roots:
D > 0, roots are real and distinct.
D = 0, roots are real and equal.
D < 0, roots are imaginary and unequal.
Hence, the quadratic equation with opposite solutions can be found when D > 0.
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Quadrilateral CDEF is similar to quadrilateral GHIJ. Find the measure of side JG. Round your answer to the nearest tenth if necessary.
30.54 units is the measurement of the side JG.
It is given that, quadrilateral CDEF and the quadrilateral GHIJ are similar,
in a similar figure, the ratio of the adjacent sides is equal,
Thus in the given figure,
FE/JI = FC/JG
11/42 = 8/JG
JG = 42*8/11
JG =30.54
Therefore, the measurement of the side JG is 30.54 units.
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Orthogonal complement to S has dimension 0 when ____.
The orthogonal complement to S has dimension 0 when the dimension of the vector space is equal to the dimension of S.
We have,
The orthogonal complement to a subspace S of a vector space is the set of all vectors in the vector space that are orthogonal (perpendicular) to every vector in S.
The dimension of the orthogonal complement is given by the difference between the dimension of the vector space and The dimension of S.
If S spans the entire vector space, then its orthogonal complement consists only of the zero vector and therefore has dimension 0.
Thus,
The orthogonal complement to S has dimension 0 when the dimension of the vector space is equal to the dimension of S.
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Whenever possible, research should be designed so that the data can be anlyzed using __________________.
a. statistics
b. SPSS
c. parametric tests
d. non-parametric tests
Whenever possible, research should be designed so that the data can be anlyzed using option (a) statistics
-This includes both parametric tests (which assume that the data is normally distributed and meet certain assumptions) and non-parametric tests (which do not make these assumptions and are useful for non-normal data). SPSS is a software program commonly used for statistical analysis, but it is not necessary for conducting statistical analyses.
a. statistics
Research should be designed so that the data can be analyzed using statistics. Statistics provide a set of methods and tools for analyzing and interpreting data, which can help researchers draw meaningful conclusions from their findings. Statistical analysis can be used to identify patterns, trends, and relationships in data, as well as to test hypothesis and make predictions.
Depending on the research question, data type, and sample size, different types of statistical tests may be appropriate. Both parametric and non-parametric tests can be used to analyze data, depending on the assumptions made about the underlying distribution of the data and the level of measurement of the variables. SPSS is a statistical software program that can be used to perform statistical analysis, but it is not necessary for designing research studies or analyzing data.
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I am a quadrilateral with diagonals that always bisect each other. Who am I?
(square, rhombus, rectangle, parallelogram, kite, isosceles trapezoid, trapezoid)
A quadrilateral with diagonals that always bisect each other is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel and equal in length. The diagonals of a parallelogram bisect each other, which means they cut each other in half, creating two equal segments.
To explain further, a parallelogram has some specific properties: 1) Opposite sides are parallel, 2) Opposite angles are equal, and 3) Adjacent angles are supplementary. In a parallelogram, the diagonals not only bisect each other but also have a unique relationship. The diagonals are not necessarily equal in length or perpendicular, but they do divide the parallelogram into two congruent triangles.
While squares, rectangles, and rhombi are also types of parallelograms with diagonals that bisect each other, they have additional properties that differentiate them from a generic parallelogram. A square has all sides equal and all angles equal to 90 degrees, a rectangle has all angles equal to 90 degrees, and a rhombus has all sides equal. Kites, isosceles trapezoids, and trapezoids do not always have diagonals that bisect each other, so they do not meet your criteria.
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Write the absolute value equations in the form x−b=c (where b is a number and c can be either number or an expression) that have the following solution set all numbers such that x>=5
The absolute value equation that has the solution set of all numbers such that x >= 5 can be written as |x - 5| = x - 5. This equation is true when x >= 5 because the absolute value of a non-negative number is equal to the number itself.
Find sen2x, cos 2x, and tan 2x if tanx=-3 and x terminates in quadrant II.
help number 3 & 4 please!!
[3] Answer: ∠DCB = 128°
Step-by-step explanation:
First, we know a straight angle is equal to 180 degrees.
3x° + 5° + x° + 11° = 180°
4x° + 16° = 180°
4x° = 164°
x° = 41°
Next, we can apply this same knowledge of straight angles to ∠DCA. We will substitute the value of x above into the expression for angle ACB.
180° - (x + 11)° = ∠DCB
180° - (41 + 11)° = ∠DCB
180° - 52° = ∠DCB
128° = ∠DCB
[4] Answer: ∠DEC = 126°, ∠BEC = 54°
Step-by-step explanation:
We will also apply the knowledge of straight angles being equal to 180 degrees here.
5x° + 36° + 3x° = 180°
8x° + 36° = 180°
8x° = 144°
x° = 18°
Next, we will substitute this value of x back into the expressions for each angle.
5x° + 36° 3x°
5(18)° + 36° 3(18)°
126° 54°
Lastly, we know that vertical angles are congruent.
∠AEB = ∠DEC = 126°
∠AED = ∠BEC = 54°
Help me with this question please and thank you
The distance between the points A and B is √58
We have,
From the graph,
The coordinates of point A = (-3, 2) and B = (4, -1).
Now,
The distance between A and B.
= √((4 + 3)² + (-1 - 2)²)
= √(7² + (-3)²)
= √(49 + 9)
= √58
Thus,
The distance between the points A and B is √58
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1.22 A bird flies 3.0 KM due west and then 2.0 KM due north. what is the magnitude of the bird's displacement?
A 2.0 km
B 3.0 km
C 3.6 km
D 5.0 km
The magnitude of the bird's displacement is 3.6 km, which corresponds to option (C).
We can use the Pythagorean theorem to find the magnitude of the bird's displacement, which is the length of the straight line between the bird's starting point and ending point (i.e., the distance between the two points).
If we draw a diagram, we can see that the bird's displacement forms the hypotenuse of a right triangle with legs of length 3.0 km (the distance traveled due west) and 2.0 km (the distance traveled due north).
So, we can use the Pythagorean theorem to find the length of the hypotenuse:
displacement = √[(3.0 km)² + (2.0 km)²] ≈ 3.6 km
Thus, the magnitude of the bird's displacement is 3.6 km.
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A cube of side 3 inches has a cube of side 1 inch cut from each corner. A cube of side 2 inches is then inserted in each corner. What is the number of square inches in the surface area of the resulting solid
The total surface area of the resulting solid is [tex]6+96=\boxed{102}[/tex] square inches.
The resulting solid after the described procedure consists of a central cube of side length 1 inch and 6 congruent smaller cubes, each of side length 2 inches. We can find the surface area of the resulting solid by adding up the surface area of each of these cubes.
The surface area of the central cube is simply [tex]6(1^2)=6[/tex] square inches.
The surface area of each of the smaller cubes is [tex]6(2^2)=24[/tex] square inches, but since each cube shares one face with the central cube and another face with its neighboring cube, we only count four of its faces, so the contribution of each smaller cube to the surface area of the resulting solid is 4(24/6)=16 square inches.
Since there are 6 smaller cubes in total, their contribution to the surface area of the resulting solid is [tex]6\times16=96[/tex]square inches.
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If a water park sold 11 child tickets and 14 adult tickets. What percentage of the tickets sold were child tickets?
If a water park sold 11 child tickets and 14 adult tickets then 44% of the tickets sold were child tickets
The number of child tickets = 11
The number of adult tickets = 14
The total number of tickets are 11+14
Total tickets = 25
We have to find the percentage of the tickets sold were child tickets
x/100×25 = 11
0.25x=11
Divide both sides by 0.25
x=11/0.25
x=44%
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ADerek bought 4 pounds of tomatoes at the grocery store. This included grape, roma, and plum tomatoes. If Derek bought 2 pounds of grape tomatoes and 14 ounces of roma tomatoes, how many ounces of plum tomatoes did he buy?s an adult, Kim's dog weighs 8 pounds. How many ounces did Kim's dog gain?
Derek bought 4 pounds of tomatoes at the grocery store. The dog gained 12.8 ounces.
Derek bought 21 ounces of plum tomatoes.
Since 1 pound is equal to 16 ounces, 4 pounds is equal to 64 ounces. Derek bought 2 pounds of grape tomatoes, which is equal to 32 ounces. He also bought 14 ounces of roma tomatoes.
To find how many ounces of plum tomatoes he bought, we can subtract the total weight of the grape and roma tomatoes from the total weight of all the tomatoes:
64 - 32 - 14 = 18 ounces of plum tomatoes
Therefore, Derek bought 18 ounces of plum tomatoes.
Kim's dog gained 128 ounces.
Since 1 pound is equal to 16 ounces, Kim's dog weighs 8 x 16 = 128 ounces.
To find how many ounces the dog gained, we need to know the new weight of the dog. If we assume that the dog gained 10% of its original weight, we can find the new weight by adding 10% of 128 to 128:
128 + (0.10)(128) = 140.8 ounces
Therefore, the dog gained 140.8 - 128 = 12.8 ounces.
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Trevor’s stack of books is 7 7/4 inches talk. Ricks stack is 3 times as tall. What is the difference in heights of their stacks of books?
The difference in heights of their stacks of books is 15 1/4 inches.
Trevor’s stack of books is 7 7/4 inches tall. Rick's stack of books is 3 times as tall as Trevor's stack, which means:
Height of Rick's stack = 3 × Height of Trevor's stack
= 3 × 7 7/4 inches
= 22 3/4 inches
The difference in height between their stacks of books can be found by subtracting the height of Trevor's stack from the height of Rick's stack:
Height of Rick's stack - Height of Trevor's stack
= 22 3/4 inches - 7 7/4 inches
= (22 - 7) + (3/4 - 7/4) inches
= 15 + 0.25 inches
= 15 1/4 inches
Therefore, the difference in heights of their stacks of books is 15 1/4 inches.
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wich answer choice below best represents the quotient 1,610=35?
Tommmy and sophia are selling tickets to a school basketball game. In 3 hours tommy sold 36 tickets
Both Tommy and Sophia can sell 162 tickets in 6 hours.
We have,
Tommy sold 36 tickets in 3 hours, so he sells:
36 tickets / 3 hours
= 12 tickets per hour
Sophia sold 60 tickets in 4 hours, so she sells:
60 tickets / 4 hours
= 15 tickets per hour
Now we can add up their ticket-selling rates to find their combined rate:
12 tickets/hour + 15 tickets/hour = 27 tickets/hour
So together, Tommy and Sophia can sell 27 tickets in one hour.
Now,
27 tickets/hour × 6 hours = 162 tickets
Therefore,
Both Tommy and Sophia can sell 162 tickets in 6 hours.
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The complete question:
Tommy and Sophia are selling tickets to a school basketball game.
In 3 hours Tommy sold 36 tickets.
In 4 hours Sophia sold 60 tickets.
How many tickets will both can sell in 6 hours?
The formula for finding the surface area of a cube is S=6e2 where e represents the length of an edge of a cube and s represents the cubes surface area. Solve this formula for e
From the formula for finding the surface area of a cube, e = √(S/6)
Here, the formula for finding the surface area of a cube is,
S = 6 × e²
where e represents the length of an edge of a cube
and S represents the cubes surface area
We solve this formula for e.
Consider S = 6 × e²
Divide each side by 6
S/6 = (6 × e²)/6
e² = S/6
Taking square root on both the sides,
e = ±√(S/6)
As we know the length of the side of a cube is always positive.
So, e = √(S/6)
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49. Group Anagrams
Given an array of strings, group anagrams together.
For example, given: ["eat", "tea", "tan", "ate", "nat", "bat"], Return:
[
["ate", "eat","tea"],
["nat","tan"],
["bat"]
]
Note: All inputs will be in lower-case.
The problem requires grouping anagrams from a given array of strings. This can be achieved by using a hash table with sorted strings as keys and corresponding anagrams as values.
To group anagrams together, we can use a hash table where the keys are sorted strings and the values are lists of strings that are anagrams of the corresponding key. Here's a Python implementation:
```
def group_anagrams(strs):
# Create a hash table
anagrams = {}
# Iterate over each string in the input array
for s in strs:
# Sort the string and use it as a key in the hash table
sorted_s = ''.join(sorted(s))
if sorted_s in anagrams:
# If the key already exists, append the string to the corresponding value
anagrams[sorted_s].append(s)
else:
# If the key doesn't exist yet, create a new key-value pair
anagrams[sorted_s] = [s]
# Return the values of the hash table as a list
return list(anagrams.values())
```
For the input `["eat", "tea", "tan", "ate", "nat", "bat"]`, this function would return `[['eat', 'tea', 'ate'], ['tan', 'nat'], ['bat']]`. Note that the order of the groups and the order of the strings within each group may be different from the example output in the prompt, but the groups themselves are the same.
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Miguel bought a soccer ball on sale for $15. The sale price was 33 1/3% less than the original price. Which fraction is equivalent to 331/3%?
The fraction which is equivalent to 33 1/3% is 1/3. The process involves removing the percent symbol, placing the result over 100, and simplifying the fraction to its lowest terms.
Explanation:The fraction that is equivalent to 33 1/3% would be 1/3. If we want to convert a percentage to a fraction, we need to follow these steps:
Take the percentage, in this case, 33 1/3%.
Remove the percent symbol and place the number over 100. This makes the fraction 33 1/3 over 100 or 100/3.
Reduce this fraction to its simplest terms.
In this case, by dividing both the numerator and denominator by 100, we get 1/3.
So, the fraction equivalent of 33 1/3% is 1/3.
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