The slope of the tangent line to the given polar curve at the point specified by the value of theta is m= 1/√3.
What is meant by tangent line?A straight line that just touches a plane curve at a particular location is referred to as the tangent line (or tangent) to the curve in geometry. It was described by Leibniz as the line connecting two points on the curve that are endlessly near to one another. A line passes through the point (c, f(c)) on the curve and has a slope of f'(c), where f' is the derivative of f. This is more properly referred to as being a tangent of the curve y = f(x) at a point x = c. Curves in n-dimensional Euclidean space and curves in space have a comparable definition.
The tangent line is "passing" through the point of tangency—the intersection of the tangent line and the curve as it travels.
Given,
r=6cosθ
f'(θ)=-6sinθ
θ=π/3
dy/dx=(f'(θ)sinθ+f(θ)cosθ)/(f'(θ)cosθ-f(θ)sinθ)
dy/dx=( -6sinθsinθ+6cosθcosθ)/(-6sinθcosθ-6cosθsinθ)
=(6cos²θ-6sin²θ)/-12 sinθcosθ
=6(cos²θ-sin²θ)/-6(2sinθcosθ)
=6cos2θ/-6sin2θ
=-cos2θ/sin2θ
=-cot2θ
Slope of the given polar curve at θ=π/3 is
m=dy/dx
m= -cot(2(π/3))
m = cot(-2π/3)
m= 1/√3
Therefore, the slope of the tangent line to the given polar curve at the point specified by the value of theta is
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The table below shows that the number of miles driven by Lydia is directly
proportional to the number of gallons she used.
Gallons Used Miles Driven
42
47
50
1591.8
1781.3
1895
If m represents the number of miles driven for any number of gallons used, g,
write a proportional equation for m in terms of g that matches the context.
the scale on a map of roswell, new mexico is $1\text{ inch}:0.51\text{ mile}$. if two buildings in roswell are $2.3$ miles apart in real life, then to the nearest tenth of an inch, how far apart are they on the map?
Two Hills in Roswell is 1.173 miles apart in real life.
The mile, sometimes called the international mile or statutory mile to distinguish it from others, is an imperial unit in the United Kingdom and a common unit of distance in the United States. Both are based on old English units that are 5,280 British feet or 1,760 yards long. The legal mile was standardized in 1959 by an international agreement between the British Commonwealth and the United States and formally redefined in SI units to be exactly 1,609.344 meters.
With the modifier, the mile is also used to describe or convert a wide range of units derived from or roughly equivalent to the Roman mile, such as the Chinese mile (now exactly 500 m). will be The Romans divided the mile into 5,000 Roman feet, but the furlong was so important in Elizabethan England that in 1593 the legal mile was equal to 8 furlongs, or 5,280 feet. This form of the mile has since spread partially to the successor states of the British Empire, where they continue to use the mile.
According to the question:
The scale is 1 inch : 0.51 miles. It means 1 inch on the map represents 0.51 miles in real life.
If we have 2.3 inches on the map, then in real life
in real life = 2.3 × 0.51
in real life = 1.173 miles.
Two hills in Roswell is 1.173 miles apart in real life
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Gary is forming capture the flag teams out of all of the students that signed up from two classes. Each team must have the same number of players and be from the same class. What is the largest number of players that gary can put on each team?.
In the kickball teams, Lee has the ability to put nine players on each team.
What does "greatest common factor" (GCF) mean?
The common number that each term in a group of terms shares, also known as the greatest common factor (GCF), is
All of the students who signed up for kickball teams from two classes are being put together into teams by Lee.
45 students from the one school have signed up to play on the kickball team. Let compose this number in factor structure as,
45 = 3*3*5
because both numbers contain the number three twice. Therefore, GCF = 3*3 GCF = 9 is the greatest common factor of two numbers.
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Full Question = Lee is forming kickball teams that include all of the students who signed up from two schools. Each team must have the same number of players and be from the same school. 45 students from the one school have signed up to play on the kickball team. What is the greatest number of players Lee can put on each team?
25 points :)))))
2+2x3
Answer:
8
Step-by-step explanation:
2+2x3
1. Use pemdas to do it
8
chase looks around at an assembly. He noticed his younger sister to his right and his older brother 16 feet ahead of him. If Chase’s brother and sister are 20 feet apart, how far apart are chase and his younger sister
The distance between Chase and his younger sister is 12 feet. This is calculated by using Pythagoras' theorem.
What is Pythagoras' theorem?The theorem that states "the square of the hypotenuse of a right triangle is equal to the sum of the squares on its other two sides" is said to be Pythagoras' theorem.
I.e., hyp² = opp² + adj²
Calculation:It is given that,
Chase looks around at an assembly. He noticed that his younger sister was to his right and his elder brother is 16 feet ahead of him.
Chase's brother and sister are 20 feet apart, then the distance between Chase and his younger sister forms a right triangle as shown in the figure.
Where SB = 20 feet; CS = X feet; and CB = 16 feet;
According to the Pythagoras theorem, the distance between Chase and his sister is
SB² = CS² +CB²
⇒ (20)² = (x)² + (16)²
⇒ 400 = x² + 256
⇒ x² = 400 -256 = 144
⇒ x = √144 = 12
Therefore, the distance between Chase and his younger sister is 12 feet.
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(3, 5), (-3, r), m = 3/4
Answer:
(35),(−3r),m=34(35),(−3),=3/4
Step-by-step explanation:
in estimating a population proportion using a large sample, the value of is assumed to be 0.35, and its 95% error margin is 0.02. find the sample size to meet the error margin.
2185 people make up the sample size.
What is proportion?
An equation in which two ratios are made equal is called a proportion. For instance, you could write the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.
The formula used to determine sample size (n) is as follows:
n = p(1 - p) (z²/ e² )
Where z = 1.96 with a 95% confidence interval (), p is the proportion, and e is the margin of error.
z = 1.96, p = 0.35, e = 0.02
n = 0.35(1 - 0.35) (1.96²/ 0.02²)
n = (0.2275)(9604)
= 2184.91
n ≈ 2185
2185 people make up the sample size.
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The distribution of heights in a population of women is approximately normal. sixteen percent of the women have heights less than 62 inches. about 97.5% of the women have heights less than 71 inches.
Use the empirical rule to estimate the mean and standard deviation of the heights in this population.
Mean and standard deviation of the height of the population using empirical rule is equal to 65inches and 3 inches.
As given in the question,
Distribution of height in women population:
Percent of women heights less than 62inches = 16%
As per Empirical rule of normal distribution,
It is less than 68% it comes in first standard deviation
μ - σ = 62 __(1)
Percent of women heights less than 71 inches = 97.5%
As per Empirical rule of normal distribution,
It is in the range of 97.5% it comes in second standard deviation
μ +2σ = 71 __(2)
Solve (1) and (2) we get,
μ - σ = 62
μ +2σ = 71
0 - 3σ = -9
⇒ σ = 3inches
⇒ μ = 62 + 3
= 65inches
Therefore, the using empirical rule the mean and standard deviation to represent the height of population is equal to 65inches and 3 inches respectively.
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-20 divided by -5
answer correctly and asap and I will give brainliest
Answer:
4
Step-by-step explanation:
negative divided by a negative is a positive
extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data. a. true
b. false
TRUE extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.
"Information available from the question"
In the question:
Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.
Answer in True or False.
Now, According to the question:
Let's Know:
What is extrapolation?
A statistical technique called extrapolation aims to understand the unknown data from the known data. It uses historical data to attempt to predict future data. For instance, using the current population size and growth rate to project the size of a population in a few years.
Predicting hypothetical values outside of a specific data set is the goal of extrapolation.
Contrary to interpolation, which typically focuses on estimating past values, extrapolation is used to predict unknown future values due to its predictive nature.
Hence, TRUE extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.
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in a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system to a semester-system. how many students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval? no information is available concerning an approximate value of p.
Total 205 students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval.
We have given that
Estimate of the proportion of students
= p
Confidence interval = 99%
As we know that the margin of error for the confidence interval is ,
MOE = Z ×√(p × (1-p)) / n
Where Z is z-score for
p --> estimate proportion confidence interval
n --> sample size
margin of error = 0 .09,
so we can set the equation as,
0.09 = Z×√(p×(1-p)) / n
Using the Z-table , the Z value for a 99% confidence interval is 2.575..
we will use p = 0.5 (since we are not given any information about value of p).
plugging all known values in above formula we get, 0.09 = 2.575√(0.5(0.5))/n
=> 0.0349 = √0.25/ n
=>0.00122 = 0.25/n
=> n = 204.6489
Since we get a decimal and we need our answer in number of students to sample, we round up to n = 205.
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HEELLPPP!!!!! An import/export business marks up imported merchandise by . If a wicker chair imported from Singapore originally costs from the manufacturer, what is the retail price?
The retail price is $?
.
The retail price is $354.65.
What is retail price?
The price at which a product's manufacturer ostensibly recommends that a retailer sell it is referred to as the list price, also known as the manufacturer's suggested retail price, recommended retail price, or suggested retail price of a product.
Given: An import/export business marks up imported merchandise by 105%.
A wicker chair imported from Singapore originally costs from the manufacturer $173.
We have to find the retail price.
Retail price = [tex]= 173 + 173*\frac{105}{100} \\[/tex]
= 173 + 181. 65
Retail price = 354.65
Hence, Retail Price is $ 354.65.
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Use the quadratic formula to solve the quadratic equation 2x²-3x -4 = 0.
Separate multiple solutions with commas if necessary.
Answer:
Step-by-step explanation:
4m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/8
Answer:
[tex]\frac{-3+\sqrt{23} }{4} , - \frac{3+\sqrt{23} }{4}[/tex]
Step-by-step explanation:
quad formula= [tex]x=\frac{b+/-\sqrt{b^{2} -4(a)(c)} }{a^{2} }[/tex]
in your case the [tex]2x^{2}[/tex] is a
[tex]-3x[/tex] is b
and [tex]-4[/tex] is c
and plug it in a calculator twice, add the first time and subtract the second time.
Decide whether a graph of the data would be points that appear to lie on a horizontal line, a vertical line, or neither. The number of books read by Avery each year from 1999 to 2005.
Evaluate the expression for the given value of the variable. 34 + 1/6r, r = -1/2
Answer:
407/12
Step-by-step explanation:
r=-1/2
Substituting, we get 34+1/6*-1/2=34+(-1/12) = 407/12.
1/2x 3/4 in the simplest form?
What does it mean when the slope is 2 to 1?
The slope is 2 to 1 means you move up or down 1 foot for every 2 feet.
The slope is 2 to 1 means you move up or down 1 foot for every 2 feet. [tex]2:1[/tex] slopes have guardrails along the edge(side) of the pavement as you drive down the highway. It can be seen from either an on or off-ramp.
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What is the vertex of the graph of the function f(x)=x^2+8x
Answer:
Step-by-step explanation:
o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...
Cathy takes out a $167,000 mortgage. She plans monthly payments to pay it off in 40 years. At the end of the term, Cathy will have paid $401,294.40 total. Choose the appropriate APR formula.
APR=2nf/P(N+1)
APR=24(234,294.4)/167,000(481)
APR=2(12)(401,294.4) / 167,000(480+1)
APR=2(12)(167,000)(401,294.4)⋅481
APR=24(284,147.2)401,294.4(480+1)
Cathy takes out a $167,000 mortgage. She plans monthly payments to pay it off in 40 years. At the end of the term, Cathy will have paid $401,294.40 total. The appropriate APR formula is APR=2(12)(401,294.4) / 167,000(480+1)
Define APR.The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR). APR is a percentage that expresses the actual annual cost of borrowing money throughout the course of a loan or the revenue from an investment. This does not account for compounding and includes any fees or additional expenditures related to the transaction. Consumers can evaluate lenders, credit cards, or investment goods using the APR as a benchmark figure.
Given,
Mortgage = $167000
Monthly plan = 40 years
End of the term, Cathy will have paid $401,294.40 total.
APR=2nf/P(N+1)
APR=2(12)(401,294.4) / 167,000(480+1)
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How do I measure 1 square meter?
Answer:
you need to know the length and width of the square or rectangle. This is also referred to as the area of the shape. The formula for calculating square meters is length x width = m2.
-9a-15-16a+9 8n it's simplest form
the simplest form of the given expression -9a-15-16a+9 is -25a - 6.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
-9a-15-16a+9
So here "a" is a variable
we have -a(9+16)+9-15
= -25a - 6
Hence the simplest form of the given expression is -25a - 6.
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Pls help me with this answer!!
Answer:
(-3, 0)
Step-by-step explanation:
You use brackets and then you place the number of x first which is -3 then you place a comma and then you place the number of y which is 0 and you close the bracket.
1/2x < 6
Please help me
Answer:
x < 12
Step-by-step explanation:
Combine multiplied terms into a single fraction
1/2x < 6
1x/2 < 6
x/2 < 6
2 times x/2 < 2 times 6 is 12 you your answer is x < 12
nt
P(1 + 1) ht
Formula: A = P
Solve the problem by answering the following questions:
An initial investment of $5575 is appreciated for 12 years in an account that earns 3.25%
interest, compounded semiannually. Find the amount of money in the account at the end
of the period.
i. What does each of these variables represent:
The amount of investment will be $8183.24 after compound interest.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
A = P(1+r/100)ⁿ
Where:
A = the future value of the investment or loan
P = the principal investment or loan amount
r = the interest rate (decimal)
n = the number of compound periods
As per the question, an initial investment of $5575 is appreciated for 12 years in an account that earns 3.25% interest, compounded semiannually.
The compounded amount will be calculated as:
A = 5575 ( 1 + 0.0325 )¹²
A = 5575 × 1.4678
A = $8183.24
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if i have 29 pencils and i give 13 away to my friend how much pencils do i have left?
If you have 29 pencils and gave 13 away to your friend, you subtract what you gave away from what you have.
[tex]29-13\\=\fbox{16}[/tex]
Find the difference between (1.1 × 108) and (4.3 × 107). Write the final answer in scientific notation.
−3.2 × 101
3.2 × 10−1
6.7 × 107
6.7 × 108
The difference between the numbers 1.1 × 10⁸ and 4.3 × 10⁷ will be 6.7 × 10⁷. Then the correct option is C.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
1.1 × 10⁸ and 4.3 × 10⁷
Then the difference between the numbers 1.1 × 10⁸ and 4.3 × 10⁷ will be given by putting a minus sign between them. Then we have
⇒ 1.1 × 10⁸ - 4.3 × 10⁷
⇒ 11 × 10⁷ - 4.3 × 10⁷
⇒ 6.7 × 10⁷
The contrast between the numbers 1.1 × 10⁸ and 4.3 × 10⁷ will be 6.7 × 10⁷. Then, at that point, the right choice is C.
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A retailer purchases 240 of a new brand of dvd player, of which 7 are defective. The purchase agreement says that if he tests 5 chosen at random and finds 1 or more defective, he receives all the dvd players free of charge. What is the probability that he will not have to pay for the dvd players? (round your answer to three decimal places. )
The probability of not paying any amount for the purchased DVD players as per the condition of 1 or more defective is equal to 0.9029.
As given in the condition,
Number of DVD players purchased by a retailer = 240
Number of defective DVD players = 7
Number of non- defective DVD players = 233
Number of DVD players chosen randomly for test = 5
Condition:
If 1 or more DVD players are defective then all players are free of charges.
Total number success rate for 5 DVD to be defective 'p' = 5 / 240
= 1 / 48
Here value of n = 5
Probability of non defective DVD is equal to:
= 1 - ( 47/ 48 )⁵
= 0.09708
Probability of 1 or more defective DVD's are
= 1 - 0.09708
= 0.9029
Therefore, the probability of not to pay any amount for DVD players is equal to 0.9029.
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data were collected on the following variables. which variable is least likely to be approximated with a normal model?
On the factors variable, information was gathered when the age distribution of all the data, expressed in years, with the right tail being longer than the left.
Given that,
On the factors variable, information was gathered.
We have to find which variable is least likely to be modeled by a normal distribution.
We know that,
The normal distribution has the following properties:
i) Symmetric
ii) unimodal
iii)asymptotic
The distribution of ages, in years, of all the residents of a town, where the right tail of the distribution is longer than the left.
This distribution is not symmetric.
It is not a normal distribution.
Therefore, On the factors variable, information was gathered when the age distribution of all the data, expressed in years, with the right tail being longer than the left.
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A sheet of 28 stickers has stars and heart stickers. There are 16 heart stickers. How many heart stickers does a pack of 140 stickers have?
To find the number of heart stickers in a pack of 140 stickers, we can use proportions. We can set up the proportion by using the number of stickers on the sheet of 28 stickers as the denominator and the number of heart stickers on the sheet of 28 stickers as the numerator. The proportion will look like this:
Copy code
(heart stickers in a pack of 140 stickers) / 140 = 16 / 28
To solve for the number of heart stickers in a pack of 140 stickers, we can first multiply both sides of the equation by 140 to get rid of the denominator on the left side:
(heart stickers in a pack of 140 stickers) = 140 * 16 / 28
Then, we can simplify the expression on the right side by dividing the numerator and denominator by 4 to get:
(heart stickers in a pack of 140 stickers) = 35
Therefore, a pack of 140 stickers would have 35 heart stickers.
Select all the numbers that show 12% as an equivalent fraction, decimal, or percent.