Answer:
infinite
Step-by-step explanation:
find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.) Parametric Equations Point x = 6 cos θ, y = 6 sin θ θ = π/4
find:
dy/dx=
d^2y/dx^2 =
slope
concavity:
The value of dy/dx is -cotθ, d^2y/dx^2 is -6cosec³θ, slope is -cotθ, concavity is -6cosec³θ.
Parametric Equations Point x = 6cosθ, y = 6sinθ and θ = π/4
We have to determine the value of dy/dx.
We can define dy/dx as;
dy/dx = (dy/dθ)/(dx/dθ)
We first define dy/dθ and dx/dθ.
x = 6cosθ y = 6sinθ
dx/dθ = -6sinθ dy/dθ = 6cosθ
Now put the value
dy/dx = 6cosθ/(-6sinθ)
dy/dx = -cotθ
Now we have to determine the value of d²y/dx².
d²y/dx² = d/dx(dy/dx)
We can write it as
d²y/dx² = \(\frac{\frac{d}{d\theta}(\frac{dy}{dx})}{dx/d\theta}\)
We first determine the value of d/dθ(dy/dx)
d/dθ(dy/dx) = d/dθ(-cotθ)
d/dθ(dy/dx) = cosec²θ
Now put the value
d²y/dx² = cosec²θ/(-6sinθ)
d²y/dx² = -6cosec³θ
Now we have to determine the slope.
Slope = dy/dx
Slope = -cotθ
Now we have to determine the concavity.
Concavity = d²y/dx²
Concavity = -6cosec³θ
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Match each drawing on the left with its word description on the right
Answer:
WHATS the question???
Step-by-step explanation:
Answer:
answer in the picture
Step-by-step explanation:
A school sports team sold candy bars to raise money for new uniforms. The table shows the amount of candy sold each week for three weeks.
Week Amount Sold
Week 1 26%
Week 2 three elevenths
Week 3 thirteen fiftieths
For which weeks did the team sell the same amount of candy bars?
Weeks 1 and 2
Weeks 1 and 3
Weeks 2 and 3
Weeks 1, 2, 3
Answer:weeks 1 and 3
Step-by-step explanation:
13 / 50 to percentage is 26%. I took the test
The team sell the same amount of candy bars in the first and the third week. Therefore, option B is the correct answer.
Given that, a school sports team sold candy bars to raise money for new uniforms.
In the first week they sold 26%, in the second week they sold 3/11 and in the third week, they sold 13/50.
What is the percentage?The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now, in the second week, they sold 3/11=3/11 ×100=27.27%
In the third week, they sold 13/50= 13/50 ×100=26%.
In the first week and the third week, they sold the same quantity of candies.
Therefore, option B is the correct answer.
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For #81-84, fill in the missing dimensions from the given expression. Then rewrite the
expression as a product.
2x+24
(81.)
(82.)
2x
(83.)
84. Expression as a product
Choices for 81-84:
A) 2
E) 12
AE) 2x
CD) 4x(x+4)
24
B) 4
AB) 14
BC) 4x
CE) 2(2x+9)
C) 6
AC) 16
BD) 4(x+6)
DE) 2(x+12)
D) 9
AD)
x
BE) 2(2x+16)
ABC) 4x(x+14)
The missing dimensions from the given expression should be completed with the following:
(81.) A) 2
(82.) AD) x
(83.) E) 12
The expression as a product should be written as: DE) 2(x + 12).
What is a factored form?In Mathematics and Geometry, a factored form can be defined as a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.
In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;
x 12
2 2x 24
Note: 2x/2 = x.
24/2 = 12.
(2x + 24) = 2(x + 12).
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I thought of a number. I subtracted 15 from my number, then divided the result by 5, and I got 9. What is my number?
Answer:
The answer is 60
Step-by-step explanation:
all you have to do is reverse the operation, you have to do 9 x 5 then add 15 to that result and you will get the answer :)
hope this helps!
To pass a certain marksmanship test, an individual is required to shoot at a target until he hits it six times. He is judged on the number of trials that are necessary to achieve this. If the probability of his hitting a target on any trial is 0.25, what is the probability that he requires 18 shots?
Answer:
The probability that he requires 18 shots is 0.04785
Step-by-step explanation:
To answer this, we shall be using the negative binomial distribution
From the question;
P = 0.25 , r = 6
q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial
P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)
P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785
Drag and drop 3 coordinates that satisfy the system above
Y<-2x + 4
2x-4y ≥ 3
The three coordinates that satisfy the system of inequalities include the following:
(0, -2)
(-7, - 5)
(-2, -8).
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
By critically observing the graph of the given system of inequalities y < -2x + 4 and 2x - 4y ≥ 3, the three required solutions that satisfies it include following;
Ordered pair = (0, -2).
Ordered pair = (-7, - 5).
Ordered pair = (-2, -8).
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1/4-5/8n is equivalent to p(2-5n)
Answer:
1/4 - 5/8n = p (2-5n)
Hey there!
The answer is \(\frac{-3}{8}n=2p-5np\)
Since they are equivalent to each other, we will set them equal to each other, because equivalent means equal to.
\(\frac{1}{4}n-\frac{5}{8}n = p(2-5n)\)
Now, we will simplify it. First, we will simplify the left side by subtracting. To do this, we can make \(\frac{1}{4}\) into \(\frac{2}{8}\). That gives us:
\(\frac{-3}{8}n=p(2-5n)\)
Now, we'll simplify the right side by distributing \(p\):
\(\frac{-3}{8}n=2p-5np\)
Have a super awesome day! :)
1. The ratio of faculty members to students at a college is 1:18. If there are 16000 students, how many faculty members are there? Round to the nearest whole number
Therefore, there are approximately 889 faculty members at the college.
What is ratio?Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.
Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.
Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.
To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.
If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:
Number of faculty members = 16000 / 18
This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.
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One side of a rectangle is three times as long as another. If its area is 363 square centimeters, find its dimensions.
Shorter side:
Longer side:
9514 1404 393
Answer:
11 cm by 33 cm
Step-by-step explanation:
You can solve this problem mentally as follows.
Consider the rectangle as 3 squares, side-by-side. Then the area of each of those squares is 363/3 = 121 cm^2. From your knowledge of the squares of numbers, you know that 121 = 11^2. So, the width of the rectangle is 11 cm, and the length is 3 times that, or 33 cm.
_____
Using variables, we can let w represent the width. Then 3w can represent the length, and the area is ...
A = LW
A = (3w)(w) = 3x^2 = 363
w^2 = 363/3 = 121
w = √121 = 11
3w = 3·11 = 33
The width is 11 cm; the length is 33 cm.
Answer:
Shorter side: 11 cm
Longer side: 33 cm
First, write down what you know:
length=3*width, this can be written as 3w
area=363 sq cm
Now we know the formula for the area of a rectangle= length * width so we can substitute what we know into the formula. It looks like this:
363 (area) = 3w (length) × w (width)
\(363=w^2\)
divide both sides by 3 to get: 121 = \(w^2\)
take the square root of both sides to get: w=11 (square root of 121 is 11)
Now that we know what the width is, we can substitute that and find the length: 3w = 3 × 11=33
So length (longer side) is 33cm and width (shorter side) is 11cm.
*To check this, plug the numbers into the area formula: Area=33 × 11 = 363 sq cm.
Please mark brainiest if you can
Please explain how you got the answer and please put, Example: Part A, then write the answer and the same for part b and c
SOLUTION:
PART A) Estimate
\(\begin{gathered} \frac{10}{12}+\frac{3}{8} \\ \text{Converting to decimal fractions} \\ 0.833\text{ - 0.375} \\ \text{Estimating} \\ (0.833\pm0.0005)\text{ -(0.375}\pm0.0005) \\ \text{upper boundary} \\ (0.833+0.0005)\text{ -(0.375+}0.0005) \\ (0.8335)\text{ -(0.375}5) \\ =0.458 \\ \\ \text{lower boundary} \\ (0.833-0.0005)\text{ -(0.375-}0.0005) \\ 0.8325\text{ - 0.3745} \\ =0.458 \end{gathered}\)Part B) ACTUAL SOLUTION
\(\begin{gathered} \frac{10}{12}-\text{ }\frac{3}{8} \\ \text{LCM is 24} \\ \frac{10(2)\text{ - 3(3)}}{24} \\ \frac{20\text{ - }9}{24} \\ \frac{11}{24} \\ \text{Converting to decimal} \\ 0.45833 \end{gathered}\)Part C) Difference between actual and estimate
0.45833 - 0.458
The difference is 0.00033.
The difference between the actual and estimate is quite small and unreasonable
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
A number, x, increased by 5 is the same
as twice the same number, decreased
by seven.
Answer:
n = 12
Step-by-step explanation:
n + 5 = 2n - 7
7+5=2n-n
12=n
12+5=2(12)-7
Births in Vietnam: In Vietnam, the probability of a baby being a boy is 0.526 (based on the
data available at this writing). For a family having four children, find the following.
a. The probability that the first child is a girl.
b. The probability that all four children are girls.
c. The probability that all four children are boys.
d. The probability that at least one of the children is a girl
In Vietnam, the probability of a baby being a boy is 0.526, Then the
(a) The probability that the first child is a girl P(G) = 0.474
(b) The probability that all four children are girls P(all Girls) = 0.05
(c) The probability that all four children are girls P(all Boys) = 0.076
(d) The probability that at least one of the children is a girl P(at least one girl) = 0.924
Based on the given conditions,
In Vietnam, the probability of a baby being a boy is 0.526
For a family having four children,
So,
(a) The probability that the first child is a girl.
P(B) = 0.526
The probability of having a boy is given in the problem, and we can take the complement to find the probability of having a girl because if the baby is not a boy, it must be a girl.
We can write,
P(G) = 1 - 0.526
P(G) = 0.474
Then,
The probability that the first child is a girl P(G) = 0.474
(b) The probability that all four children are girls
P(all Girls) = \((0.474)^{4}\)
Calculate the probability that all the children are girls using the Multiplication Rule, which for independent events lets us raise the probability of one event to a power n to find the probability of only that event happening n times in a row.
P(all Girls) = 0.05
Then,
The probability that all four children are girls P(all Girls) = 0.05
(c) The probability that all four children are boys
P(all Boys) = \((0.526)^{4}\)
Calculate the probability that all the children are boys using the Multiplication Rule, which for independent events lets us raise the probability of one event to a power n to find the probability of only that event happening n times in a row.
P(all Boys) = 0.076
Then,
The probability that all four children are girls P(all Boys) = 0.076
(d) The probability that at least one of the children is a girl
P(at least one girl) = 1 - 0.076
Take the complement of the probability they are all boys to get the probability of at least one girl.
P(at least one girl) = 0.924
Then,
The probability that at least one of the children is a girl P(at least one girl) = 0.924
Therefore,
(a) The probability that the first child is a girl P(G) = 0.474
(b) The probability that all four children are girls P(all Girls) = 0.05
(c) The probability that all four children are girls P(all Boys) = 0.076
(d) The probability that at least one of the children is a girl P(at least one girl) = 0.924
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Select all quadrilaterals that have 180 degree rotational symmetry,
A. trapezoid
B. isosceles tapezoid
parallelogram
D. rhombus
E. rectangle
F. square
Parallelogram and Rectangle has rotational symmetry of 180 degree.
Trapezoid has rotational symmetry = 360 degree.
Isosceles Trapezoid has rotational symmetry = 360 degree.
Parallelogram has rotational symmetry = 180 degree.
Rhombus has rotational symmetry = 90 degree.
Rectangle has rotational symmetry = 180 degree.
Square has rotational symmetry = 90 degree.
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Roberto took a sample of 5 recent matches for his favorite soccer team. Here is how many goals the team scored in each match: 0, 2, 1, 2, 5 Roberto found the mean was xˉ=2 goals. He thinks the standard deviation is sx =(2−2)2 + (1−2)2 +(2−2)2 +(5−2)24−−−−−−−−−−−−−−−−−−−−√ What is the error in Roberto's standard deviation calculation?
Roberto did not include the first term of the numerator (0-2)^2 in his calculation.
The mean of the data is also known as average.
Given the set of data 0, 2, 1, 2, 5
Mean = 0+2+1+2+5/5
Mean = 10/5
Mean = 2.0
To get the standard deviation, we will use the SD formula as shown:
\(\sigma=\sqrt{\frac{\sum (x-\overline x)^2}{N} }\)
\(\sigma =\sqrt{ \frac{(0-2)^2+(2-2)^2+(1-2)^2+(2-2)^2+(5-2)^2}{5}}\\ \sigma = \sqrt{\frac{4+0+1+0+9}{5}} \\\sigma = \sqrt{\frac{14}{5} }\\\sigma = 1.673\)
Comparing this with Roberto's calculation, we can see that Roberto did not include the first term of the numerator (0-2)^2 in his calculation.
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Answer:
B
Step-by-step explanation:
25 POINTS!!! answer the question and ill give brainliest if your correct.
Answer:
qwertyuiopplkhgf12345678rrd6
Step-by-step explanation:
Preciate ittttttttttt
NEED HELP PLEASE!! Don’t know how to do this
By working with percentages we will see that the down payment is of $11,010 and the first monthly payment is of $275.25
How to work with percentages?
First, the total cost is $110,100.
And we know that you initially pay the 10% of that, so the amount that you pay initially is:
P = 0.10* $110,100 = $11,010
So the down payment is of $11,010
The rest is financed over 30 years, so the rest is:
$110,100 - $11,010 = $99,090
Dividing by the number of months:
N = ( $99,090)/(30*12) = $275.25
And there is an interest of the 9%, then the amount that you pay on month x is given by:
\(P(x) = $275.25*(1.09)^{x-1}\)
Currently (on the first month, so x = 1)
Your pay will be of $275.25
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Help Quickly! The table shows bear population data gathered by researchers in the Wild Horse Forest. If the total bear population was 2,008 bears in May 2002, estimate the number of total bears counted in 2002 to complete the chart. (Click the picture to zoom in more)
A. 1,060 bears
B. 2,008 bears
C. 1,101 bears
D. 1,823 bears
The number of total bears counted in 2002 will be: A. 1060 bears.
How to determine the total bear estimateTo determine the total bear estimate, we will use the mark-recapture formula. In this formula, we equate the number of the population to MC/R where:
M = Number marked initially
C = Number captured in the second sample
R = The recaptured number
Also, R/C = M/N
For the given problem,
M = 2008
C = 38
R = 72
So, N = 2008 * 38/72
= 1059 approximately 1060 bears.
So, the bear population will amount to 1060.
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The graph of the function f(x) = (x-4)(x + 1) is shown
below.
4-2
64
Mark this and return
6
2
T
6
2
6
X
Which statement about the function is true?
The function is increasing for all real values of x
where
x<0.
O The function is increasing for all real values of x
where
x < -1 and where x > 4.
O The function is decreasing for all real values of x
where
-1 < x < 4.
O The function is decreasing for all real values of x
where
x < 1.5.
Answer: The function is decreasing for all real values of x where x < 1.5.
Step-by-step explanation:
The axis of symmetry is \(x=\frac{4-1}{2}=1.5\)
Since the coefficient of \(x^2\) is positive, the graph opens upwards.
So, the function is decreasing for all real values of x where x < 1.5.
Point E is added to the given figure so that point E lies on segment BD exactly halfway between points B and D. Which statement correctly compares the angle measures?
Answer:
there is no picture but m∠EBD = m∠EBD would be one of the best one as a guess to what the photo might be
Step-by-step explanation:
Point E is added to the given figure so that point E lies on segment BD and it is exactly halfway between points B and D
rolan painted his bedroom using 5/6 liters of brown paint and 2/3 liter of green paint. how much was used in all?
I hope someone answer it :(
Answer:
9/6 or 1 1/2 liters of paint
Question 1 (Essay Worth 10 points) (07.02 HC) A chef draws cookies randomly from a box containing 6 cookies of the same shape and size. There Is 1 chocolate cookle, 3 almond cookies, and 2 butter cookies. He draws 1 cookle and then draws another cookie without replacing the first one. Find the probability of picking 1 almond cookie followed by another almond cookie, and show the equation used.
Probability of picking two almond cookies = 1 / 5
Calculation of Probability Probability Formula = Favourable outcomes / Total outcomes Total outcomes, given = 6 cookies Pr (first almond cookie) = 3 / 6 Pr (second almond cookie), without replacement = 2 / 5 So, Prob (Two almond cookies) = ( 3 / 6 ) x ( 2 / 5 ) 6 / 30 = 1 / 5
Marni has 24 ounces of walnuts. she needs 14 ounces for one recipe and 1/2 pounds for another. how many total ounces does she need to make her recipes?
The total ounces she needs to make her recipes is 22 ounces
Calculating quantityFrom the question, we are to determine how many total ounces Marni needs to make her recipe
From the given information,
Marni has 24 ounces of walnuts
Also,
She needs 14 ounces for one recipe
and
1/2 pounds for another
First, we will convert 1/2 pounds to ounces
NOTE: 1 pound = 16 ounces
∴ 1/2 pound = 8 ounces
Then, we can rewrite that
She needs 14 ounces for one recipe
and
8 ounces for another
The total ounces she needs to make her recipes = 14 ounces + 8 ounces
The total ounces she needs to make her recipes = 22 ounces
Hence, the total ounces she needs to make her recipes is 22 ounces
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A test has 4 true/false questions and 3 multiple choice questions (answers a, b, c). We assume that each question only has one correct answer.
(a) In how many different ways can this test be answered if each question is answered?
(b) If a person randomly guesses an answer for each question, what is the probability that he answers ALL questions correctly?
(c) If a person guesses an answer for each question, what is the probability that he gets them ALL wrong?
(d) If a person guesses an answer for each question, what is the probability that he gets AT LEAST ONE answer correctly?
a) There are 16 x 27 = 432 different ways to answer the entire test.
b) The probability is 1/432.
c) The probability is 1/54.
d) The probability is 53/54.
(a) Since there are 4 true/false questions and 2 choices for each question, there are\(2^4 = 16\) ways to answer these questions. Similarly, there are 3 multiple choice questions with 3 choices each, so there are \(3^3 = 27\) ways to answer these questions.
(b) If a person randomly guesses an answer for each question, the probability of getting all 4 true/false questions correct is \((1/2)^4 = 1/16,\)and the probability of getting all 3 multiple choice questions correct is \((1/3)^3 = 1/27.\) To find the probability of getting all questions correct, we multiply these probabilities: (1/16) x (1/27) = 1/432.
(c) Similarly, the probability of getting all 4 true/false questions wrong is also\((1/2)^4 = 1/16\), and the probability of getting all 3 multiple choice questions wrong is \((2/3)^3 = 8/27\). To find the probability of getting all questions wrong, we multiply these probabilities: (1/16) x (8/27) = 1/54.
(d) The probability of not getting any answer correct is the same as getting all answers wrong, which we found to be 1/54. Therefore, the probability of getting at least one answer correct is 1 - 1/54 = 53/54.
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digit shows a number written in words 2. expanded form shows a number written using digits 3. period one of the numerals from 0 to 9 4. place value the position of a digit in a number, which determines its value 5. standard form each three-digit part of a whole number, separated by commas 6. word form shows a number written as an addition statement
The statements can be arranged correctly as follows:
1. Word Form shows a number written in words.
2. Standard form shows a number written using digits.
3. Digit is one of the numerals from 0 to 9
4. Place value the position of a digit in a number, which determines its value.
5. Period each three-digit part of a whole number, separated by commas
6. Expanded form shows a number written as an addition statement
How to determine the termsWe can determine the terms by first understanding the mathematical meanings. Word form is a term used in math to denote expressions written in word B.
Also, the standard form is a way of shortening large numerical values using digits. Digits are single numbers that run between 0 to 9 and they make up the higher values of numbers.
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Write the set using the roster method.
Set D is the set of positive two-digit even numbers greater than 74
that do not contain the digit 8
.
The set using Roster method is, D = {76, 90, 92, 94, 96}
What is Roster Method?The roster technique is defined as a method for displaying the elements of a set by listing the elements within brackets.
A roster method example is to write the set of numbers from 1 to 10 as
{1, 2, 3, 4, 5, 6, 7, 8, 9, and 10}.
Given:
Set D is the set of positive two-digit even numbers greater than 74
that do not contain the digit 8
First, Even numbers greater than 74 are
76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98.
Now, Even Number doe not contain 8 are 76, 90, 92, 94, 96.
Using Roster method the set is
D= {76, 90, 92, 94, 96}
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If cos(o) = 3/V24and angle o is in Quadrant I, what is the exact value of tan(2o) insimplest radical form?
In order to solve this question, we need to use the following properties of trigonometric functions:
\(\begin{gathered} \tan \theta=\frac{\sin\theta}{\cos\theta} \\ \\ \sin 2\theta=2\sin ^{}\theta\cos \theta \\ \\ \cos 2\theta=\cos ^2\theta-\sin ^2\theta \\ \\ \sin ^2\theta=1-\cos ^2\theta\text{ }\Rightarrow\sin \theta=\sqrt[]{1-\cos ^2\theta} \end{gathered}\)Using those properties, we can write tan2θ in terms of cosθ, and then use the given information cosθ = 3/√24.
We have:
\(\begin{gathered} \tan 2\theta=\frac{\sin 2\theta}{\cos 2\theta} \\ \\ =\frac{2\sin \theta\cos \theta}{\cos ^2\theta-\sin ^2\theta} \\ \\ =\frac{2\cos \theta\sqrt[]{1-\cos^2\theta}}{\cos ^2\theta-(1-\cos ^2\theta)} \\ \\ =\frac{2\cos \theta\sqrt[]{1-\cos^2\theta}}{2\cos ^2\theta-1} \\ \\ =\frac{2\cdot\frac{3}{\sqrt[]{24}}\sqrt[]{1-\frac{9}{24}}}{2\cdot\frac{9}{24}-1} \\ \\ =\frac{2\cdot\frac{3}{\sqrt[]{24}}\sqrt[]{\frac{15}{24}}}{\frac{9}{12}-1} \\ \\ =\frac{\frac{6}{24}\sqrt[]{15}}{-\frac{3}{12}} \\ \\ =\frac{6}{24}\cdot(-\frac{12}{3})\sqrt[]{15} \\ \\ =-\sqrt[]{15} \end{gathered}\)Therefore:
\(\tan 2\theta=-\sqrt[]{15}\)Find the perimeter of this shape
The perimeter of the given shape as represented in the task content is; 29 cm.
What is the perimeter of the given shape?It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.
Since each grid line has 1cm as it's length;
The perimeter of the shape is the sum of all side lengths of the shape;
Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1
P = 29 cm
Hence, the perimeter of the shape is; 29 cm.
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lisa made 300 doller in 6 hours. find the untit rate
Answer:
Step-by-step explanation:
The unit rate is 50
Hope it helps