The grid below contains the $16$ points whose $x$- and $y$-coordinates are in the set $\{0,1,2,3\}$:A square with all four of its vertices among these $16$ points has area $A$. What is the sum of all possible values of $A$

The Formula is p(A and B) = p(A) * p(B|A)

1) In general, the formula for finding the probability of the intersection of two events, A and B, is:

p(A and B) = p(A) * p(B|A)

This is also known as the conditional probability formula, where p(B|A) is the probability of event B occurring given that event A has already occurred.

2) The addition rule for disjoint events is:

p(A or B) = p(A) + p(B)

This rule applies when events A and B are disjoint, meaning they cannot occur at the same time. In other words, the two events have no common outcomes.

The general addition rule, on the other hand, is:

p(A or B) = p(A) + p(B) - p(A and B)

This rule applies when events A and B are not disjoint, meaning they can occur at the same time. In this case, we need to subtract the probability of the intersection of A and B, as we have double-counted the outcomes that are common to both events.

3) Joint probability refers to the probability of two or more events occurring together, also known as the probability of the intersection of the events. It is the probability of multiple events occurring at the same time.

4) Conditional probability refers to the probability of an event occurring, given that another event has already occurred. It is the probability of an event A happening, given that event B has already happened. The conditional probability of A given B is represented as P(A|B).

5) Conditional probability is the probability of an event occurring given that another event has already occurred. It is a way to express how likely an event is given that another event has already occurred. It is represented as P(A|B) where A and B are events, it is the probability of event A happening given that event B has already happened.

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sin 60= x/10

that is.

sin 60×10=x

(√3/2) × 10= x.

x= 5√3

The value of the size of angle PSQ of the given triangle is; 61°

From the given triangle ΔPQR, we see that;

m∠QPS = 65°

m∠PRQ = 43°

Now, it is clear that Line PSR is a straight line divided in the ratio;

size of angle PQS : size of angle SQR = 3:1

m∠PQS : m∠SQR = 3:1

Thus, since sum of angles in a triangle is 180°, then we say that;

∠PQR = 180° - (∠QPS + ∠PRQ)

Plugging in the relevant values;

∠PQR = 180° - (65° + 43°)

∠PQR = 72°

Using the concept of angle addition postulate, we have that;

∠PQR = m∠PQS + m∠SQR

Since m∠PQS : m∠SQR = 3:1, then we have;

m∠PQS = 3 × m∠SQR

Thus;

∠PQR =  (3 × m∠SQR) + m∠SQR

∠PQR = 4 × m∠SQR

4 × m∠SQR = ∠PQR

4 × m∠SQR  = 72°

m∠SQR = 72°/4

m∠SQR  = 18°

m∠PQS = 3 × m∠SQR

m∠PQS = 3 × 18°

m∠PQS  = 54°

Finally;

∠PSQ = 180° - (65° + 54°)

∠PSQ  = 61°

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Answer:

272 units^2

Step-by-step explanation:

1) Find area of whole figure which is a trapezoid.

Area of trapezoid = ((18+34)/2)*16 We are adding the bases, dividing by 2 and multiplying by height. This is the formula to find the area of a trapezoid.

So Area of trapezoid = 416 units^2

2) Find area of non-shaded figure which is a triangle.

Base= 18, Height= 16

Area of triangle = (16*18)/2 We are multiplying the base and height which is the formula to find the area of a triangle.

So Area of triangle = 144 units^2

3) Subtract non-shaded figure from whole figure to get shaded figure.

416-144 = 272 units^2

Hope this helps :)

Answer:

A = 18π cm²

Step-by-step explanation:

the area (A) of the shaded sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{80}{360}[/tex] ( r is the radius , here r = 9 )

 = π × 9² × [tex]\frac{8}{36}[/tex]

 = 81π × [tex]\frac{2}{9}[/tex]

= 9π × 2

= 18π cm²

The total number of games did they played is 80

The term total in math is also known as sum is defined as the result of arithmetically adding numbers or quantities.

Here we have given that the team wins 20 games.

And the number of games won by the team is 80% of the number of games played.

Then the calculation is done as follows:

Here let us consider that the total number of games played be 100 units.

As we can say that the number of games won by the team will be 80 units.

Then according to the question it can be written as

=> 50 units = 40

Then for 100 units (40 x 100)/80 = 80

Therefore the total number of games played by the team is 80.

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We can use algebra to set up and solve a system of equations to determine the size of a rectangle given the given information.

Step 1: Assign the rectangle's width and length the letters "w" and "l," respectively. We can determine the rectangle's 24 cm perimeter from the problem. The formula P = 2l + 2w = 24 cm can be used to draw up an equation since the perimeter of a rectangle is equal to the total of its four sides.

 Step 2: Using the additional knowledge that the length is 3 cm longer than the width, we can construct a second equation as follows: l = w + 3 cm.

Step 3: We can change the variable "l" in the first equation to read "w + 3," making P = 2(w + 3) + 2w = 24 cm. As a result, we can calculate 2w + 2(w + 3) = 24 cm.

Step 4: Finding the value of w: 24 cm = 2w + 2w + 6.

Step 5: Condensing the formula: 4w = 18 cm.

Sixth step: multiply both sides by 4 to get w = 4.5 cm.

Step 7: Using the second equation, we can get the length now that we know the width: l = w + 3 cm = 4.5 + 3 = 7.5 cm.

  Therefore the answer is option c , width is 4.5 and length is 7.5 .

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Step-by-step explanation:

61 pounds for 8 acres

1 pound for 8/61 = 0.131147541... ≈ 0.13 acres

6 pounds for $4

$1 for 6/4 = 3/2 = 1.5 pounds

Answer:

153.958 [tex]cm^{2}[/tex]

Step-by-step explanation:

a = [tex]\pi r^{2}[/tex]

a = 3.142([tex]7^{2}[/tex])     The radius is half of the diameter 14/2 = 7

a = 3.142(49)

a = 153.958

The Linear Equations that shows the given problem statement will be the ones given in option D.

i.e.

x + y = 50

2x + 3y = 120

What are linear equations?

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the C is a constant.

e.g.

y = 8x - 9    -   Linear

y = x2 - 7    -   Non-Linear, the power of the variable x is 2

Now,

Let's let x = the number of Multiple choice problems and

y = the number of free response questions.

Therefore, the equation will be

x + y = 50

Since the multiple choice problems are worth 2 points and the free response questions are worth 3 points and the total number of points is 120, then, the equation will be

2x + 3y = 120

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Answer: The Linear Equations that shows the given problem statement will be the ones given in option D.i.e.x + y = 502x + 3y = 120What are linear equations?A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the C is a constant.e.g.y = 8x - 9    -   Lineary = x2 - 7    -   Non-Linear, the power of the variable x is 2Now,Let's let x = the number of Multiple choice problems andy = the number of free response questions.Therefore, the equation will bex + y = 50Since the multiple choice problems are worth 2 points and the free response questions are worth 3 points and the total number of points is 120, then, the equation will be2x + 3y = 120

Step-by-step explanation:hope this helps 0^0

Answer:

111,111,111^2

Step-by-step explanation:

so the denominator is just 1+2+3+4+5......+8 added together multiplied by two since it goes down, then +9 as the middle. So 1+2+3....... to 8 is basically just 1+8, 2+7, 3+6, etc. so we have 4 pairs of 9 which is 36. 36*2 is equal to 72, them plus 9 is 81. 999,999,999*999,999,999 can be written as 999,999,999^2. the bottom is 81 so we can square root both top and bottom to get 999,999,999/9 right, and we just square it back so that equals 111,111,111^2 .

let me know if its correct! also pls give brainliest, thank you! :) so sorry i forgot to add the square but now its updated

The sum of the measures of the interior angles, in degrees, of a decagon (10-sided polygon) is 1440°

A polygon having ten sides (or a ten-sided polygon) is called a decagon or ten-gon, in geometry. Also, it has ten vertices and ten angles.

The summation of the interior angles of a polygon is ( n - 2 ) x 180 where n is the number of sides.

The sum of interior angles = (10 - 2) x 180

The sum of interior angles = 1440º

Therefore the measure of each angle is

10 angles = 1440

1 angle = 1440 ÷ 10 = 144º

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Answer:

  43.5 square units

Step-by-step explanation:

You want to know the area of shading in a 12 by 7 rectangle with a white right triangle of side length 9 removed.

The area of the white triangle is ...

  A = 1/2bh

  A = 1/2(9)(9) = 40.5 . . . . square units

The area of the rectangle is ...

  A = LW

  A = (12)(7) = 84 . . . . square units

The shaded area is the area of the rectangle that is not included in the triangle.

  Shaded area = 84 -40.5 = 43.5 . . . . square units

__

Additional comment

The given figure cannot actually be constructed. The triangle is too large to be inscribed in the rectangle. An inscribed right triangle can have a side length between 7 and √74 ≈ 8.6.

The three consecutive integers are 137 , 138 and 139

Given that

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Consecutive Even Numbers:

Even numbers are numbers that end with 0, 2, 4, 6 or 8. The examples of consecutive even numbers are:0, 2, 4, 6, 8, 10, 12, …

Consecutive Odd Numbers:

Odd numbers are numbers that end with 1, 3, 5, 7 or 9. The examples of consecutive odd numbers are:1, 3, 5, 7, 9, 11, 13, 15, ….

there are three consecutive integers

let's assume that consecutive integers are x, x+1 and x+ 2

given that  the sum of the first and the third number is two hundred and seventy-six

x + (x+2) = 276

2x + 2 = 276

2x = 276 - 2

2x = 274

x = 137

The three consecutive integers are 137 , 138 and 139

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This statistic is misleading because Howard surveys only his department and not members of all the departments that the company has.

When studying anything from a population, it is usual practice in statistics to identify a sample of that group.

However, the sample has to be representative.

For example: I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, let's say, 1000 randomly selected Buffalo residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. This is not representative of all New York State residents, just Buffalo residents.

Howard wants to know the proportion of employees of a company who use the company's healthcare. He asks only his department. However, a company as multiple departments, which leads to the statistics found in Howard's survey being misleading.

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if a kite is also a parallelogram, then it must be a rhombus is the correct statement

Is A rhombus a parallelogram?

Also, every rhombus is considered as a parallelogram but the converse is always not true. Parallelogram: A parallelogram is a flat-shaped figure. It has four sides. The pair of opposite faces/sides of a parallelogram are parallel and congruent to each other.

The only set of two parallelograms is the third one: square and rhombus.

Parallelograms are quadrilaterals (polygons with 4 sides) whose opposite sides are parallel.

Square, rhombus and rectangle are parallelograms.

Some kites may be parallelograms but not all the kites are parallelograms and trapezoid are not parallelograms.

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The number of ways to arrange the pets such that at least one pair of cats are next to each other is:
(n+m)!/(n!m!) - (m+n-1)!/(m!(n-1)!). Considering n as catcats and m as dogs

There are a few different ways to approach this problem, but one possible method is to use the complement principle, which states that the total number of ways to arrange the pets minus the number of ways to arrange them such that no cats are next to each other will give the number of ways to arrange them such that at least one pair of cats are next to each other.

Let n be the number of cats and m be the number of dogs. The total number of ways to arrange the pets in a row of chairs is (n+m)!/(n!m!), which is the number of ways to arrange n identical cats and m identical dogs. To arrange the pets such that no cats are next to each other, we can first arrange the cats in n! ways and then place the dogs between the cats in (m+n-1)!/(m!(n-1)!) ways, since there are m+n-1 spaces to place the m dogs and n-1 dividers between the n cats.

Therefore, the number of ways to arrange the pets such that at least one pair of cats are next to each other is:
(n+m)!/(n!m!) - (m+n-1)!/(m!(n-1)!)

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Answer: 67 degrees

Step-by-step explanation: If you add two angles together, this is actually equal to the second angle because it has to be if you pay attention to the complementary angles.

To find the number of distinct possibilities for the values in the diagonal going from the top left to the bottom right of a BINGO card, we need to look at the values in each of the five squares that make up the diagonal.

In the first column, there are 5 possible values (1-15), in the second column, there are 4 possible values (16-30), in the third column there are no possible values because the middle square is WILD, in the fourth column there are 4 possible values (46-60) and in the fifth column there are 5 possible values (61-75).

We need to find the total number of possible combinations of these values. To find the total number of combinations, we can use the formula for combination:

C(n, k) = n! / (k! (n-k)!)

where n is the number of items to choose from and k is the number of items to choose.

In this case, we have 5 items to choose from in the first column, 4 items in the second column, 0 items in the third column, 4 items in the fourth column and 5 items in the fifth column. So we have:

C(5, 1) * C(4, 1) * C(0, 0) * C(4, 1) * C(5, 1) = 5 * 4 * 1 * 4 * 5 = 400

There are 400 distinct possibilities for the values in the diagonal going from top left to the bottom right of a BINGO card.

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Answer: 26

Step-by-step explanation:

Simplify
2x-6y
Plug in numbers
2(4)-6(-3)

Answer:

26

Step-by-step explanation:

We want to find the value of the following expression:

[tex](x-3y)2[/tex]

We are given the following variable values:

[tex]x=4[/tex]

[tex]y=-3[/tex]

Start by simplifying the given expression with the distributive property:

[tex]2x-6y[/tex]

Now, plug in the provided variable values:

[tex]2(4)-6(-3)[/tex]

Simplify:

[tex]8+18[/tex]

Finally, add to get the simplified expression:

[tex]26[/tex]

The product of the value of the area of square ABCD and the value of the perimeter of square ABCD is 500 cm^3.

According to the provided data, as each dot is 1 cm from its nearest horizontal and vertical neighbors and the square is located on the 5 by 5 square grid, the length of each side of square is 5 cm. The formula for the area of square is given by:

Area = s^2 where s is the side of a square

When s = 5 cm

Area = 5^2 = 25 cm^2

The formula for the perimeter of square is given by:

Perimeter = 4s

Perimeter = 4(5) = 20 cm

Hence, the product of the area and perimeter = 25cm^2*20cm = 500 cm^3.

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To compare the costs of the two cell phone packages, we need to find the total cost for a given amount of talk-time.

(i) Linear equations representing the packages of a company A and B are : (a) y=34 + 0.5 x, y= 40 +0.4 x

(ii) If the average number of minutes used monthly by Sunil is 1160, then which of the following is true?

(a) Company A offers the better package.

(iii) If Sunita pays a total bill of Rs 208 to company B then the number of minutes used by her:

(b) 420

(iv) The shape of the graph represented by the equations in part (i) is :

(d) Pair of lines

(v) The number of minutes of talk time that results in equal monthly bills from both the companies is :

(c) 55

For Company A, the total cost for x minutes of talk-time is given by the equation:

C(x) = 32 + (0.07x)

For Company B, the total cost for x minutes of talk-time is given by the equation:

C(x) = 47 + (0.06x)

To compare the costs, we need to find the value of x for which the two costs are equal. We can set the two equations equal to each other and solve for x:

32 + (0.07x) = 47 + (0.06x)

Subtracting 32 from both sides we get:

(0.07x) = (47-32) + (0.06x)

Simplifying we get:

0.01x = 15

x = 1500

So, for 1500 minutes of talk-time, the two companies have the same cost.

For more than 1500 minutes of talk-time, company A is cheaper, for less than 1500 minutes of talk-time company B is cheaper.

This means that if you are a heavy talker, company A is the better option for you. But if you don't talk much, company B is cheaper.

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Complete Question is:

Two cell phone companies offer different packages. Company A charges a fixed monthly fees of  Rs 34 plus Rs 0.5/ minute talk time. Company B charges a fixed monthly fees of Rs 40 plus Rs  0.4 / minute talk time. Take x as the charges per minute for the talk time and y as the total amount. Based on above information answer the following question: (i) Linear equations representing the packages of a company A and B are : (a) y=34 + 0.5 x, y= 40 +0.4 x (b) y=34 + 0.4 x, y= 40 +0.5 x (c ) x=34 + 0.5 x, y= 40 +0.4 y (d) x=34 + 0.4y, y= 40 +0.5y (ii) If the average number of minutes used monthly by Sunil is 1160, then which of the  following is true? (a) Company A offers the better package (b)Company B offers the better  package (c ) Both companies offer the same package (d) None of the above (iii) If Sunita pays a total bill of Rs 208 to company B then the number of minutes used  by her : (a) 400  (b) 420 (c) 410 (d)390 (iv) The shape of the graph represented by the equations in part (i) is : (a) Rectangle (b) Circle (c) Parabola (d) Pair of lines (v) The number of minutes of talk time that results in equal monthly bills from both the  companies is : (a) 50  (b) 60  (c) 55  (d)65  

The equation of the tangent line at any point on the curve is y = f'(x)x + c. For the line to be horizontal, its slope has to be zero, meaning that f'(x) = 0. Therefore, the coordinates of all points on the curve with a horizontal tangent line are those points (x, f(x)) such that f'(x) = 0.

The equation for any line tangent to a curve at a given point (x, f(x)) is given by the equation y = f'(x)x + c, where c is a constant. This equation is derived from the definition of the derivative, which is the instantaneous rate of change of a function at a given point. The slope of this line is equal to the derivative of the curve at the given point, or f'(x). A line is horizontal when its slope is equal to zero, meaning that f'(x) = 0. Therefore, the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal are all points (x, f(x)) such that f'(x) = 0. This is because a line with a slope of zero is always horizontal, regardless of the value of the constant c. So, in order to find the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal, we must find all points (x, f(x)) such that f'(x) = 0.

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Answer:

Slope of a parallel line :      [tex]\boxed{-\frac{7}{5}}[/tex]

Slope of a perpendicular line:      [tex]\boxed{\frac{5}{7}}[/tex]

Step-by-step explanation:

Parallel lines have same slope

Perpendicular line will have a slope which is the negative of the reciprocal of the line. In other words, the product of the two slopes should be - 1

[tex]\textrm{First convert the line equation to slope-intercept form } y = mx + b\\\\-7x - 5y = -1\\\\\textrm{Add 7x to both sides }\\\\-5y = 7x -1\\\\\textrm{Divide both sides by -5}\\\\y = -\dfrac{7}{5} x+ \dfrac{1}{5}\\\\[/tex]

The slope of this line is
[tex]-\dfrac{7}{5}[/tex]
which is the coefficient of x

A parallel line will also have the same slope of
[tex]-\dfrac{7}{5}[/tex]  
ANSWER 1

A perpendicular line will have slope
[tex]- \dfrac{1}{-\dfrac{7}{5}} = \dfrac{5}{7}[/tex]
ANSWER 2

Check by multiply both slopes to see if it results in  - 1

[tex]-\dfrac{7}{5} \times \dfrac{5}{7} = -1[/tex]

Step-by-step explanation:

always bring the equation into the form

y = ...

in that case the slope is simply the factor of x.

-7x - 5y = -1

-5y = 7x - 1

y = (-7/5)x + 1/5

so, the slope is -7/5.

a parallel line must have the same slope : -7/5.

a perpendicular slope turns the original y/x slope upside-down and flips the sign :

5/7

The correct answer is option D , which states that , both estimators are unbiased, and var() < var().

The efficiency pf an unbiased estimator, is known as the estimator's precision when divided by the precision's upper bound . It's the lower bound on the variance which is when  divided by the estimator's variance.

The ratio of the precisions of two unbiased estimators represents their relative efficiency . In case of a biased estimators, relative efficiency is defined as the MSE ratio.

If we want to compare the efficiency of two estimators it can be done by  simply comparing the variance of the estimators. The one having a lower variance is said to be more efficient. It should satisfy certain conditions like,

The two estimators are used to predict the same parameter of the population.

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The ratio of 2 or more integers is known as fraction. The answer to the given expression is 10

Fractions are written as a ratio of two integers. Fractions are written in the form a/b

The expression in question is given as 5/8 * 16

Simplified form of the expression

On solving, we will have;

5/8 * 16

5 * 16/8

Since the ratio of 18 to 8 is 2, hence the expression will be further simplified as;

5 * 16/8 = 5 * 2

5 * 16/8 = 10

Hence the answer to the given expression is 10

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a) To find the 5-number summary for these data, we need to find the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values.

Minimum: the smallest value in the data set
Q1: the value that separates the lowest 25% of the data from the rest
Median: the middle value of the data set (when the data is arranged in numerical order)
Q3: the value that separates the highest 25% of the data from the rest
Maximum: the largest value in the data set
b) To sketch a boxplot, we can represent the data using a box that goes from the Q1 to Q3, with a line (the median) in the middle. Whiskers extend from either end of the box to the minimum and maximum values, with any observations outside of the whiskers represented as dots (outliers).

c) The shape of the data is not specified in the problem statement. However, it can be described as skewed, symmetric or normal. The center of the data can be described as the mean or median, and the spread can be described as the range or interquartile range.

d) It is not possible to determine if there are any outliers without the data set.

Please note that the data is not provided, so the above steps are theoretical.

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The times more six letter combinations can be formed than four letter combinations will be 26² times.

It should be noted that scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.

Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format. As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation.

In this case, the number four letter combination that can be formed with the English alphabet is 26 to the fourth power. The number of six letter combination that can be formed is 26 to the sixth power.

The number of times more six letter combinations can be formed than four letter combinations will be:

= 26^6 / 26^4

= 26^2

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Answer:

26^2

Step-by-step explanation:

On solving the provided question we can say that By the help of the Trigonometry [tex]dθ/dt = (1/0.866) [-4/(82)] (-0.30) rad/sec = 0.0217 rad/sec\\[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

By the help of the Trigonometry -

θ = angle between hypotenuse and water

r = length of hypotenuse

[tex]sinθ = 4 / r\\cosθ dθ/dt = (-4/r2) dr/dt\\dθ/dt = (1/cosθ)(-4/r2) dr/dt\\dr/dt = -0.30 m/s \\[/tex]

When the line is 8m out,

r = 8m

[tex]cosθ = √(1 - sin2θ) = √[1 - (4/r)2] = √[1 - (4/8)2] ≅ 0.866\\dθ/dt = (1/0.866) [-4/(82)] (-0.30) rad/sec = 0.0217 rad/sec\\[/tex]

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