TREES From point A,
the angle of elevation to the top of a pine tree is 42°.
From point B,
on the same side of the tree, the angle of elevation to the top of the tree is 50°.


If point A
and point B
are located 12
feet apart and are both at ground level, what is the approximate height of the tree to the nearest foot?

Jimmy’s total income is $91838.61

You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period

The given parameters that will help us to determine the income are

wages from accounting job,             $75,937.84;

interest,                                                   $839.40

wages from museum job,                  $14,937.92;

dividends,                                                $123.45.

Therefore Jimmy's total income is the sum of all the incomes

$(75,937.84 + 839.40 + 14,937.92 + 123.45)

Total income = $91838.61

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The unit tangent vector T and the curvature k is √2/3

Unit Tangent Vector and Curvature are two important concepts in vector calculus that are used to describe the behavior of curves in space.

To find the Unit Tangent Vector, we must first find the derivative of the curve. The curve is defined as (t) = <9 cos t, 9 sin t, √(3) t>, so taking the derivative with respect to t, we get:

d(t) / dt = < -9 sin t, 9 cos t, √(3) >

Next, we want to normalize this vector to get the Unit Tangent Vector, T. To do this, we divide the vector by its magnitude, which is given by:

=> √((-9 sin t)² + (9 cos t)² + (√(3))²)

=> √(81 + 81 + 3) = 9 √(3)

So, the Unit Tangent Vector is given by:

T = d(t) / dt / |d(t) / dt|

T = < -9 sin t / 9 √(3), 9 cos t / 9 √(3), √(3) / 9 √(3) >

T = < -sin t / √(3), cos t / √(3), 1 / 3 √(3) >

To find the Curvature, we use the formula:

k = |dT / dt|

where T is the Unit Tangent Vector and dT / dt is the derivative of the Unit Tangent Vector. To find dT / dt, we take the derivative of T with respect to t:

dT / dt = < cos t / √(3), -sin t / √(3), 0 >

Finally, the magnitude of dT / dt gives us the Curvature:

=> √((cos t / √(3))² + (-sin t / √(3))² + (0)²)

=> √(1 / 3 + 1 / 3) = √(2 / 3) / √(3)

So, the Curvature is given by:

k = √(2 / 3) / √(3)

k = √2 / 3

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A calculus cheat sheet can be a helpful tool to assist you in studying and reviewing calculus concepts.

Here are some tips for how to use a calculus cheat sheet effectively:

1. Familiarize yourself with the content: Take the time to read through the entire cheat sheet to get a sense of what topics are covered and how the information is organized.

2. Use it as a study aid: A calculus cheat sheet can be a helpful study aid to review concepts and formulas before a test or exam. Work through practice problems and apply the concepts you have learned.

3. Keep it handy: Print out the cheat sheet or save it to your phone or computer so that you can refer to it whenever you need to.

4. Use it as a reference: As you work on calculus problems, use the cheat sheet to remind yourself of key concepts, formulas, and rules.

5. Customize it: You can create your own cheat sheet, which includes the formulas and concepts that you find most challenging. This will help you focus on the areas that you need to improve upon.

Remember that while a calculus cheat sheet can be a helpful tool, it is important to develop a deep understanding of calculus concepts through practice, problem-solving, and building intuition. The cheat sheet should be used as a supplement to your learning, not a replacement for it.

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Step-by-step explanation:

Perimeter of a Semicircle

[tex](\pi )(r) + 2r[/tex]

R = 0.6 since that's half the diameter

[tex](3.14)(0.6) + (2)(0.6)[/tex]

[tex]1.884 + 1.2 = 3.084[/tex]

Which rounds to 3.1

The first step is to describe the method to take

To solve the system of equations 4x + 2y = 11 and 3x - y = 9, the first step would be to choose a method to solve the system.

There are several methods for solving systems of equations, including:

One common method is the substitution method, which involves solving one equation for one variable and then substituting the expression for that variable into the other equation.

For example, we could solve the second equation 3x - y = 9 for y to get:

y = 3x + 9

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Tables and figures area way of presenting data in an organized form or more in a presentable way to attract more audience.

With tables and figures, it arranges your data to a simplified form and also it makes the content easy to understand for the front person.

Tables and figures in scientific papers are wonderful ways of presenting data. Effective data presentation in research papers requires understanding your reader and the elements that comprise a table.

It also several elements, including the legend, column titles, and body.

With all this tables in a research paper helps the reader understand the content for the data more effectively and efficiently.

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there just reflected because the shape is just refected to the other side it the same but smaller

The surface area of the given pyramid is 336 square feet. the correct answer would be an option (F) 336 ft².

A square pyramid's total surface area is the total area covered by its four triangular sides and square base. The formula may be used to calculate the total surface area of a square pyramid with slant height.

The surface area of a square pyramid = a² + 2al

The figure of the square pyramid is given in the question, as shown

The surface area of the pyramid = a² + 2al

Here a = 12 ft and l = 8 ft

Substitute the values of a = 12 ft and l = 8 ft in the formula,

The surface area of the pyramid = 12² + 2 × 12 × 8

The surface area of the pyramid = 336 square feet

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The question seems incomplete, the correct question would be as:

When a negative number is divided by a positive number, the result is always negative.

Let's use the example (-6) / 2 again. We can write this expression as:

(-6) / 2 = (-1) * 6 / 2

We can then simplify the expression on the right-hand side by multiplying -1 and 6, which gives us:

(-1) * 6 / 2 = -6 / 2

Now, we can divide 6 by 2, which gives us:

-6 / 2 = -3

So we see that the quotient is negative.

We can generalize this to any negative number divided by a positive number. Let's say we have a negative number -a and a positive number b. We can write the expression as:

(-a) / b = (-1) * a / b

Multiplying -1 and a gives us:

(-1) * a / b = -a / b

So we see that the quotient is negative, since -1 times a is negative, and dividing a negative number by a positive number results in a negative quotient.

Therefore, we can conclude that when a negative number is divided by a positive number, the result is always negative.

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The area of the left over wood is

Area of the kite

perimeter of the kite

The area of the left over wood is given by

= area of the circle - area of the pentagon

area of the circle

= pi * r^2

= pi * 5^2

= 78.54 square cm

area of the pentagon

= 5/2 * a * 5

solving for a

360 / 5 = 72

72 / 2 = 36

cos 36 = a / 5

a = 5 cos 36 = 4

area of the pentagon = 5/2 * 4 * 5 = 50 sq cm

left over wood = 78.54 - 50 = 28.54 square cm

Area and perimeter of kite

area of kite = product of the two diagonals

length of one of the diagonals = 2 * KT = 2 * 12 = 24 cm.

The second diagonal

tan 30 = KT / x

x = 12 / tan30 = 20.78

the length = 12 + 20.78 = 32.78

area of the kite = 32.78 * 24 = 786.72 square cm

perimeter of the kite

= addition of the sides = 2(shorter side + longer side)

Using Pythagoras rule

shorter side = √(12² + 12²) = 16.97

longer side =  √(20.78² + 12²) = 24

perimeter = 2 (16.97 + 24) = 81.94 cm

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Following are the given complete statements:

(a) Another name for plane X is plane EABC.

(b) F, D, and C are distinct points that are collinear.

(c) A, B, C and G are distinct points that are coplanar.

A plane is a flat, two-dimensional surface that extends infinitely in all directions. It is a mathematical concept used in geometry and is often represented as a flat sheet or a graph on a coordinate system. In the real world, a plane can be thought of as a flat surface such as a tabletop, a piece of paper or a wall.

(a) Another name for plane X is plane EABC.

(b) F, D, and C are distinct points that are collinear.

(c) A, B, C and G are distinct points that are coplanar.

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True. Because they have comparable angles, the offered figures are comparable figures.

Similar figures are described as two shapes that share the same shape but differ in size. For instance, similar objects are depicted but are not consistent in different-sized images of a person, such as passport size, stamp size, etc. In geometry, two comparable shapes with different side lengths or sizes are those whose dimensions are equal or have a common ratio. Examples of these shapes are similar triangles, similar rectangles, and similar squares. Scale factor is the name given to the common ratio. The matching angles are also of equal measure.

If two figures are similar, then they are represented by the symbol ‘∼’. Let us say there are two triangles, ABC and PQR, which are similar, then they are represented as;

∆ABC ~ ∆ PQR

Now if the two triangles are similar to each then their corresponding sides should be in proportion. Hence,

AB/PQ = BC/QR = AC/PR

∠A = ∠P, ∠B = ∠Q, ∠C = ∠R

Since, we can see that the angles in both the given figures are exactly the same. Thus, the given figures are similar figures.

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The value of x is 77.5. In order to solve for x, we need to use the Triangle Angle Sum Theorem.

Value is a subjective concept that referred to the word of importance that an individual group of people places on something it is often associated with principal beliefs and standard that are accepted by society when you can be seen as a measure of how important something is true person of organization it is often seen as a reflection of ones worldview and can help to save attitudes decision and behaviors believe is not an absolute and very depending on the context of the looks like commands.

In order to solve for x, we need to use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180°. Since angle BAC is bisected by segment AD, the two angles must be equal. Therefore, we can set up the following equation to solve for x:

180° = angle BAC = (x + 7) + (x + 18)

We can solve this equation by combining like terms and isolating the variable x.

180° = 2x + 25

2x = 155

x = 77.5

Therefore, the value of x is 77.5.

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Answer:

OUT OF BUSINESS

Step-by-step explanation:

you cant afford it on food stamps my guy

If the height of a triangle is 2 cm more than base and the area of the triangle is 10 cm then the height is, 7 cm

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

The area of a triangle is given by the formula:

Area = (base x height) / 2

We are given that the area is 10 cm² and that the height is 2 cm more than the base.

Let's call the base "b".

Then, the height is "b + 2".

We can substitute these values into the area formula:

10 = (b x (b + 2)) / 2

Expanding the right side:

10 = (b² + 2b) / 2

Multiplying both sides by 2:

20 = b² + 2b

Subtracting b² from both sides:

20 - b² = 2b

Factoring the left side:

(10 - b)^2 = b²

Taking the square root of both sides:

|10 - b| = b

Adding b to both sides:

10 = 2b

Dividing both sides by 2:

5 = b

So, the base of the triangle is 5 cm and the height is b + 2 = 5 + 2 = 7 cm.

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The measure of arc CDE is, 154°

The measure of arc BC is, 26°

The measure of arc AB is, 90°

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Now, By the figure, we have;

⇒ ∠APE + ∠EPD = 180°

⇒ (25x + 15)° + (33x - 9)° = 180°

⇒ 58x + 6 = 180

⇒ 58x = 180 - 6

⇒ 58x = 174

⇒ x = 3

Hence, The measure of arc CDE is,

⇒ (20x + 4)° + (33x - 9)°

⇒ (20×3 + 4)° + (33×3 - 9)°

⇒ 64° + 90°

⇒ 154°

And, The measure of arc BC is,

⇒ 90° - (20x + 4)°

⇒ 90° - (20×3 + 4)°

⇒ 90° - 64°

⇒ 26°

The measure of arc AB is,

⇒ arc AB + 90° = 180°

⇒ arc AB = 90°

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Answer:Y = 7x – 16,

y = 2(2x – 5)

Step-by-step explanation:

he answer to the system of equations is (2,-2)

First, we can substitute in  for y in the other equation

This will give us

Next, we distribute the 2 throughout the parenthesis

Now we can solve for x. Begin by adding 16 to each side

Now we can subtract 4x from each side

Lastly, we can divide each side by 3

Now, we need to substitute in the value that we got for x into one of the equations to find the y value.

This becomes

So

This means that the solution to the system of equations is (2,-2)

Answer:

Example 2:

Find m∠P  and  m∠Q

if ∠P  and  ∠Q

are supplementary, m∠P=2x+15

, and m∠Q=5x−38

.

The sum of the measures of two supplementary angles is 180°

.

So, m∠P+m∠Q=180°

Substitute 2x+15

for m∠P

and 5x−38

for m∠Q

.

2x+15+5x−38=180°

Combine the like terms. We get:

7x−23=180°

Add 23

to both the sides. We get:

7x=203°

Divide both the sides by 7

.

7x7=203°7

Simplify.

x=29°

To find m∠P

, substitute 29

for x

in 2x+15

.

2(29)+15=58+15

Simplify.

58+15=73

So, m∠P=73°

.

To find m∠Q

, substitute 29

for x

in 5x−38

.

5(29)−38=145−38

Simplify.

145−38=107

So, m∠Q=107°

.Example 2:

Find m∠P  and  m∠Q

if ∠P  and  ∠Q

are supplementary, m∠P=2x+15

, and m∠Q=5x−38

.

The sum of the measures of two supplementary angles is 180°

.

So, m∠P+m∠Q=180°

Substitute 2x+15

for m∠P

and 5x−38

for m∠Q

.

2x+15+5x−38=180°

Combine the like terms. We get:

7x−23=180°

Add 23

to both the sides. We get:

7x=203°

Divide both the sides by 7

.

7x7=203°7

Simplify.

x=29°

To find m∠P

, substitute 29

for x

in 2x+15

.

2(29)+15=58+15

Simplify.

58+15=73

So, m∠P=73°

.

To find m∠Q

, substitute 29

for x

in 5x−38

.

5(29)−38=145−38

Simplify.

145−38=107

So, m∠Q=107°

.

73 kg is equivalent to approximately 160.937 pound (lbs).

Kilogram (kg) and pound (lb) are both units of mass commonly used in different parts of the world. Kilogram is the base unit of mass in the International System of Units (SI) and is defined as the mass of the International Prototype of the Kilogram, which is a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France.

Pound, on the other hand, is a unit of mass commonly used in the United States, the United Kingdom, and other countries, which is defined as exactly 0.45359237 kilograms. This value is based on the international avoirdupois pound, which is defined as exactly 0.45359237 kg.      

To convert kilograms to pounds, you can use the conversion factor of 2.20462 lbs/kg. To convert pounds to kilograms, you can use the conversion factor of 0.45359237 kg/lb.

To convert 73 kilograms (kg) to pounds (lbs), you can use the conversion factor of 2.20462.

So,

73 kg * 2.20462 lbs/kg = 160.937 lbs (rounded to three decimal places)

Therefore, 73 kg is equivalent to approximately 160.937 lbs.

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The value of the exponent is 4¹⁴

Index forms are defined as mathematical models of writing numbers that are large or small in more convenient forms.

The other names are scientific notations and standard forms.

The rules of index forms;

From the information given, we have;

4^3/4^6 times 4^17

subtract the bases

4 ³⁻⁶ ⁺¹⁷

Add the values

4¹⁴

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Answer:

undefined slope

Step-by-step explanation:

The graph of the equation x = -5 is a vertical line That passes through point (-5, 0).

The slope of a vertical line is undefined.

The solution to the expression is x = 1/9

From the question, we have the following parameters that can be used in our computation:

27**** = 3³x² x 9​

Express properly

27 = 3³x² * 9​

We can start solving this equation by rearranging it to isolate the variable x:

27 = 243x

Now we divide both sides by 243 to find x

x = 27/243

Evaluate

x = 1/9

Hence, the solution is 1/9

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Answer:

Alaskan huskies take 10h 34min.

Siberian huskies take 8h 45min.

Step-by-step explanation:

Alaskan huskies : 15km/h + 18min rest after 3h

18/3= 6min rest/h

1h= 60min

60/15= 4min/km

4*145= 580min

         = 9h 40min

There is three 3h in 9h 40min.

3*18= 54min

9h 40min+54min= 10h 34min

Siberian huskies : 20km/h + 30min rest after 2h

30/2= 15min rest/h

60/20= 3min/km

3*145=435min

         = 7h 15min

There is three 2h in 7h 15min.

3*30= 90min

       = 1h 30min

7h 15min+1h 30min= 8h 45min

The X, Y, and Z axes define a three-dimensional coordinate system, which is commonly used to represent physical objects or mathematical functions in space.

The X, Y, and Z axes are terms commonly used in mathematics, physics, engineering, and computer graphics to refer to the three dimensions in a three-dimensional coordinate system.

The X-axis is the horizontal axis and is used to represent values along the horizontal plane. It is often called the "abscissa" and is typically drawn as a horizontal line that intersects with the Y-axis at the point where they meet, which is called the origin.

The Y-axis is the vertical axis and is used to represent values along the vertical plane. It is often called the "ordinate" and is typically drawn as a vertical line that intersects with the X-axis at the origin

.The Z-axis is the third axis and is used to represent values along the depth or height plane. It is often called the "applicate" and is typically drawn as a line that is perpendicular to both the X and Y axes, intersecting with both at the origin.

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Answer:

Below    

Step-by-step explanation:

Since all of the lines are parallel and cut by a transversal .... the

 corresponding  angles are equal

8x - 11 = 7x +8

x = 19

Answer:

Step-by-step explanation:

sin angle S = [tex]\frac{opposite}{hypotenuse}[/tex]

sin S = [tex]\frac{30}{hypotenuse}[/tex]

To complete the ratio we need to find the hypotenuse:

a² + b² = c²

16² + 30² = c²

256 +  900 = c²

1156 = c²

√1156 = √c²

34 = c

Now substitute 34 in the sin ratio:

[tex]\frac{30}{34}[/tex] = .8824

nearest hundredth = .88

Answer: To solve this problem, we can use the Pythagorean theorem. Let's call the depth of the treasure "d".

We can create a right triangle with the following sides:

The sensor on the boat is at the top of the triangle and is 200 meters away from the treasure diagonally.

The line from the sensor to the treasure, which we can call "x", is at a 25-degree angle from the surface of the water.

The line from the treasure to the ocean floor, which we can call "d", is perpendicular to the surface of the water.

Since we know that the angle of depression is 25 degrees, we can use tangent to find the length of x.

tan(25) = x/d

x = d * tan(25)

Now, we have two sides of a right triangle and can use the Pythagorean theorem to find d:

x^2 + d^2 = 200^2

d^2 = 200^2 - x^2

d^2 = 200^2 - (d * tan(25))^2

Solving for d, we find that d = 174.59 meters. Rounding to the nearest tenth of a meter, we get d = 174.6 meters.

Step-by-step explanation:

Answer:

The solution to this problem is x = 26 over 11 , y =  6 over 11.

Step-by-step explanation:

Hope this helped!

Errors in calculations are mistakes or inaccuracies that occur when performing mathematical calculations. They can be caused by a variety of factors, including human error, equipment malfunction, incorrect assumptions or data, and flawed methodology.

There are several types of errors that can occur in calculations, including:

Transcription errors: These occur when a number or a calculation is copied down incorrectly from one place to another, such as from a calculator to a piece of paper.

Calculation errors: These occur when the wrong calculation is used, or when a mistake is made in performing a calculation, such as forgetting to carry a digit when doing long division.

Rounding errors: These occur when numbers are rounded to a certain number of decimal places, and the resulting calculation is not as precise as it could be.

Measurement errors: These occur when the instruments used to measure quantities are not accurate, or when the measurements are not taken correctly.

Conceptual errors: These occur when the underlying concepts or principles of the problem are not fully understood, leading to incorrect calculations.

It is important to identify and correct errors in calculations to ensure the accuracy and validity of the results. Checking calculations multiple times and using multiple methods of verification can help to reduce the risk of errors.

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The principal sum of the given compound interest is Rs 5000.

The total amount of money borrowed (or invested), not including any interest or dividends, also called sum.

Given that, a sum of money amounts to Rs. 6050 in 2 year and Rs. 6655 in 3 years. we are asked to find the principal amount or sum,

CI = P(1+r/100)ⁿ

P = principal amount, CI =  compound interest, r = rate, n = time

Therefore,

CI = 6050(1+r/100)²....(i)

CI = 6655(1+r/100)³....(ii)

Diving eq(ii) by eq(i)

6655 / 6050  = (1+r/100)

1+r/100 = 1.1

r/100 = 1.1-1

r/100 = 0.1

r = 10%

Put r = 10% in eq(i)

6050 = p(1.1)²

p = 5000

Hence, the principal sum of the given compound interest is Rs 5000.

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