Two lamp posts are of equal height. A boy standing mid-way between then observes the elevation of the top of either post to be 30∘. After walking 15 m towards one of them, he observes the elevation of it stop to be 45∘. Find the heights of the posts and the distance between them.​(Ans:20.49m,70.98m)

Answer:

10.7 °

Step-by-step explanation:

In this problem, there are two angles with degrees of 2x + 6 and two angles of degrees of 15x - 8. We know the sum of the four angles is 360, as stated in the problem. Thus we can set up the following equation:

2(2x + 6) + 2(15x - 8) = 360

4x + 12 + 30x -16 = 360

34x - 4 = 360

34x = 364

x ≈ 10.7 °

The length of the cable is, 252.57 m.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A cable is used to support a 245-m television tower.

And, the angle the cable makes with the ground is 78°.

Let the length of the cable = x

Hence, We can formulate;

⇒ sin 78° = 245 / x

⇒ 0.97 = 245 / x

⇒ x = 245/0.97

⇒ x = 252.57 m

Thus, The length of the cable is, 252.57 m.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The temperature of the hot chocolate will decrease over time and after 4 minutes, it will be around 56 degrees Fahrenheit.

When you put something hot into a freezer, the temperature of the item will decrease over time until it reaches the temperature of the freezer. The rate of temperature decrease depends on the difference between the original temperature and the temperature of the freezer. In this case, the difference is 190 degrees Fahrenheit. The rate of temperature decrease should be roughly 1 degree Fahrenheit per second. After 4 minutes, the temperature of the hot chocolate should be around 56 degrees Fahrenheit. This is because, after 4 minutes, the hot chocolate would have lost around 190-56 = 134 degrees Fahrenheit of temperature. To be more precise, you would have to factor in how quickly the freezer can cool the hot chocolate, which is usually related to the size of the freezer, the size of the container the hot chocolate is in, and the amount of hot chocolate.

Learn more about temperature here

https://brainly.com/question/29768169

#SPJ4

Answer:

Kurt originally knitted the scarf to be 3.75 feet + 0.5 feet = 4.25 feet long.

I found the answer by using basic addition. I added the length that Kurt had to unravel (0.5 feet) to the remaining length of the scarf (3.75 feet) to find the original length of the scarf (4.25 feet).

Step-by-step explanation:

The height of the other tree is 7.25 meters

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

Using the above as a guide, we have the following:

Ratio = Height : Shadow

So, we have

Height : Shadow = 4 : 16

Simplify

Height : Shadow = 1 : 4

So, we have

Height : 29 = 1 : 4

This means that

Height = 29 * 1/4

Evaluate

Height = 7.25

Hence the height is 7.25 meters

Read more about similar shapes at

https://brainly.com/question/14285697

#SPJ1

Answer:

The height of the other tree is 7.25 meters

Step-by-step explanation:

The First graph represents the equation y = 3x

The y intercept = 1.5

The horizontal asymptote = infinity

The y -intercept is a point at which the graph of the function touches the y -axis. It is only possible for a function to have zero or one y -intercept.

A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.

Therefore the y intercept is 1.5 from the graph. and the horizontal asymptote is infinity

The power of the numerator is great than that of denominator.

3x²/1x^0

= 2/0

= infinity.

learn more about intercept and horizontal asymptote from

https://brainly.com/question/27171654

#SPJ1

Rounding to 2 decimal places, the shaded area is 234 cm².

What is the radius of circle?

The radius of a circle is the distance from the center of the circle to any point on the circumference of the circle. It is half of the diameter of the circle.

The diameter of the circle is 0.2 meters, which means the radius of the circle is 0.2 / 2 = 0.1 meters.

The height of the square is a fifth of the diameter of the circle, so the height of the square is 0.2 / 5 = 0.04 meters.

To find the shaded area in cm, we need to find the area of the circle and subtract the area of the square. The area of the circle is given by the formula πr², where r is the radius of the circle. The area of the square is simply the height multiplied by the width, which is equal to the diameter of the circle.

So, the area of the circle is π * 0.1² = 0.0314 square meters. The area of the square is 0.2 * 0.04 = 0.008 square meters. The shaded area is the difference between these two, or 0.0314 - 0.008 = 0.0234 square meters.

To convert the area to cm², we need to multiply by 10⁴. The shaded area in cm² is 0.0234 * 10⁴ = 234 cm².

Rounding to 2 decimal places, the shaded area is 234 cm^2.

To learn more about radius of circle, Visit

https://brainly.com/question/14068861

#SPJ1

The solution to the equation is a = 3 1/3

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

a + 5 and two-thirds = 9

Express properly

So, we have

a + 5 2/3 = 9

Subtract 5 2/3 from both sides of the equation

This gives

a = 9 - 5 2/3

Evaluate the difference

a = 3 1/3

Hence, the solution is a = 3 1/3

Read more about equations at

https://brainly.com/question/2972832

(a) We can represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel as f(24.9).

(b) We can represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel as f(49.71).

(a) We have to determine how can we represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel.

We can create the a table and function to describe that statement but F(24.9) is the best representation of Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel.

(b) We have to determine how can we represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel.

We can create the a table and function to describe that statement but F(49.71) is the best representation of Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel.

To learn more about function link is here

brainly.com/question/21145944

#SPJ4

The complete question is:

In the previous modules we developed formulas, tables, and graphs to represent how two varying quantities change together. For example, we considered how Kristin's height above the ground changed as her total distance traveled increased while riding a Ferris wheel.

We even assigned letters to represent the possible varying values each quantity can assume.

• Let d represent the distance Kristin has traveled (in meters) around the Ferris wheel starting at the bottom.

• Let h represent Kristin's height above the ground (in meters).

Note that the way we are thinking about this relationship is that we vary Kristin's distance traveled and observe what happens to her height above the ground.

What if you want to communicate information about her position after she traveled some number of feet? You could write it out in words, like "Kristin was 16.3 meters above the ground when she had traveled 23.7 meters around the Ferris wheel". However, that's a lot to have to write out, especially if you want to talk about multiple values. You could also draw a table or create a graph, but mathematicians developed a tool called function notation to help them represent values in a covarying relationship.

[Note: We will define the exact meaning of "function" later in this investigation. For now, just think of "function" as meaning the same thing as "relationship".]

First, we pick a letter to represent the name of the relationship. Let's call this relationship "f". Now, instead of saying "the relationship between Kristin's height above the ground (in meters) and her total distance traveled (in meters)" we can simply say "relationship f".

Also, we can use f(d) to represent values of Kristin's height above the ground (values of h). We read this as "f of d", and the parentheses here are just part of the notation. They do NOT indicate multiplication.

For example, f(13) represents Kristin's height above the ground (in meters) when she has traveled 13 meters around the Ferris wheel.

a. How can we represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel?

(Hint: you should use function notation.) Preview syntax error Enter an algebraic expression (more..]

b. How can we represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel? x Preview

Answer:

108 cm³

Step-by-step explanation:

V = a²(h/3) = 6²(9/3) = 36·3 = 108 cm³

The area of the given given shape which consists of a triangle and a quarter circle to 1 decimal place would be =161.04m².

The formula used to calculate the are of triangle= ½base×height.

where; Base= 12m

height= 20-12 = 8 m

area = 1/2×12×8 = 48m²

The formula for the area of a quarter circle = πr²/4

where r = 12m

Area = 3.14 × 12²/4

= 3.14×144/4

= 452.16/4

= 113.04m²

Therefore, the area of the figure = 48+ 113.04 = 161.04m²

Learn more about triangle here:

https://brainly.com/question/28470545

#SPJ1

Answer:

4min:1min

Step-by-step explanation:

60:15

divide by 5

12:3

divide by 3

4:1

When a region is rotated about the x-axis, a cylinder is formed. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder.

The volume of a cylinder is the amount of space the cylinder takes up. It is found by multiplying the area of the cylinder's base by its height. The formula for finding the volume of a cylinder is V = πr²h, where r is the radius of the cylinder's base, and h is its height.

The radius of the cylinder is equal to the distance from the x-axis to the highest point on the graph of y = 9/(x² + 3x + 2).

To find the highest point on the graph, we differentiate the function and find the critical points.

Differentiating y = 9/(x² + 3x + 2):

dy/dx = -18x / (x² + 3x + 2)²

Setting dy/dx = 0 and solving for x:

-18x / (x² + 3x + 2)² = 0

x = -3, 2

For x = -3, y = 9/(-3² + 3(-3) + 2) = 9/1 = 9

For x = 2, y = 9/(2² + 3(2) + 2) = 9/8 = 1.125

To learn more about volume of a cylinder
https://brainly.com/question/9554871
#SPJ1

Answer:

Step-by-step explanation:

4) SinC = 30/34

C = sin^-1(30/34)

C = 61.93 degrees

A = 90-61.93

A = 28.07 degrees

5) SinA = 24/26

A = sin^-1(24/26)

A = 67.38

As the firm develops a specific sort of sensor and ships them in boxes of four, each sensor weighed 10 grams at first.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

Let's call the original weight of each sensor "w". The total weight of 4 sensors would be 4w.

With the new design, each sensor weighs 9 grams more, so each sensor weighs w + 9 grams. The total weight of 4 sensors is 76 grams, so we can write an equation:

4(w + 9) = 76

Expanding the left-hand side and solving for w, we have:

4w + 36 = 76

4w = 40

w = 10

So each sensor originally weighed 10 grams as company manufactures a special type of sensor, and packs them in boxes of 4 for shipment.

To know more about equation,

https://brainly.com/question/2228446

#SPJ4

The measure of <D is 130 degree.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given:

<C= (x-4)

and, <D = 9x+ 4

and, <E = 2x+ 12

Now, In triangle CDE using Angle Sum Property

<D+ <E+ <F= 180

x - 4+ (9x+ 4) + 2x+ 12 = 180

12x + 12 = 180

12x = 168

x= 168/12

x = 14

So, the measure of <D = 9x+ 4 = 9(14) + 4 =  130 degree.

Learn more about Angle sum Property here:

https://brainly.com/question/4316040

#SPJ1

The price paid for the chair will be $90.18

The price for the pen will be $4.23.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

The price paid for the chair will be:

= $83.50 + (8% × $83.50)

= $90.18

The price for the pen will be:

= $4.50 - (60% × 4.50)

= $4.23

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

LN is tangent to circle O at point M and QM is a diameter. The measure of ∠QML and ∠PMN are 90° and 63° respectively.

1) To Determine the degree measurement of ∠QML

Based on the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection

So, the radius OM is perpendicular to line LN at point M.

Hence,

The value of ∠QML = 90°

2) To determine the degree measurement of angle PMN

∠QMN = ∠QMP + ∠PMN

By the angle addition postulate, we can calculate this measurement as follows:

∠QMN = 90°

∠QMP = 27°

Replace with and substitute the value of angle QML into the equation.

90° = 27° + ∠PMN

∠PMN = 90° - 27° = 63°

Therefore, the value of  ∠PMN is 63°

Learn more about perpendicular tangent theorem here brainly.com/question/30306156

#SPJ4

Answer:

1 1/3  or just 1/3

Step-by-step explanation:

What percent of the shape is shaded in?

Alright to start, let's look at the shape, it is divided into 4 equal parts, one part is shaded, which gives us 1/4, or 25% or 0.25. Then there's another part, which is half shaded, that'll be half of 1/4 or 25% or 0.25, which is 1/8 or 12.5% or 0.125. Now all you have to do is add them together.

1/4 + 1/8 = 3/8

25% + 12.5% = 37.5%

0.25 + 0.125 = 0.3725

These are your three answers you can choose from, I guess the second one won't work because the problem states not to include a % sign.

Hope this helped!

The amount in the account after t years is given as follows:

A(t) = A(0)(1 + r)^t.

In which:

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

For an increasing exponential function, the rate of change is given as follows:

b = 1 + r.

In which r is the growth rate, as a decimal.

Considering that the balance increases according to the yearly dividend, the equation is given as follows:

A(t) = A(0)(1 + r)^t.

The problem is incomplete, hence the general procedure in obtaining the equation was presented, which can be used to analyze the statements.

More can be learned about exponential functions at https://brainly.com/question/30113628

#SPJ1

Answer:

c (c - 8)

Step-by-step explanation:

c² - 8c

First, you have to find the GCF

The Greatest Common Factor is the factor that all have in common. Here the GCF is c

So, we factor c out and has left (c - 8)

So, our equation is

c (c - 8)

The factor of quadratic equation is x√17

A quadratic equation is one that contains a second-degree polynomial. They are extensively utilized in a wide range of disciplines, including engineering, architecture, finance, biology, and, of course, mathematics.

Factoring is frequently the simplest way to solve a quadratic equation. Finding expressions that can be multiplied together to get the expression on one side of the problem is the process of factoring. A quadratic equation is represented as a product of linear terms if it can be factored.

First you need to find perfect square factors of 17

17 = 1*17

√17  = √1*√17 = 1√17 = √17

we had also √x² = x

So the answer is x√17

To learn more about quadratic equation visit:

brainly.com/question/1863222

#SPJ1

The equations with no solutions are   −60x+32=−60x+60 and −60x+32=−60x−32. Options B and D

Algebraic expressions are described as expressions that are made up of terms, variables, coefficients, constants and factors.

They are also composed of arithmetic operations, such as;

From the information given, we have that the expression or equation without solutions are those with the value of x as 0.

−60x+32=−60x+60

collect like terms

-60x + 60x = 28

Hence, the equations are  −60x+32=−60x+60 and −60x+32=−60x−32

Learn about algebraic expressions on:

https://brainly.com/question/4344214

#SPJ1

The sum of the expressions -x² + 2 and 3x² - 7x + 8 is 2x² - 7x + 10

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Find the sum of -x² + 2 and 3x² - 7x + 8. The sum of the expression is:

= (-x² + 2) + (3x² - 7x + 8)

Collecting like terms:

= -x² + 3x² - 7x + 2 + 8

Simplifying:

= 2x² - 7x + 10

The sum is 2x² - 7x + 10

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: true

Step-by-step explanation:

The center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).

The center of gravity, or the center of mass, of a two-dimensional object can be found by taking the weighted average of the x-coordinates and y-coordinates of the individual masses making up the object.

In this case, the two circles can be treated as point masses, with the mass of each circle being proportional to its area. The area of a circle with radius r is given by pi * r^2.

So, for circle c1 with radius 2, its mass is given by:

m1 = pi * 2^2 = 4 * pi

And for circle c2 with radius 1, its mass is given by:

m2 = pi * 1^2 = pi

The x-coordinate of the center of gravity is given by the weighted average of the x-coordinates of the two masses:

x = (m1 * 0 + m2 * 0) / (m1 + m2) = 0

Similarly, the y-coordinate of the center of gravity is given by the weighted average of the y-coordinates of the two masses:

y = (m1 * 0 + m2 * 4) / (m1 + m2) = 4 * (m2 / (m1 + m2)) = 4 * (pi / (4 * pi + pi)) = 4 * (pi / 5 * pi) = 4/5

So, the center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).

Learn more about circles here :

brainly.com/question/15482239

#SPJ4

The expected value of M does not change in a predictable manner when sample size increases; it can increase, decrease, or stay the same.

The expected value of M, or the mean of a sample, is determined by the values of the individual elements that comprise it. As such, when the sample size increases, the expected value of M could increase, decrease, or remain constant, depending on the particular values of the individual elements in the sample. This is because the expected value of M is the average of the individual elements and the contribution of each element to the average depends on its value and the number of elements in the sample. Therefore, the expected value of M does not change in a predictable manner when sample size increases. Depending on the individual elements in the sample, the expected value of M could be higher, lower, or constant.

Learn more about expected value here

https://brainly.com/question/18523098

#SPJ4

The function increased to a maximum value and then decreased.

We know that a graph can be obtained when we plot the points of the data on a graph. In this case we can see that the data have been graphed accurately as we can see here.

If we look at the graph, we can see that the graph went up and then it started coming down. The implication of that is that the function has attained a maximum point and then began to decrease.

This is clear from the graph that has been shown.

Learn more about graphs:https://brainly.com/question/17267403

#SPJ1

The inequality that represents the given situation is 8x + 10y ≥ 600

and, x ≥ 40.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The cost for one calendar = $8

The cost for one coffee mug = $10

Dominique must sell at least $600 of merchandise and it should include at least 40 calendars.

let x be the number of calendars and y be the number of coffee mugs;

then, the inequality is

8x + 10y ≥ 600

and, x ≥ 40

Learn more about inequality here:

brainly.com/question/28823603

#SPJ1

Answer:

the last one, option D, 8x + 10y ≥ 600 and x ≥ 40

Step-by-step explanation:

took the test xx

the bus value is depreciating, thus is Decay

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &250000\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=years \end{cases} \\\\\\ A = 250000(1 - 0.2)^{t} \implies \boxed{A = 250000(0.8)^t} \\\\\\ \stackrel{\textit{after 6 years, t=6}}{A=250000(0.8)^6}\implies \boxed{65536}[/tex]