Mathematics High School

The figure shows a person estimating the height of a tree by looking at the
top of the tree with a mirror. Assuming that both the person and the tree form
right angles with the ground, which of the following proportions can be used
to estimate the height of the tree?

Answers

Answer 1

Answer:

The proportion that can be used to estimate the height of the tree is option;

A. $\dfrac{h}{12} = \dfrac{6}{5}$

Step-by-step explanation:

The given parameters in the question are;

The medium through which the person looks at the top of the tree = A mirror

The angle formed by the person and the tree with the ground = Right angles = 90°

The distance of the person from the mirror, d₁ = 5 ft.

The height of the person, h₁ = 6 ft.

The distance of the tree from the mirror, d₂ = 12 ft.

The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂

Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;

TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar

The corresponding legs are;

The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively

The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively

∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR

The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB

Given that θ₁ = θ₂, we have;

tan(θ₁) = tan(θ₂)

∴ tan(∠TMR) = tan(∠AMB)

$tan\angle X = \dfrac{Opposite \ leg \ length \ to \ reference \ angle}{Adjacent \ leg \ length \ to \ reference \ angle}$

$tan(\angle TMR) = \dfrac{TR}{MR} = \dfrac{h}{12}$

$tan(\angle AMB) = \dfrac{AB}{BM} = \dfrac{6}{5}$

From tan(∠TMR) = tan(∠AMB), we have;

$\dfrac{h}{12} = \dfrac{6}{5}$

$\therefore h = \dfrac{6 \, ft.}{5 \, ft.} \times 12 \, ft. = 14.4 \, ft.$

The height of the tree, h = 14.4 ft.

Therefore, from the proportion $\dfrac{h}{12} = \dfrac{6}{5}$ the height of the tree can be estimated.

Related Questions

determine whether the ordered pair (2/3, 7) is a solution of the linear equation y=-3/2x+8

Answers

No, it is not a solution of the linear equation y=-3/2x+8.

What is Linear Equation?

When the maximum power of the variable is consistently 1, an equation is said to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0. The variables x and A in this situation are variables, whereas B is a constant. The typical form of a linear equation with two variables is Ax + By = C. In this case, we have the variables x and y, the coefficients A and B, and the constant C.

To check whether the ordered pair (2/3, 7) is a solution of the linear equation y=-3/2x+8 is by putting the values of x and y in the equation and to that L.H.S = R.H.S

x = 2/3

y = 7

Putting the values in the linear equation we get

7 = (-3/2)(2/3) +8

7 = -1 +8

7 = 7

L.H.S = R.H.S

Hence, (2/3, 7) is a solution of the linear equation y=-3/2x+8
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There were 224 roses growing in the back garder. If 50% of the roses were red. How many were not red?

Answers

Answer:

112

Step-by-step explanation:

Divide 224 by two, to get 112. That's how many 50% is in the situation, so 112 roses are not red.

distributive property to write an equation that's equivalent to -2(-6 +3y -1)

Answers

Answer:

-2(-6+3y-1) = -6y+14

Step-by-step explanation:

100 points five stars a thank you, dont need to awnser first. i will repeat this question every 3 and a half minutes. ive got nine hundred points to burn

Answers

Answer:

thx

Step-by-step explanation:

true or false, we can compare a model to before using a transformation on x or y to a model after using a transformation by using the corresponding values of sse.

Answers

True, we can compare a model before using a transformation on x or y to a mode before using a transformation by using the corresponding values of the sum of squares error SSE.

For example, to compare two models, one of which has a transformation on the outcome of the variable, that is:

First model$y=x+z$

Second model:$y^{1/k} =x+z$

The best logical approach might be to look at the comparative performance obviously with predicted transformed values back-transformed and then look at the models sum of squares error of these predictions. It has to be random predictions and comparisons because the error distributions are also transformed.

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a ship sails 20km due north. It changes direction and then sails 15 due east. How far is it from its starting point?

Answers

It is 35km from its starting point

SOMEONE HELP ASAP!!! PLAeASE

Answers

Answer:

55 MPH

Step-by-step explanation:

55 x 2.4 = 132

33 x 4 = 132

The sum of 4 consecutive integers is 38. What is the greatest of these integers?

Answers

Answer:

Step-by-step explanation:

let the consecutive integers be

n, n + 1, n + 2, n + 3 , then

n + n + 1 + n + 2 + n + 3 = 38 , that is

4n + 6 = 38 ( subtract 6 from both sides )

4n = 32 ( divide both sides by 4 )

n = 8

n + 1 = 8 + 1 = 9

n + 2 = 8 + 2 = 10

n + 3 = 8 + 3 = 11

The greatest of the integers is 11

n + (n+1) + (n+2) + (n+3)= 38
4n + 6 =38
4n =32
n = 8
So the four consecutive integers are 8, 9, 10 and 11.
So your answer of greatest integer is 11

Question One Assume there is a toll bridge in your city. Suppose that if the toll is abolished and crossing the bridge becomes free, there will be 30,000 vehicles crossing the bridge each year; with $1 of price increase, the number of vehicles crossing the bridge will drop by 100 each year. On the other hand, the city claims that maintenance of the bridge is costly. If there is no toll charge, the city would allow no cars to use the bridge; with $1 of price increase, the number of vehicles that the city would allow to use the bridge increases by 100 . a) Use the given information to write down the demand and supply functions of the bridge usage. (4 Marks) b) Solve for the equilibrium price and quantity of the bridge usage. (4 Marks) c) Suppose due to the decrease in transportation needs, the demand for the bridge usage decreased by 10% this year. Calculate the new equilibrium price and quantity of the bridge usage. (6 Marks) d) Assume the government enforces a toll charge of $100. Use the demand function derived in Part c) and the original given supply function to check if there will be an excess demand or excess supply with the government enforcement. If there is, what is the amount? (5 Marks) e) Suppose the toll bridge needs maintenance and repairs, and the supply of the bridge decreases by a half. What is the new supply function? Combine this new supply function with the demand function derived in Part c) to calculate a new set of equilibrium price and quantity of the bridge usage. (6 Marks)

Answers

a) Demand function: Qd = 30,000 - 100P, Supply function: Qs = -P b) Equilibrium price: $303.03, Equilibrium quantity: 27,697 vehicles. c) New equilibrium price: $333.33, New equilibrium quantity: 24,000 vehicles. d) Excess demand of 417 vehicles. e) New equilibrium price: $250, New equilibrium quantity: 24,750 vehicles.

a) The demand function for the bridge usage can be written as:

Qd = 30,000 - 100P

Where Qd represents the quantity demanded (number of vehicles crossing the bridge) and P represents the toll price.

The supply function for the bridge usage can be written as:

Qs = -P

Where Qs represents the quantity supplied (number of vehicles allowed to use the bridge by the city) and P represents the toll price.

b) To find the equilibrium price and quantity, we set the quantity demanded equal to the quantity supplied:

30,000 - 100P = -P

Simplifying the equation, we get:

30,000 = 99P

P = 303.03

Substituting the value of P back into either the demand or supply function, we find:

Qd = 30,000 - 100(303.03)

Qd = 27,697

Therefore, the equilibrium price is $303.03 and the equilibrium quantity is 27,697 vehicles.

c) If the demand for the bridge usage decreases by 10%, the new demand function becomes:

Qd = 0.9(30,000 - 100P)

Setting the new demand equal to the supply function:

0.9(30,000 - 100P) = -P

Solving the equation, we find:

P = 333.33

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(333.33))

Qd = 24,000

Therefore, the new equilibrium price is $333.33 and the new equilibrium quantity is 24,000 vehicles.

d) With a toll charge of $100, we use the demand function from part c) and the original supply function:

0.9(30,000 - 100P) = -100

Solving the equation, we find:

P = 305.56

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(305.56))

Qd = 24,417

Since the quantity demanded is greater than the quantity supplied, there is an excess demand of 24,417 - 24,000 = 417 vehicles.

e) If the supply of the bridge usage decreases by half, the new supply function becomes:

Qs = -0.5P

Setting the new supply equal to the demand function from part c):

0.9(30,000 - 100P) = -0.5P

Solving the equation, we find:

P = 250

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(250))

Qd = 24,750

Therefore, the new equilibrium price is $250 and the new equilibrium quantity is 24,750 vehicles.

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What is the difference of -3 multiplied by a number and the product of two and another number

Answers

Let a number be "a" and the other number be "b".

-3 multiplied by a number "a" is:

$-3\cdot a$

The product of two and another number "b" is:

$2\cdot b$

And the difference between the numbers is:

$-3a-2b$

Answer: - 3a - 2b.

classify 3x^5-8x^3-2x^2+5

Answers

The given polynomial, 3$x^{5}$ - 8$x^{3}$ - 2$x^{2}$ + 5, is classified as a polynomial of degree 5.

A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. The degree of a polynomial is determined by the highest power of the variable present in the expression. In this case, the highest power of x is 5, so the polynomial is of degree 5.

Polynomials are often classified based on their degree. Common classifications include linear polynomials (degree 1), quadratic polynomials (degree 2), cubic polynomials (degree 3), and so on. Since the given polynomial has a degree of 5, it falls under the category of quintic polynomials.

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Using an integrating factor, solve y-y-5 CD- in the method for solving a first-order linear differential equation, the first step is to put the equation in the standard form y alty bit). is the given equation in the standard form? No Yes Identify a(t) and bit)

Answers

The value of a(t) is -1 and b(t) is 55 + $e^t$

No, the given equation y' - y = 55 + $e^t$ is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + $e^t$

Therefore, The value of a(t) is -1 and b(t) is 55 + $e^t$

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In the metric system, multiplying by 1,000 would be the same as moving the decimal point ______ place(s)to the right.
a. one
b. two
c. three
d. four

Answers

In the metric system, multiplying by 1,000 would be the same as moving the decimal point three places to the right. So the correct option is C.

We move the decimal point to the right by the same number of places as the multiplier's number of zeros after one when the multiplier is 10, 100, or 1000. The decimal point in the multiplicand must be moved three places to the right in order to multiple a decimal by 1000. The number 644.67 was multiplied by 1000 in this case, moving us three spaces to the right. So the sum will be:

=644.67 × 1000

= (64467/100) × 1000

= 64467 × 10

= 644670

Remember that a decimal will move right the same number of places as the multiplier's number of zeros when multiplied by 10, 100, 1000, etc. If the multiplier contains more zeros than the numbers after the decimal point, the answer must also have more zeros.

Multiplying by 1,000 in the metric system corresponds to shifting the decimal point three places to the right. Thus, C is the correct option.

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Find the area of the circle.
Use 3.14 for it.
(
d = 8 cm
A = [?] cm2
A=Tr2

Answers

What the make no sense but I believe it is 50.24 hope that helps

Please help, Solve Systems of Linear Equations

Answers

Answer:

x = 1 , y = 1 , z = -3

Step-by-step explanation using elimination:

Solve the following system: