1. In the example above, what is the height of the tunnel 12 ft away from the center towards the other direction?2. What is the height of the tunnel 20 ft away from the center? What happens to the height of the tunnel as you go away from the center?3. How far from the center of the tunnel have a height of exactly 16 ft? Before solving problems involving conic sections, it is a must that we know what algebraic operations can bedone with their equations. In the previous modules, we've done finding the discriminant, squaring, completingthe square, rewriting from one form to another, etc. One thing we haven't done yet is "evaluation".To evaluate these conic equations, we simply substitute their variables with constants, perform any operationand then simplify.Example 1.The height of a semi-circular twnnel is 24 ft at the center. What is itsheight 12 ft away from the center?It is obvious that this problem deals with a cirde, so we use itsequation (x – h)² + (y – k)? = r² to solve this problem. From theproblem, we know the radius r = 24 ft. Since the center (h, k) is unknown in the problem, we assume that itis located at (0, 0) and that h = 0, and k = 0. This makes the equation (x – 0)² + (y – 0)² = 24°. This can befurther simplified resulting in a shorter equation that is x² + y² = 576. Looking at the illustration, we canobserve that the part of the circle where x is at zero (x = 0), y is at 24 (y = 24). That means we have to findy when x is at 12. To do this, we evaluate the equation using 12 as a value of x.Solution:12, 20.78)x + y = 576122 + y = 576144 + y? - 576Y? = 576 – 144Y = 4321818141220.7810Y = /432Y = 20.78 When x = 12, y = 20.78 and 20.78 ftis the height of the tunnel 12 ft awayfrom the center.(12. 0)16 18 20This example is for circles but the same principle can be applied to other types.

From the example above, We can see that we are using the…

1. In the example above, what is the height of the tunnel 12 ft away from the center towards the other direction? 2. What is the height of the tunnel 20 ft away from the center? What happens to the height of the tunnel as you go away from the center? 3. How far from the center of the tunnel have a height of exactly 16 ft?

1. In the example above, what is the height of the tunnel 12 ft away from the center towards the other direction? 2. What is the height of the tunnel 20 ft away from the center? What happens to the height of the tunnel as you go away from the center? 3. How far from the center of the tunnel have a height of exactly 16 ft?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: 10) What type of triangle has coordinates R(-3, 1), S(1, 3), and T(2,-4)? a. Equilateral b.…

Q: 16. Find the length of in the circle. Y is the center point. YZ = 5, and MLXYZ = 45. %3D rloso eme…

A: We have given a circle and the radius of the circle YZ=5 angle XYZ= 450

Q: . At what angle must be a 5 meters ladder leans on a wall 4.5 meters high to reach its topmost? 2.…

Q: 4. A utility pole casts a 25' shadow on the ground. If a 48' wire is attached to the top of the pole…

Q: 2' 5 1/2' 3' 3' WINDOW 7 1/2' DOOR

Q: 2. Find the length of chord HT that is 4 cm from the center of circle A with a radius of 5. Hint:…

Q: D 3. How long is the radius of this circle if the length of BC = 20 m? Use 3.14 for t A

Q: 22. From a point C on ground level, the angle of elevation to the top of a tree is 30°. From a point…

A: Consider the diagram.

Q: of a circle. Find the area of the sector 4. 8. The sector below Is In terms of T. 5 cm

A: Find the answer below. Dear learner , from next time please upload one question at once, as per…

Q: If qs represents an angle bisector, solve for x.

A: Given, QS represents an angle bisector and the triangle is shown below :

Q: 1. Are any of these triangles similar? Explain how you know. 60 12 ft 60 45 6 ft 8.5 ft 6 t 5.2t 30…

A: Note: according to the company guidelines we should answer only one question at a time, please…

Q: a. The sides of a triangle are 18cm, 24cm, and 34cm. Find the length of the median, angle bisector,…

Q: Which of the following can not give you a cross section that is a triangle? Cone O Cube O Cylinder…

A: The answer for this question is "cylinder". A cross section is the non-empty intersection of a solid…

Q: Given that triangle RST has the following points: R(-3,1), S(4,8) and T(4,1). Find the measures of…

Q: б. An equilateral triangle has a side length of 7 cm. If a perpendicular is dropped from a corner,…

A: Properties of equilateral triangle : All sides are equal . All angles are equal and equal to 60° .…

Q: 4. Standing on a level road 50 feet from the base of a billboard, the angle of inclination to the…

Q: 13) Use the figure below to find the length of the hypotenuse. Round to the nearest meter. 529 15 m…

Q: 3. A ramp is placed at the back of a truck that is 15 ft. high. The base of the ramp is 20 ft. away…

Question

1. In the example above, what is the height of the tunnel 12 ft away from the center towards the other direction?
2. What is the height of the tunnel 20 ft away from the center? What happens to the height of the tunnel as you go away from the center?
3. How far from the center of the tunnel have a height of exactly 16 ft?

Before solving problems involving conic sections, it is a must that we know what algebraic operations can be
done with their equations. In the previous modules, we've done finding the discriminant, squaring, completing
the square, rewriting from one form to another, etc. One thing we haven't done yet is "evaluation".
To evaluate these conic equations, we simply substitute their variables with constants, perform any operation
and then simplify.
Example 1.
The height of a semi-circular twnnel is 24 ft at the center. What is its
height 12 ft away from the center?
It is obvious that this problem deals with a cirde, so we use its
equation (x – h)² + (y – k)? = r² to solve this problem. From the
problem, we know the radius r = 24 ft. Since the center (h, k) is unknown in the problem, we assume that it
is located at (0, 0) and that h = 0, and k = 0. This makes the equation (x – 0)² + (y – 0)² = 24°. This can be
further simplified resulting in a shorter equation that is x² + y² = 576. Looking at the illustration, we can
observe that the part of the circle where x is at zero (x = 0), y is at 24 (y = 24). That means we have to find
y when x is at 12. To do this, we evaluate the equation using 12 as a value of x.
Solution:
12, 20.78)
x + y = 576
122 + y = 576
144 + y? - 576
Y? = 576 – 144
Y = 432
<equation>
<substitution>
18
18
14
12
20.78
10
Y = /432
Y = 20.78 <final result>
When x = 12, y = 20.78 and 20.78 ft
is the height of the tunnel 12 ft away
from the center.
(12. 0)
16 18 20
This example is for circles but the same principle can be applied to other types.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area of a Circle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

4. The circumference of a circle is C = 2πr. Solve for the radius r.
13. Consider the Sirpinski Triangle below. If we double the length of the sides how many copies of the original triangle do we have? а. 1 b. 2 С. 3 d. 4 е. there will be no copies.
14. What is the length of the diameter of the circle having equation x² + y² - 12x +22y + 76=0? Round to nearest tenth. A 9.0 B. 15.3 C. 18.0 D. 30.6
11.) Which of the following does NOT have an area of 40 ft2? a. a right triangle with legs 16 feet and 5 feet b. a trapezoid with bases 4 feet and 6 feet, and height of 4 feet c. an acute triangle with base 8 feet and height 10 feet d. a parallelogram with a base of 8 feet, side length 4.5 feet, and height of 5 feet
Given three points ?(−1,3,1), ?(6,0,−1) and ?(2,1,1). Find the area of the triangle ???. Round your answer to two decimal places.