1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off
at 4°. Can Brooke walk out to bring the boat back without getting water over the
tops of her hip boots which are 1 m tall? Explain your reasoning.
2. are the engineer who designed a new branch for the Mountain Railroad
Company. You sent your plans calling for 100 km of track up Bixby Mountain
taking trains 99 km east of the city of Bixby, to the City Council for approval.
But before the Council got around to looking at your plans, they passed a
regulation that no railroad tracks could go up their mountain at an angle of more
than 8°. Will your plans be approved? Why or why not?
3. The residents of Quietville, a little town 9 km from the San Francisco Airport,
insist that any plane flying over their town disturbs them if it is lower than 3 km.
Will a plane that took off at a 21° angle disturb them? Why?
4. You are an air pollution inspector, checking that factories in your city have
chimneys at least 65 m tall. Standing 50 m from the Ore Smelting Company’s
chimney, you find the angle from the ground to the chimney top is 51°. Can the
company use that chimney legally? Explain.
6. River City is offering a $3 million contract to build a bridge between points A and
C on opposite sides of City River. Along the side of the river that makes a right
angle with the line of the bridge at point C, a surveyor walked 72 m to point B
where she measured the 55° angle form B to A. Long Company will build the
bridge for $3 million if it is not more than 103 m from point A to point C. Short
Company agrees to build it if it is no more the 100 m. Which contracting firm
will be awarded the contract? Why?
7. An elderly woman is trapped 17 m up in her burning home. Can a fireman reach
her on his 26 m ladder if it has to make a 43° angle in order to clear the woman’s
greenhouse under her window? Explain your reasoning.
8. A ski lift 1000 m long goes at a 29° angle up Mt. Gentleslope. Does the lift take
skiers all of the way up to the top of the mountain where there is a snack bar at
the 500 m elevation? Explain your reasoning.
9. Mr. Johnson is a jet pilot who just moved with his family to Suburbia, 26 km
from Toledo Airport. His seven-year-old son, Eric, would like to see his father’s
plane as it flies over their new home for the first time today, but there is a layer of
clouds 5 km above the house. Will Eric be able to see his Dad’s plane if it takes
off at a 9° angle? Explain.
10.You are the cost control expert for an engineering firm designing a giant
television tower having several metal braces, each built in 21 m from the base at a
73° angle with the ground. Part of your job is to decide which standard length of
metal brace wastes less metal: the brace that comes 71 m long, or the one that is
73 m long. What is your decision?
Answers
The correct responses found using trigonometric ratios are as follows;
Brooke's cannot bring the boat back without getting water over her boots.The plan will not be approvedThe plane will not disturbThe company can not use the chimney legallyThe Long company will build the bridgeThe fireman can reach her.The lift does not take the skiers up to the bar.Eric will be able to see his Dad's plane.The 73 m. braceHow can trigonometric ratios be used to find the right responses?1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
Brooke's cannot bring the boat back without getting water over her boots.2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
The plan will not be approved.3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
The plane will not disturb.4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
The company can not use the chimney legally.6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
The fireman can reach her.8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
The lift does not take the skiers up to the bar.9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
Eric will be able to see his Dad's plane.10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.Learn more about trigonometric ratios here:
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Related Questions
Find the volume of the composite figure.
Answers
The blue dot is at what value on the number line?
-10
-6
Answers
Answer:
0
Step-by-step explanation:
The scale of the number line is by 2's. You can determine this because the number between -10 and -6 is -8. SO if you continue this pattern of increasing the number by 2, you get -6, -4, -2, then 0.
Which equation has roots -3 and 4
Answers
Answer:
x^2 - x - 12 (this is the second answer choice)
Step-by-step explanation:
Multiply (x + 3)(x - 4) and simplify the result:
x^2 - 4x + 3x - 12, or x^2 - x - 12 (this is the second answer choice)
x + 4y = 28 Where does the graph intersect the vertical axis
Answers
The graph intersects the vertical axis at (0,7). The solution has been obtained by using the concept of intercepts.
What are intercepts?
The slope of the line passes through a point on the y-axis known as an intercept.
The two primary intercepts are X and Y intercepts. The points where the line crosses the x and y axes, respectively, are known as the x-intercept and y-intercept of the line.
We are given an equation as x + 4y = 28
The graph intersects the vertical axis i.e. the y-axis when x coordinate is 0.
So, substituting x = 0 in x + 4y = 28, we get
⇒0 + 4y = 28
⇒4y = 28
⇒y = 7
Hence, the graph intersects the vertical axis at (0,7).
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Find the present value that will grow to $1000 if the annual interest rate is 5.5% compounded quarterly for 10 years
Answers
Answer:
1708.14 rounded
Step-by-step explanation:
Y= a•b^x
5.5% = 0.055
1+0.055=1.055
Y= 1000•1.055^10
Y= 1708.14
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Factor the expression 49t4 - 25 using the polynomial identity (x2 - y2) = (x - y)(x + y)
Answers
Answer:
Step-by-step explanation:
49t^4-25
(7t^2-5)(7t^2+5)
Which of the following numbers is irrational?
Answers
Oliver did the high jump three times. His scores were 7.016 feet, 5.42 feet, and 8.308 feet. How many feet did he jump in total? pleas help im in test
Answers
The total height of the three jumps is A = 20.744 feet
Given data ,
1st high jump score: 7.016 feet
2nd high jump score: 5.42 feet
3rd high jump score: 8.308 feet
On adding the scores , we get
7.016 + 5.42 + 8.308 = 20.744 feet
On simplifying the equation , we get
A = 20.744 feet
Hence , Oliver jumped a total of 20.744 feet in the three high jumps
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A 7-pound box of grapes costs $30.24. What is the price per ounce?
Answers
A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1)
, that is, on the due north position. Assume the carousel revolves counterclockwise.
What are the coordinates of the child after 90
seconds?
Answers
The child's position after 90 seconds would be (0, -1).
How to find the child's positionThe carousel revolves 360 degrees in one minute, which means it revolves 360/60 = 6 degrees per second.
After 90 seconds, the carousel would have revolved 90 * 6 = 540 degrees.
When the carousel revolves counterclockwise, the point (0, 1) would rotate to a new position by 540 degrees.
To find the new position, we can use the transformation:
540 - 360 = 180
hence the transformation is 180 degrees which is reflection across x axis
The rule for a reflection over the x -axis is (x, y) → (x, −y)
point (0, 1) → (0, −1)
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30 is 2/3 of what number
Answers
Answer:45
Step-by-step explanation:
Key Word:of
30*2/3 = 45
Answer:
Step-by-step explanation:
let the number be x.
then,
2/3 of x = 30
=> 2/3x = 30
=> x = 30 × 3/2
=> x = 45
so, the required number is 45 .
hope it helps...!!!
A kitten gained 12 ounces it’s four months after it was born. If this rate continues, how many ounces will the kitten have gained at one year?
Answers
Answer:
In 4 month's it's 12 ounces, so in 8 months, it's 24 ounces. That means that in 12 months, a year, the cat will be 36 ounces.
Answer:
36oz
Step-by-step explanation:
12oz every 4 months
24oz in 8 months
36oz in 12 months
12 months in 1 year so the kitten will weigh 36oz
Use a rectangular array to write the products in standard form
Answers
2x + 20
Explanation:Given:
\(2(x\text{ + 10\rparen}\)To find:
To use a rectangular array to write the products in standard form
To use a rectangular array for the product, we will construct rectangles representing x and 10:
Next, we will multiply the expression outside by 2. The results will be in each box
The product in standard form will be the sum of each expression in the box = 2x + 20
\(2(x\text{ + 10\rparen = 2x + 20}\)
Which relationships describe the angle pair x° and 71º?
Select each correct answer.
complementary angles
adjacent angles
vertical angles
supplementary angles
Answers
Answer:
complementary angles, Adjacent angles
Step-by-step explanation:
Complementary angles always add up to 90⁰
Use a graphing calculator to sketch the graph of the quadratic equation, and then give the coordinates for the x-intercepts (if they exist).
y = negative x squared + 15 x minus 56
a.
(-7, 0); (-8, 0)
c.
(-7, 0); ( 8, 0)
b.
( 7, 0); (-8, 0)
d.
( 7, 0); ( 8, 0)
Please select the best answer from the choices provided
Answers
When y = -x² + 15x - 56 then coordinates are is (c) (-7, 0); (8, 0).
What are the quadratic functions?Quadratic functions are a type of polynomial function of degree 2, which can be expressed in form f(x) = ax² + bx + c, where a, b, and c are constants, and x is the variable.
The graph of the given quadratic equation y = -x² + 15x - 56 can be plotted using a graphing calculator or any graphing tool. The x-intercepts are the points on the x-axis where the graph intersects the x-axis, i.e., the points where y = 0. By plotting the graph, we can determine the x-intercepts to be (-7, 0) and (8, 0), which correspond to option (c) (-7, 0); (8, 0).
Option (a) and (b) have incorrect x-coordinates for the x-intercepts, and option (d) has both positive x-coordinates for the x-intercepts, which is not correct based on the graph of the given quadratic equation.
Hence, option (c) is the correct answer.
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Which are equivalent expressions?
Check all that are true.
A)8xy = 4x + 4y
B)x + 6x = 7x
C)x + 6y = 6xy
D)9x + 6y = 3(3x + 2y)
E)9a + 6b + 3c = 3(3a + 2b + c)
Answers
Answer:
DE
Step-by-step explanation:
D)9x + 6y = 3(3x + 2y)
E)9a + 6b + 3c = 3(3a + 2b + c)
there have the same concept
3*3x equals 9x and 3*3a is 9a
Nvm I found the answer
Answers
Determine the turning points and distinguish between them when necessary y=x³ - 3x - 9x + 4
Answers
The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).
To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.
1. Find the derivative of the function:
y' = 3x² - 6x - 9
2. Set the derivative equal to zero and solve for x:
3x² - 6x - 9 = 0
3. Factorize the quadratic equation:
3(x² - 2x - 3) = 0
4. Solve the quadratic equation by factoring or using the quadratic formula:
(x - 3)(x + 1) = 0
This gives us two possible values for x: x = 3 and x = -1.
5. Substitute these critical points back into the original function to find the corresponding y-values:
For x = 3:
y = (3)³ - 3(3)² - 9(3) + 4
= 27 - 27 - 27 + 4
= -23
For x = -1:
y = (-1)³ - 3(-1)² - 9(-1) + 4
= -1 - 3 + 9 + 4
= 9
6. Therefore, the turning points are (3, -23) and (-1, 9).
Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.
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I put a screenshot, you do the math
Answers
Answer:
= 1.156 × 10^9
(scientific notation)
= 1.156e9
(scientific e notation)
= 1.156 × 10^9
(engineering notation)
(billion; prefix giga- (G))
= 1156000000
Step-by-step explanation:
Simply subtract A from B = 1,156,000,000 and convert the answer to scientific notation.
Answer:
D. 1.156 times 10^9
First we subtract the difference,
1,300,000,000 - 144,000,000 = 1156000000
Next, we find the number 1156000000 written in scientific notation.
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 115,600,000
New Number: 1.15600000
Step 2
Now, to find b, count how many places to the right of the decimal.
New Number: 1 . 1 5 6 0 0 0 0 0
Decimal Count: 1 2 3 4 5 6 7 8
There are 8 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10b
a = 1.156 (Please notice any zeroes on the end have been removed)
b = 8
Now the whole thing:
1.156 x 108
Step 4
Check your work:
108 = 100,000,000 x 1.156 = 115,600,000
Thus, 115,600,000 written in scientific notation is 1.156 times 10^9 estimated.
Tires regularly priced at $44 each are on sale for $37. How much would a truck owner save by buying four tires at the sale price?
A. $7
B. $28
C. $49
D. $81
Answers
Answer:
B
Step-by-step explanation:
the truck owner saves 7$ from every tires by buying at the selling price.
Tyrone walked 8 miles in a walkathon at a speed of 2 miles per hour. How long was he walking?
4 hours
6 hours
10 hours
16 hours
Answers
Answer:
4 hours
Step-by-step explanation:
Answer:
the answer is 4 HOURS
Step-by-step explanation:
i took the exam
How high would the rent have to be to qualify as an outlier
Answers
Answer:
1500+
Step-by-step explanation:
Need help please ?!!!!!
Answers
B. 45/182
C. 38/116
D. 18/182
Tell whether the function shown by the table below is linear or nonlinear.
х
3
0
-3
1
2
2
7
3
12
4.
17
A linear
B. nonlinear
Answers
A number, y, is equal to twice the sum of a smaller number and3. The larger number is also equal to 5 more than 3
times the smaller number.
Answers
2x-y = -6 and 3x-y = -5
pls I need help with this
Answers
Answer:
38
Step-by-step explanation:
25+13=38
Answer:
I believe the total change in altitude would be 38 feet.
Step-by-step explanation:
25 + 13 = 38
14.Subtraction is the opposite operation of which of the following?
A. Additio
B. Square Root
C. Division
D. Multiplication
Answers
Answer:
A. addition
Step-by-step explanation:
Hope it helps.
Answer:
Step-by-step explanation:
Addition
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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A summer camp has 550
campers who will be going on an outing. Estimate the number of vans needed to accommodate the entire camp if each van can comfortably hold 11
passengers. Then calculate the actual number of vans that will be needed.
Answers
Answer: 50
Step-by-step explanation:
1 van = 11 campers
Number of vans that will be needed = 550/11
=50