The angle of depression of a rabbit from the top
of a cliff is 24°. After the rabbit hops a distance
of 80 m horizontally towards the base of the cliff,
the angle of depression of the rabbit from the
top of the cliff becomes 32°. Find the height of
the cliff.
Answers
The angle of depression is the angle formed with the horizontal, when an object is viewed below the horizontal level. Thus, the height of the cliff is approximately 123.86 m.
Let the height of the cliff be represented by h, so that:
From the triangle 1, we have:
tan [tex]32^{o}[/tex] = [tex]\frac{h}{x}[/tex]
⇒ h = tan [tex]32^{o}[/tex]*x
h = x tan [tex]32^{o}[/tex] ............. 1
Also, from the bigger triangle, we have:
tan [tex]24^{o}[/tex] = [tex]\frac{h}{80 + x}[/tex]
⇒ h = tan [tex]24^{o}[/tex] (80 + x) ......... 2
Now equating the expressions for h in equations 1 and 2, we have:
x tan [tex]32^{o}[/tex] = tan [tex]24^{o}[/tex] (80 + x)
0.6249x = 0.4452 (80 + x)
= 35.616 + 0.4452x
0.6249x - 0.4452x = 35.616
0.1797 x = 35.616
x = [tex]\frac{35.616}{0.1797}[/tex]
x = 198.2 m
Substitute the value of x in equation 1;
h = x tan [tex]32^{o}[/tex]
= 198.2 * 0.6249
= 123.8552
h = 123.86 m
Therefore, the height of the cliff is approximately 123.86 m.
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Related Questions
The final grade on your math exam was determined by the function f(x) = 100 − 2x. Which statements are correct?
A) 100 is the maximum grade.
B) y equals your final grade.
C) This is an exponential function.
D) 2 is what each question is worth.
E) x is the number of correct problems.
Answers
Answer:
A. True
B. True
C. False
D. True
E. False
Step-by-step explanation:
A. True, you cannot get higher than 100 on this test , as you cannot get a negative amount of questions wrongs
B. True, as y = f(x)
C. False, as there is no exponents
D. True, as if x=1, you lose 2 points
E. False, as x is the number of wrong problems
1/2x - 5 = 10 - 3/4x Please show work !
Answers
Answer:
x=[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
1/2x - 5 = 10 - 3/4x
4x/2x - 5 × 4x = 10 × 4x - [tex]\frac{3 x 4x}{4x}[/tex]
2 -5 × 4x = 10 × 4 - 3
2 - 20x = 40x - 3
-20x - 40x = -3 - 2
-60x = -3 - 2
-60x = -5
x = [tex]\frac{-5}{-60}[/tex]
x = [tex]\frac{1}{12}[/tex]
A muffin recipe calls for 2 eggs to make 12 muffins.
If you want to make 36 muffins, what should you do?
Answers
2 eggs/ 12 muffins = x eggs/ 36 muffins
They will have to be proportional
2/12 = x/36
12 * 3 = 36
2 * 3 = 6 eggs
You will need 6 eggs
Answer:
6 eggs
Step-by-step explanation:
since recipe states that to make 12 muffins you need 2 muffins
2. = 12
represent the unknown with x
2. = 12
x. = 36
Then you'll cross multiply
36 × 2 = 72
12x = 72
x = 72 ÷ 12
x = 6
Here is a list of five numbers.98^53 98^64 98^73 98^88 98^91Find the lowest common multiple of these five numbers.
Answers
Answer:
98^91
Step-by-step explanation:
Since the base of all the numbers is 98,
the LCM is simply the one with the greatest exponent
example
98^53 * 98^38 = 98^91
the points (3,5) and (-2,10) lie on a line. what is the slope
Answers
Answer:
-1
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 10-5)/(-2-3)
=5/-5
= -1
I am a student in 7th honers and was wondering if someone can help me learn the basics of pre-algebra because I understand none of it.
Answers
Answer:
I reccommend using an AoPS book. You can learn more at aops.com
Step-by-step explanation:
A. Complete the table if y varies
directly as x or x2
B. Complete the table if y varies inversely as x.
Answers
Direct variation is represented by the equation y = k × x and inverse variation is represented by y = k/x
Table 1:
y = k × x
30 = k × 5
30 = 5k
k = 30/5
k = 6
So,
y = 30
y = 30 k = 6
y = 30 k = 6x = 5
y = 30 k = 6x = 5Equation: y = 6x
y = k × x
y = 10 × 8
y = 80
So,
y = 80
y = 80 k = 10
y = 80 k = 10x = 8
y = 80 k = 10x = 8Equation: y = 10x
y = 3x
18 = 3x
x = 18/3
x = 6
So,
y = 18
y = 18k = 3
y = 18k = 3x = 6
y = 18k = 3x = 6Equation: y = 3x
y = 2x²
72 = 2x²
x² = 72/2
x² = 36
x = √36
x = 6
So,
y = 72
y = 72k = 2
y = 72k = 2x = 6
y = 72k = 2x = 6Equation: y = 2x²
Table 2:
y = k/x
5 = k/6
5 × 6 = k
30 = k
So,
y = 5
y = 5k = 30
y = 5k = 30x = 6
y = 5k = 30x = 6Equation: y = 30/x
y = k/x
y = 36/4
y = 9
So,
y = 9
y = 9k = 36
y = 9k = 36x = 4
y = 9k = 36x = 4Equation: y = 36/x
y = 60/x
20 = 60/x
20x = 60
x = 60/20
x = 3
So,
y = 20
y = 20k = 60
y = 20k = 60x = 3
y = 20k = 60x = 3Equation: y = 60/x
y = 24/x
y = 24/12
y = 2
So,
y = 2
y = 2k = 24
y = 2k = 24x = 12
y = 2k = 24x = 12Equation: y = 24/x
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Pls help will give 10 pts
Answers
Answer:
276 guests
Step-by-step explanation:
Let the number of guests be n. We are to find the value of n.
Then (1/3)n + (5/12)n + 69 = n, or
(9/12)n + 69 = n or (12/12)n
Solving for n, we get (3/12)n = 69, or (1/12)n = 23, or n = 12(23) = 276
There were 276 guests at the wedding.
Check: Does (1/3)(276) + (5/12)(276) + 69 work out to 276? yes
y/4 − 2 = 9
what does y =
Answers
Answer:
y = 44
Step-by-step explanation:
First, add 2 on both sides to get y/4 = 11, then multiply 4 on both sides to get y = 44.
Hope this helps :)
Turns into
y/4 = 11
Then multiply both sides by 4 to get rid of the division
y = 44
this is the very last question I swear :-)
Answers
Answer:
x= (p+10)/5
Step-by-step explanation:
first you take the peaches and add 10, p+10, and then divide by 5
Answer:
(p + 10)/5
Step-by-step explanation:
Question 1: Select the property shown
by the statement: 3a • 5b = 3.5 a.
b
A. Commutative
B. Associative
C. Reflexive
D. Symmetric
E. Transitive
Answers
Answer:
E BC itsay 3a 5b = 3.5 so it E
NEED HELP show your work
Simplify the expression √8x^5 / z1
Answers
Answer:
3/4
Step-by-step explanation:
46 pts to first correct and brainliest. Help ASAP PLZ. GOD BLESS YOU
Answers
Answer:
a^4
Step-by-step explanation:
First evaluate the quantity inside the parentheses: (a^(-3)).
Then raise this result to the power -1:
(a^(-3))^(-1) = a^4
Answer:
a^3
Step-by-step explanation:
1/a^-1 a^-2
a^-1a^-2= a^-3
1/a^-3
1/1/a^3
a^3/1
a^3
In total there are 53,444 adults at a football match there are 4300 more women then men at the match how many men are at the match
Answers
Answer:
There are 24,572 men.
Step-by-step explanation:
Let men = m, let women = w.
m + w = 53,444
w = 4300 + m
m + (4300 + m) = 53,444
m + m + 4300 = 53,444
2m + 4300 = 53,444
2m = 53,444 - 4300
2m = 49144
m = 49144/2
m = 24,572
help? plssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answers
Answer:
you're right, d measures 180 degrees
Step-by-step explanation:
the protractor is measuring a straight line and straight lines measure 180 degrees
hope this helps
What does "for example" tell readers about the sentence it introduces?
1. that they're about to be introduced to a new idea
2. that it's a sentence that will show them a similarity
3. that it's sentence will show them a difference
4. that they're about to hear an example of the idea in the previous sentence
Answers
Answer:
The answer is option 4., but this question does not belong in the math section.
Find an ordered pair (x,y) that is a solution to the equation. 3x-y=8
Answers
Answer:
(2,-2)
Step-by-step explanation:
[tex]3x-y =3(2) -(-2)= 6 +2 = 8[/tex]
What is the slope of the red line if the green is 2/3
Answers
explanation: perpendicular line have the opposite reciprocal of the line.
Answer:
a
Step-by-step explanation:
What times 5/8 equals 1
Answers
Answer:
1.6
Step-by-step explanation:
5/8 = .625
1/.625 = 1.6
.625* 1.6 = 1
Answer:
8/5.
Step-by-step explanation:
That is the inverse of 5/6:- 8/5.
Which value of m is a counterexample for the following statement?
If m is an odd prime number, then m + 2 is also prime.
Group of answer choices
7
3
5
9
11
Answers
Answer:
3
Step-by-step explanation:
because 3 is a prime number and 3+2=5 which is also a prime number
Can someone please help solving for x
Answers
Answer:
x=6.7
Step-by-step explanation:
In relation to the given angle, we are given the triangle's opposite side and hypotenuse. Therefore, we use the sine function to set up a proportion and solve for x:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]sin(31^\circ)=\frac{x}{13}[/tex]
[tex]13sin(31^\circ)=x[/tex]
[tex]x=13sin(31^\circ)[/tex]
[tex]x\approx6.7[/tex]
So, the opposite side is about 6.7 inches
Find the missing side.
09
9.5
10
C
7 cm
10.6
8 cm
HELP PLEASE
Answers
Answer:a
Step-by-step explanation:
i know
ANSWER PART B
Sia designs a board game in which a card is drawn on each turn.
• A blue card means move forward 4 squares.
• A red card means move back 6 squares.
Liam suggests adding some other cards to Sia's game
Part A
Liam explains that drawing a yellow card is equivalent to drawing a blue card followed by a red card. How many spaces forward or backward does a player move after drawing a yellow card? Justify your answer.
ANSWER PART B
How could Liam use red, blue, and yellow cards to describe each of the following motions? Write equations to support your answer. • A green card means move forward 2 spaces. • An orange card means move 8 spaces backward. • A purple card means move forward 10 spaces.
Answers
Answer:
Answer:Back 2
Step-by-step explanation:Blue + Red=-2
Step-by-step explanation:
What is the solution to 1/2 |x| = -3
Options:
x = -6
x = -6 or x = 6
x = -6 or x = 2
No solutions exist.
Answers
Answer:
No solution
Step-by-step explanation:
multiplying both sides by 2 gives |x|=-6 but an absolute value can't be negative so there are no solutions
see more at: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/cc-6th-absolute-value/a/intro-to-absolute-value
50 POINTS!!
Mr. reed and Mr. Bob are conducting a sensitive physics experiment and are standing
on a coordinate grid. They need to place a motion sensor exactly halfway between
them. If Mr. To is standing at coordinates (–7, 3), and Mr. Syal is standing at (5, -5),
where should the motion sensor be placed?
Answers
Answer:
(-1,-1) I think
Which number represents
27,860,000 using scientific notation ?
Answers
Answer:
B. 2.786 x 10 ^ 7
Step-by-step explanation:
For scientific notation you have 1 number to the left of the decimal point and 10 gets raised to the power of the number of decimal places it takes to get that one number.
Each year, the students in seventh grade go to an environmental camp. This year, the total cost is $1,580 for 79 students. Which equation represents the cost, y, of attending the camp for x number of students?
Select the correct answer.
y = 20x
y = 79x
y = 79x + 1580
y = 1580x + 79
Answers
Answer:
y=20x
Step-by-step explanation:
You have to find the cost by dividing the amount of money by the amount of students, to see house much each student paid. You are finding the unit price. Which is 20 because...
1.580/79=20
In conclusion,
Each student paid $20
When using re-grouping to solve 25 x 45, what are the four problems that would be calculated to find the final answer?
A.20 x 40; 5 x 40; 20 x 5; 5 x 5
B.20 x 20; 40 x 40; 20 x 5; 5 x 5
C.20 x 40; 20 x 5; 40 x 5
D.20 x 40; 5 x 20; 20 x 5; 5 x 5
Answers
Answer:
It is number 1
Step-by-step explanation:
I tried it.
Which ratio is equivalent to 5:9?
O 10:36
O 10:27
O 20:27
O 20:36
Answers
Write equations for the horizontal and vertical lines passing through the point (1,7) .
Answers
Answer:
horizontal line: y = 7
vertical line: x = 1
Step-by-step explanation: