The points G and H, 19m apart are on the same side of a tree. The angles of elevation of the top T, of the tree from G and H on the horizontal ground with the foot of the tree are 430 and 38° respectively. (1). Illustrate the information in a diagram. (i). Find, correct to one decimal place, the height of the tree.
Answers
Using relations in a right triangle, it is found that
The height of the tree is of 91.6 meters.
The graph for this problem is given at the end of the answer.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.From the diagram graphed, we can build two relations involving the tangent of the angles, as follows:
From the smaller right triangle:
tan(43º) = h/x
0.9325 = h/x
x = (1/0.9325)h.
x = 1.0724h (we want to find h, hence we write x as a function of h).
From the larger right triangle:
tan(38º) = h/(x + 19).
tan(38º) = h/(1.0724h + 19).
0.7813 = h/(1.0724h + 19).
Applying cross multiplication:
h = 0.7813(1.0724h + 19).
h = 0.8379h + 14.8447.
0.1621h = 14.8447
h = 14.8447/0.1621
h = 91.6 meters.
The height of the tree is of 91.6 meters.
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Related Questions
which pair of numbers have a greatest common factor of 7? select each correct answer. 7 and 14 7 and 14 28 and 7 28 and 7 7 and 1 7 and 1 21 and 3
Answers
The numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.
What is the greatest common factor?The largest factor of the two numbers which divides both the numbers is called as greatest common factor or GCF. In other words, the greatest common factor is the largest positive number which can be divided into given numbers evenly.
Given the number is 7 the pair of numbers having the greatest common factor is calculated below:-
For pairs 7 and 14. Both the numbers are the multiple of 7 it can be divided by 7. The greatest common factor will be 7 for pairs 7 and 14.
Similarly for pairs 7 and 28. Both the numbers are the multiple of 7 it can be divided by 7. The greatest common factor will be 7 for pairs 7 and 28.
Therefore, the numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.
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a number from 1 to 10. the product of 3 less than this number and 2 more than this number is equal to 14. which equation could be used to solve for kevin's number, x?
Answers
The number is 5, the equation used is [tex]x^{2}[/tex] - x - 20 = 0
Let x be the number which is between 1 to 10.
From the question we get to know the equation:
(x-3)(x +2) = 14
x(x+2) -3(x+2) =14
[tex]x^{2}[/tex] +2x -3x - 6 =14
[tex]x^{2}[/tex] - x - 6 =14
[tex]x^{2}[/tex] - x - 20 = 0
This is the equation used to solve for Kevin's number.
Now we have to find the value of x.
[tex]x^{2}[/tex] - 5x + 4x -20=0
x(x-5) + 4(x-5) = 0
(x-5)(x+4) = 0
x = 5, -4
Hence we get two values of x which is 5, -4. But we have to find the number between 1 and 10.
Hence from the value of 5 and -4 , the number is 5 which is between 1 and 10 as -4 is not in the range of 1 to 10.
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The complete question is:
a number from 1 to 10. the product of 3 less than this number and 2 more than this number is equal to 14. which equation could be used to solve for kevin's number, x?
a) [tex]x^{2}[/tex]- x - 6 =0
b) [tex]x^{2}[/tex] - x - 20 = 0
c) [tex]x^{2}[/tex]- 6x + 14 =0
d) [tex]x^{2}[/tex] - x + 8 = 0
Here is a rule that can be used to build a sequence of numbers once a starting number is chosen: Each number is two times three less than the previous number.
a. Starting with the number 0, build a sequence of 5 numbers.
b. Starting with the number 3, build a sequence of 5 numbers.
c. Can you choose a starting point so that the first 5 numbers in your sequence are all positive? Explain your reasoning.
Answers
Answer:
a. 0, -6, -18, -21, -90
b. 3, 0, -6, -18, -42
c. A starting point of any number ≥ 6 will result in a sequence of positive values
Step-by-step explanation:
Here the sequence is governed by the rule:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]
[tex]\textsf {where $a_n$ is the nth term and $a_{n-1}$ is the previous term}}[/tex]
1) Starting with a₁ = 0 we get
a₂ = 2(a₁ - 3) = 2(0 - 3) = -6
a₃ = 2(a₂ - 3) = 2(-6 -3) = 2(-9) = -18
a₄ = 2(a3 - 3) = 2(-18 - 3) = 2(-21) = -42
a₅ = 2(a₄ - 3) = 2(-42- 3) = 2(-45) = -90
So the first 5 numbers in the sequence starting with 0 are:
0, -6, -18, -21, -90
2) I will approach this slightly differently
We have the relationship:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]
Expanding the brackets we get
[tex]\sf a_{n} = 2a_{n-1} - 6[/tex]
We have a₁ = 3
a₂ = 2(a₁) - 6 = 2(3) - 6 = 6 - 6 = 0
a₃ = 2(a₂) - 6 = 2(0) - 6 = -6
a₄ = 2(a₃) - 6 = 2(-6) - 6 = -18
a₅ = 2(a₄ ) - 6 = 2(-18) - 6 = -42
The sequence starting with 3 is:
3, 0, -6, -18, -42
Both methods work exactly the same, some students find expanding the brackets easier to deal with
c. We can see that as a₁ increases, the number of negative numbers decreases by 2. So, in order for all numbers to be positive (> 0) we should start with a sufficiently large number so that all numbers are positive
The smallest such number is 6.
When a₁ = 6, the sequence is all 6s because
a₂ = 2(6) - 6 = 12 - 6 = 6
So the next number is a₃ = 12(6) - 6 = 6 and so on
So any starting point ≥ 6 will yield positive values. At 5 the sequence would be: 5, 4, 2, -2, -10 so starting point of 5 will not work
Tìm x biết:
a) (50 − x) + 12 = 31 ; b) 75 ∶ (x − 2) + 4 = 7 ;
c) 125 − 3(x + 3) = 65 ;
Answers
- x + 62 = 31
- x = - 31
x = 31
b) 75 . ( x - 2 ) + 4 = 7
75x - 150 + 4 = 7
75x - 146 = 7
75x = 153
75x/75 = 153/75
x = 51/25
x = 2 1/25
c) 125 -3(x + 3 ) = 65
125 -3x - 9 = 65
3x + 116 = 65
3x = - 51
x = - 17
Yesterday Sarah read 15% of her entire book. Today she read another 17% of the entire book.
In lowest terms, what fraction of the book is left for her to read?
a) 7/25
b) 3/10
c) 17/25
d) 7/10
answer quick please!!!!
Answers
i think the answer is 3/10
Help please if u can show ur work please
Answers
Answer: 28 feet
Step-by-step explanation: The ratio of length to width is 2:1. Add the 2 numbers and it will give you 3. Then, divide 84 by 3 and it will give you 28. Times this by 1 (as the ratio of the width is 1). This will give you 28.
FIND THE ERROR The accuracy of a rain gauge is the positive difference between the amount of
rain in the rain gauge g and the actual amount of rain r. Sam says the absolute value expression
|g| – |r| is equivalent to the accuracy of a range gauge. Is Sam correct? Explain your reasoning.
Answers
Answer:
no
Step-by-step explanation:
i don't think he is correct because it's asking whats the difference between the two
Which statement is true for the function y = log3x
Answers
Answer:
Step-by-step explanation:
Find the value of the variable(s).
Answers
the variable(s) x have a value of 13.
What in mathematics is a variable?A variable is any property, amount, or number that can be measured or counted. A data item is another name for a variable. Age, sex, business income and expenses, place of birth, capital expenditures, class grades, eye color, and car kind are only a few examples of variables.
A variable is a value that could change based on the details of an experiment or the parameters of a mathematical problem. A variable is typically identified by a single letter. The letters x, y, and z are the universal symbols for variables that are most frequently employed.
According to given value ;
4x+(7x+37)=180
sum of three angle equal to 180
4x+7x+37=180
4x+7x=180-37
11x=143
x=143/11
x=13
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jack's age next year will be twice jill's age last year. their present ages total 45. how old is each no
Answers
We get the age of Jack is 29 years and the age of Jill is 16 years.
We are given that the sum of Jack's age and Jill's age is 45 years.
Let Jack's age be x.
Let Jill's age be y.
x + y = 45
x = 45 - y
Now, we are also given that jack's age next year will be twice Jill's age last year.
Jack's age next year = x + 1
Jill's age last year = y - 1
ATQ, We get the equation as:
x + 1 = 2( y - 1)
x + 1 = 2 y - 2
x = 2 y - 2 - 1
x = 2 y - 3
We get that:
45 - y = 2 y - 3
2 y + y = 45 + 3
3 y = 48
y = 48 / 3
y = 16 years.
x + y = 45
x + 16 = 45
x = 45 - 16
x = 29 years.
Therefore, we get the age of Jack is 29 years and the age of Jill is 16 years.
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Mario uses 14 pound of walnuts to make muffins. he uses the same amount of walnuts in each of 6 muffins. what is the amount of walnuts in each muffin?
Answers
Answer:
he uses 2.33333333333 amount of walnuts in each muffin
Step-by-step explanation:
14 divided by 6 = 2.33333333333
Have a nice day!
an unreliable study can occur if the . a. survey is very clear b. survey yields consistent results c. test administration is inconsistent
Answers
An unreliable study can occur if the test administration is inconsistent
Consistency is the key to success in anything and it implies to the studies and surveys as well. If you want the results of the study to be reliable, then you must be consistent in test administration.
Inconsistency can lead to various issues like improper representation of the feedback which may alter the results. This can lead to various problems.
For example, test performed at certain time may have a different set of people and absence of periodic tests can accommodate feedback from irrelevant people.
Therefore, a proper set schedule must be followed for the tests with consistency.
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The function h=−16t^2+1936 gives an object’s height h, in feet, at t seconds. When will the object be 912 feet above the ground?
Answers
next you can click 2nd trace then 5
which means the two will intersect at 8
(y=912 x=8)
meaning the object will be 912 feet above the ground at 8 seconds
he brazilian free-tailed bat can travel 99 miles per hour. after sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. how long before these bats cover an area of 80,000 square miles? use π
Answers
The bat colony will cover an area of 80,000 square miles in 1.612 hours.
What is defined as the circle?A circle is the collection of all the points together in plane that are equally distant from the a given point known as the circle's center. A circle is represented by the symbol. A radius of a circle is a line segment that connects the center of a circle toward any point on the circle.
Now, as per the given question;
The area covered (A) by the colony, evaluated in square miles, is depicted by the mentioned geometrical formula as the bat colony emerges from a cave & spreads out in a circular pattern:
A = π R²
R = the bat's distance from the cave, calculated in miles.
Furthermore, each bat moves at a constant speed, and distance is depicted by the following kinematic formula:
R = r₀ + rΔt
r₀ = The bat's initial distance from the cave, estimated in miles.
r = Bat speed, estimated in miles per hour.
Δt = Time, expressed in hours.
Substitute the value of R in the formula of area.
A = π (r₀ + rΔt)²
(r₀ + rΔt)² = A/ π
(r₀ + rΔt) = √(A/ π)
rΔt = √(A/ π) - r₀
Δt = (√(A/ π) - r₀)/r
r = 99 miles per hour
The distance between the bat and the cave has now been substituted, and time has been cleared:
A = area of 80,000 square miles
π = 3.14
r₀ = 0 miles per hour
Substituting all the values in the A we calculate the time.
Δt = (√( 80,000/3.14) - 0)/99
On solving;
Δt = 1.612 (approx)
Thus, It will take 1.612 hours for the bat colony to cover an area of 80,000 square miles.
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The complete question is-
The Brazilian free-tailed bat can travel 99 miles per hour. after sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. how long before these bats cover an area of 80,000 square miles? use pi = 3.14.
An equation and some of the steps used to solve the equation are shown below. One step is missing:
2(x-3) + 10x = 5(3 + x)
?
2x-5x + 10x = 15 + 6
7x = 21
x=3
Which set of statements is most likely the missing step and the property that justifies the step?
Answer choices listed in picture(Sorry for quality, taken from my laptop) (Will mark brainliest)
Answers
Answer 5795
Step-by-step explanation:
What are the first five terms of the following sequence a1=42, an=an-1-7
Answers
The first five term of the sequence are 42, 35, 28, 21 and 14.
According to the given question.
We have a rule for finding the terms of a sequence i.e. [tex]a_{n} = a_{n-1} -7[/tex].
Also, the first term of the sequence is a1 = 42
Therefore,
The second term of the sequence is given by
Second term [tex]a_{2}[/tex] = [tex]a_{1}[/tex] - 7
⇒ Second term = 42 - 7 = 35
Similarly,
The third term of the sequence, [tex]a_{3}[/tex] = [tex]a_{2}[/tex] - 7 = 35 - 7 = 28
Fourth term of the sequence = 28 - 7 = 21
Fifth term of the sequence = 21 - 7 = 14
Hence, the first five term of the sequence are 42, 35, 28, 21 and 14.
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A line segment has the endpoints K(0, 2) and L(0, 6). Find the coordinates of its midpoint M.
Write the coordinates as decimals or integers.
M =
Answers
A line segment has the endpoints as K and L that are (0,2) and (0,6).The midpoint M is (0,4).
Given that,
The line segment has the endpoints as K and L that are (0,2) and (0,6).
The Formula for the Midpoint of a Line Segment
Let the line segment's termination point be ([tex]a_{1}[/tex], [tex]b_{1}[/tex]) and ([tex]a_{2}[/tex], [tex]b_{2}[/tex]) respectively. The following is the midpoint formula for a line segment connecting these two points:
(a,b)=[tex](\frac{a_{1} -a_{2} }{2}, \frac{b_{1} -b_{2} }{2} )[/tex]
Where
[tex]a_{1} =0,b_{1} =2 \\and \\a_{2} =0,b_{2} =6[/tex]
[tex](a,b)=(\frac{0+0}{2},\frac{2+6}{2}) \\(a,b)=(0,4)[/tex]
Therefore, When the line segment with the endpoints k and L the midpoint M is (0,4).
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What are the values of b and c?
J
b =
C=
C
O
O
b
H
74°
I
Answers
the length of a rectangle is twice the width if the perimeter is 20 cm find the width
Answers
Answer:
10/3 ( width)
Step-by-step explanation:
the length of a rectangle is twice the width if the perimeter is 20 cm find the width
we can solve with an equation
(2x + x) * 2 = 20
3x * 2 = 20
6x = 20
x = 20 : 6
x = 10/3 ( width)
-----------------------
check Remember PEMDAS
(10/3 * 2 + 10/3) * 2 = 20
(20/3 + 10/3) * 2 = 20
30/3 * 2 = 20
60/3 = 20
20 = 20
the answer is good
Help out please I don’t understand
Answers
Answer:
C. [tex] \frac{ - 15x - 53}{ {x}^{2} + 8x + 15 }≥ 0[/tex]
Step-by-step explanation:
See attached image for explanation
I hope it helps youWrite each set using braces to list the elements, in interval notation, and in set-builder notation. If not possible, explain why
Answers
Answer: B
Step-by-step explanation:
every morning jim runs for 30 minutes. if jim runs 10 miles per hour, how far does he travel?
Answers
Answer:
5 miles
Step-by-step explanation:
distance = rate times time
distance = (10 miles per hour)( 30 minutes) 30 minutes is equal to 1/2 hour
distance = [tex]\frac{10 miles}{hour}[/tex] [tex](\frac{1 hour}{2} )[/tex] You can cancel words, like like cancelling numbers The hours cancel out and you are left with [tex]\frac{10 miles}{2}[/tex] which is equal to 5 miles.
Answer: 5 miles
Step-by-step explanation:
Jim runs 10 miles per hour, and 30 minutes is half an hour, so divide 10 by 2.
jamie is pedaling due south a 8 mi/hr. his sister, martha, is pedaling due west at 5 mi/hr. after 2 hours, how fast are the two cyclists moving apart?
Answers
Both cyclist are moving apart at a speed of 9.434 mi/hr.
What is velocity?Velocity is the direction at which an item is moving and serves as a measure of the rate at which its location is changing as seen from a certain point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a basic idea. A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of velocity; it is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI (metric system).
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Which expression uses the GCF and the distributive property to rewrite the sum 42 +72?
A. 6(7 +12)
B. 7(6 + 9)
C. 12(3+6)
D2(40+70)
Answers
Answer:
A. 6(7 +12)
You need to add the numbers in the parenthisis. Then, multiply 6 with the number.
You're flying from joint base lewis-mcchord (jblm) to an undisclosed location 18 km south and 122 km east. mt. rainier is located approximately 56 km east and 40 km south of jblm. if you are flying at a constant speed of 800 km/hr, how long after you depart jblm will you be the closest to mt. rainier? convert hours into minutes in the final solution.
Answers
After you depart jblm you will be the closest to mt. rainier after 4 minutes 35.5 seconds
The distance from JBLM to Mt. Rainier is found using the Pythagorean theorem:
d = √((56 km)² +(40 km)²) = 8√74 km
The bearing from JBLM to Mt. Rainier is ...
arctan(40/56) ≈ 35.538° . . . . . south of east
The heading of the airplane to its destination is ...
arctan(289/218) ≈ 8.393° . . . . . south of east
Then the difference between these angles is ...
8.393° - 35.538° ≈ -27.145°
and the distance to the point of closest approach is ...
8√74×cos(-27.145°) ≈ 61.238 . . . . km
The relation between time, speed, and distance is ...
time = distance / speed
Then the time from JBLM to the point of closest approach is ...
time = (61.238 km)/(800 km/h) ≈ 0.07654819 h ≈ 4.5928 minutes
≈ 4 minutes 35.5 seconds
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232x100 what is the answer
Answers
Answer:
23200
Step-by-step explanation:
13. Justina wants to buy a cover for the top of
her circular pool, but she doesn't know the
area. If the diameter of the pool is 20 feet,
what is the area of the pool? Use 3.14 for .
Answers
The area of the cover require by Justina to cover the pool is 314 ft²
What is the Area of a circle ?
In geometry, the area enclosed by a circle of radius r is πr². Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
Given,
Diameter, d = 20 ft
radius, r = d/2 = 20/2 = 10 ft
Area of a circle = [tex]\pi[/tex]*r² = 3.14*10*10
= 314 ft²
Therefore, The area of the cover require by Justina to cover the pool is 314 ft².
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Point Q is on line segment PR. Given PQ=x,QR=6, and PR =2x-10, determine the numberical length of PR
Answers
When Point Q is on line segment PR, if PQ=x,QR=6, and PR =2x-10, then the length of PR is 18 units
Given,
That point Q is on line segment PR
The length of PQ = x
The length of QR = 6
The length of PR = 2x-10
We know,
Point Q is on line segment PR
So, the length of the PR = Length of PQ + Length of QR
Substitute the values in the equation
2x-10 = x+6
2x-x=6+10
x=14
Substitute the value of x in the equation of the length of line PR
PR= 2x-10
=2×14-10
=28-10
=18 units
Hence, when Point Q is on line segment PR, if PQ=x,QR=6, and PR =2x-10, then the length of PR is 18 units
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Yo i need help asap can yall help me fast?
Answers
By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.
Which pair of fractions is equivalent to each other?
According to the statement, we have the equation of a fraction and we need to find the expression by simplify the former expression. In this situation we must use factor decomposition and algebra properties to make simplification effective:
42 / 49 Given
(2 × 3 × 7) / (7 × 7) Factor decomposition
(2 × 3) / 7 × (7 / 7) Commutative and associative properties / Multiplication of fractions
6 / 7 × 1 Definition of division / Existence of the multiplicative inverse
6 / 7 Modulative property / Result
By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.
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factor the expression completely. begin by factoring out the lowest power of each common factor. 10x−1/2 7x1/2 x3/2
Answers
The method of factoring
x^(-1/2) (x + 5)(x + 2)
[tex]10x^{-1/2} + 7x^{1/2} + x^{3/2} = x^{-1/2} (10 + 7x + x^{2} )\\ = x^{-1/2} (x + 5)(x + 2)[/tex]
The method of factoring is critical to the simplification of many algebraic expressions and is a useful device in fixing higher diploma equations. In truth, the process of factoring is so crucial that little or no of algebra beyond this point can be done without information it.
In earlier chapters the difference among phrases and factors has been stressed. You should take into account that phrases are introduced or subtracted and elements are expanded. 3 important definitions follow.
terms arise in an indicated sum or difference. elements arise in an indicated product.
An expression is in factored shape only if the entire expression is an indicated product.
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