Using the Laplace transform, the value o y' − 2y = (t − 4), y(0) = 0 is⇒y(t) = 0 e^-t + u(t -1)e^1-t
Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in regions of physics, electrical engineering, control optics, arithmetic and sign processing.
y' − 2y = (t − 4),
y(0) = 0
Taking the Laplace transformation of the differential equation
⇒sY(s) - y (0) + Y(s) = e-s
⇒(s + 1)Y(s) = (0+ e^-s)/s + 1
⇒y(t) = L^-1{0/s+1} + {e ^-s/s + 1}
⇒y(t) = 0 e^-t + u(t -1)e^1-t
The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.
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Solve the equation. Write the smaller value of x. x^2-4x-5=0
Given the system of equations, what is the solution? x 3y = 5 x - 3y = -1 {(-4, -3)} {(2, 1)} {(-2, 3)}
The solution of the equation is (2, 1).
x=2 and y=1
What do you meant by equation?A mathematical assertion that two expressions are equal is known as equating. It can be expressed as either an identity, in which case the variables can take on any value, or a conditional equation, in which case the variables can only have specific values (roots).
According to the given information:We have two options for finding the answer. The first is to solve the equations via term elimination:
x + 3y = 5 ..............1
x - 3y = -1 ...............2
2x = 4 ..............3
With the equation, we can determine x. (3)
x = 4/2
x = 2
To determine y, we may now swap out x=2 in equation (1).
x + 3y = 5
2 + 3y = 5
3y = 3
y = 1
We've discovered x and y now.
x=2
y=1
The second method involves removing x from equation 1.
x + 3y = 5
x = 5 - 3y
In the equation right now, we may substitute x = 5 - 3y......... (2)
x - 3y = -1
(5 - 3y) - 3y = -1
5 - 6y = -1
6y = -6
y = 1
Currently, we can change y=1 in equations (1), (2), or (4) to find x.
We'll apply the equation (1)
x + 3y = 5
x + 3(1) = 5
x + 3 = 5
x = 2
The two variants x = 2 and y = 1 have allowed us to confirm this.
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Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play. A score consecutive number of points from smallest to greatest in respect to the order of the name is mentioned. How many points does Lewis score? Options:
A. 19 p
B. 20 p
C. 21 p
D. 18 p
Based on the fact that the number of points scored are consecutive numbers, the number of points scored by Lewis is D. 18 points.
How many points did Lewis score?Lewis is the player who scored the least amount of points as they are first in the order.
To find the total number of points scored in the game therefore, you need to assume Lewis's points based on the options, and then sum up the three numbers above it to see if they add up to 78 points.
If Lewis scored 19 points as the lowest then the total points would be:
= 19 + 20 + 21 + 22
= 82 points
If Lewis scored 20 points, the total points would be:
= 20 + 21 + 22 + 23
= 86 points
Lewis therefore scored less than 19 points.
If Lewis scored 18 points, the total is:
= 18 + 19 + 20 + 21
= 78 points
Lewis therefore scored 18 points.
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Diameter 2
Find the area of the shape
Answer:
pi or 1 pi
Step-by-step explanation:
Area = 1/4 * pi * r^2 (because it is 1/4 of a full circle)
1/4 * pi * 2^2 (the radius is 2 because it is given in the picture)
1/4 * pi * 4 = 1 pi
area = pi
hope this helps! <3
The function f(x) = x2 4 is defined over the interval [-2, 2]. if the interval is divided into n equal parts, what is the height of the right endpoint of the kth rectangle?
the height of the endpoint of the kth rectangle equals the heights of the first and kth preceding rectangles.
= -2 +k*(5/n)
What is Coordinate geometry?The study of geometry utilizing coordinate points is referred to as coordinate geometry (or analytic geometry). Finding the distance between two points, dividing lines in the m:n ratio, locating a line's midpoint, and computing the area of a triangle in the Cartesian plane can all be done using coordinate geometry.
The range for the definition of the function f(x) = x^2 + 4 is (-2, 2).
Between this interval, there are a total of 5 equal pieces.
Height of each rectangle's right endpoint equals if the interval is divided into n equal pieces. k=(5/n)
Therefore, the height of the endpoint of the kth rectangle equals the heights of the first and kth preceding rectangles.
= -2 + k*(5/n)
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Please use elimination method to solve
The answer is x = 4, y = -1 or (4, -1).
We are given :
2x + 7y = 13x + 4y = 8Multiply the 1st equation with 3 and 2nd equation with 2.
3. 3(2x + 7y) = 3(1) ⇒ 6x + 21y = 3
4. 2(3x + 4y) = 2(8) ⇒ 6x + 8y = 16
Now, subtract : Equation 3 - Equation 4.
6x + 21y - 6x - 8y = 3 - 1613y = -13y = -1Substitute in the 1st equation.
3x + 4(-1) = 83x - 4 = 83x = 12x = 4Answer:
(4, - 1 )
Step-by-step explanation:
2x + 7y = 1 → (1)
3x + 4y = 8 → (2)
multiplying (1) by 3 and (2) by - 2 and adding will eliminate x
6x + 21y = 3 → (3)
- 6x - 8y = - 16 → (4)
add (3) and (4) term by term to eliminate x
0 + 13y = - 13
13y = - 13 ( divide both sides by 13 )
y = - 1
substitute y = - 1 into either of the 2 equations and solve for x
substituting into (1)
2x + 7(- 1) = 1
2x - 7 = 1 ( add 7 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
solution is (4, - 1 )
1/2.x + 3 ( x-1 ) - 5 = 30
Answer:
1/2.x+3(x-1)-5=30
1/2.x+3x-3-5=30
(1/2+3)x-8=30
7/2.x-8=30
7/2.x=38
7x=76
x=76/7
CMIIW
If a member states, "i don’t know what to say to my father" during a role play. The best response from the leader will be?
The sentence "If this is the last chance you have to speak to him, what do you want to tell him" will be the best response from the leader.
What is a role play?This refers to the act of imitating the character and behaviour of someone who is different from yourself which an example is a training exercise which involves imitating of another people.
Sometimes, during the role play, the member of the group can run out of words while presenting a role, hence, as the member states, "i don’t know what to say to my father", the sentence "If this is the last chance you have to speak to him, what do you want to tell him" will be the best response from the leader to induce the member to talk.
Therefore, the Option C is correct.
Missing word "a. What or whom do you want to get away from? b. What made you come if you didn't want to be here today? c. If this is the last chance you have to speak to him, what do you want to tell him? d. What do you imagine will happen if you don't talk about it?"
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Determine the qualities of the given set. (select all that apply. ){(x, y) | x > 0, y > 0}
The qualities of the set {(x,y): x>0,y>0} is as under:
All points lie in first quadrant.All values are positive and greater than zero.Given a set {(x,y),x>0,y>0}.
We are required to determine the qualities of the set.
We know that a set is a collection of things,numbers, fractions, etc.
In any set the values of x represents the domain of the function and the values of y represents the value of codomain of the function with which the set belongs to.
Set={(x,y): x>0,y>0}
From the above set we can find the qualities stated below:
All points lie in first quadrant as the first quadrant only contains positive values of x and y.All values are positive because it is given that they are greater than zeroHence the qualities of the set {(x,y): x>0,y>0} are that all values should be in first quadrant and all the values are positive.
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(08.05 MC)The following box plot shows the number of books sold each day at a bookstore for 40 days. How many days did the bookstore sell 2 to 12 books?
A box plot is drawn with end points at 0 and 16. The box extends from 2 to 12 and a vertical line is drawn inside the box at 7
2
4
10
20
Considering the given box-and-whisker plot, it is found that the bookstore sold between 2 to 12 books in 20 days.
What does a box-and-whisker plot shows?A box and whisker plot shows three things:
The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.From the plot given in this problem, the have that:
The 25th percentile is of 2.The median is of 7.The 75th percentile is of 12.This means that the percentage of days in which between 2 to 12 books were sold is:
P = 75 - 25 = 50%.
Hence, out of 40 days, the amount of days is:
0.5 x 40 = 20 days.
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It is October and that means it is State Fair time again! Your uncle took you and 2 of your friends to the
fair. Admission for everyone to get into the fair was $20.00. You then went to the Midway, where they
have all of the rides, and he bout all-day ride passes for you and your friends. If your uncle spent a total
of $65.00 at the fair, how much did each of the all-day ride passes cost?
Answer: All-day ride passes cost $15 each
Step-by-step explanation:
It was $20 in total for everyone to get in, so subtract that from $65 to just focus on the all day passes
65-20=45
So the all day passes all together cost $45
Since your uncle bought it for you and 2 friends that's 3 people in total so divide 45 by 3
45 divided by 3 = 15
So each of the all day passes cost $15
Hope this helped :)
What is the value for x when solving the equation –x (–1) = 3x (–5) using algebra tiles? x = –1 x = 1 x = 2 x = 3
The value of x in the equation –x (–1) = 3x (–5) is x = 1
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
–x (–1) = 3x (–5)
Remove the bracket in the above equation
-x - 1 = 3x - 5
Collect the like terms in the above equation
3x + x = 5 - 1
Evaluate the like terms in the above equation
4x = 4
Divide both sides by 4 in the above equation
x = 1
Hence, the value of x in the equation –x (–1) = 3x (–5) is x = 1
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Answer:
-3, or D
Step-by-step explanation:
What is the exponential function that best models the number of gnats the scientists have
gathered after the number of hours listed in the table below?
Answer:
(b) f(x) = 12.5(1.6^x)
Step-by-step explanation:
An exponential model is generally of the form ...
f(x) = a·b^x
where 'a' is the initial value (for x=0), and 'b' is the growth factor, the multiplier when x increases by 1.
Growth factorThe ratio of the f(x) values for x=0 and x=1 is 20/12 ≈ 1.67. A number close to this will be the growth factor in the exponential function. There is only one answer choice showing a growth factor near 1.6. (Eliminates choices A, C, D.)
An exponential regression model can be produced by many graphing calculators and spreadsheets. The attachment shows a model that has the values matching choice B.
A weaver bought a bundle of grass of 50.00 dollars from which he made 8 mats if each mats was sold for 15.00 dollars find the percentage profit
The percentage profit is 140%
What is percentage?
Percentage can be described as the expression of a number in hundredth.
The formula for calculating percentage profit is
profit/cost price × 100
cost price= $50
selling price= $15
number of mats produced= 8
selling price of the mat= 15 × 8
= 120
Profit= selling price-cost price
= 120-50
$70
Therefore the percentage profit can be calculated as follows
= 70/50 × 100
= 1.4 ×100
= 140
Thus, the percentage profit is 140%
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The vertices of an isosceles triangle are A(3, 6), B(7, 2), and C4, 3).
What is the equation of the triangle's line of symmetry?
Answer:
[tex]y=x-1[/tex]
Step-by-step explanation:
The line of symmetry of an isosceles triangle is perpendicular to its base.
Given vertices of the isosceles triangle:
A = (3, 6)B = (7, 2)C = (4, 3)By sketching the triangle with the given points, we can see that AB is its base. (See attached graph).
To find the equation for the line of symmetry, first find the slope of the line AB. To do this, use the coordinates of points A and B and the slope formula.
Define the points:
[tex]\textsf{Let }(x_1,y_1)=(7, 2)[/tex][tex]\textsf{Let }(x_2,y_2)=(3, 6)[/tex][tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{3-7}=-1[/tex]
As the line of symmetry is perpendicular to line AB, its slope is the negative reciprocal of the slope of line AB.
Therefore, the slope of the line of symmetry = 1.
The line of symmetry will pass through point C (4, 3).
Therefore, substitute the found slope and the coordinates of point C into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=1(x-4)[/tex]
[tex]\implies y-3=x-4[/tex]
[tex]\implies y=x-1[/tex]
Therefore, the equation of the given isosceles triangle's axis of symmetry is:
[tex]y = x - 1[/tex]
If we graph the points
then we will get AC=CB
That means C is the point from where the axis of symmetry passes
Foot of perpendicular is midpoint of AB
Midpoint of AB
((3+7)/2,(6+2)/2)(10/2,8/2)(5,4)Find equation of C and foot of perpendicular
Slope
m=(4-3)/(5-4)=1Equation
y-3=1(x-4)y-3=x-4y=x-1Does anybody know this? Evaluate the following expression using the correct order of operations.
Answer:
-4
Step-by-step explanation:
Wehn dealing with order of operations, we can remember the expression PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction.
So, our first step in the above problem is the parentheses:
[tex]2(3-5)^3+4(-4+7)\\2(-2)^3+4(3)[/tex]
The second step is exponents:
[tex]2(-2)^3+4(3)\\2(-8)+4(3)[/tex]
The third step is multiplication:
[tex]2(-8)+4(3)\\-16+12[/tex]
The fourth and final step is addition:
[tex]-16+12\\-4[/tex]
Which values below belong in this table? Select all that apply.
The possible value of y are 16, 32 and 64
How to find the values of an exponential table?The table above is an exponential table.
Therefore, let's confirm the ratio of the y axis.
8 / 4 = 2
4 / 2 = 2
Therefore, the other y axis can be gotten as follows:
y = 8 × 2 = 16
y = 16 × 2 = 32
y = 32 × 2 = 64
y = 64 × 2 = 128
Therefore, the possible value of y are 16, 32 and 64
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Which do you think is easier to understand and why do you think so, multiplying radicals or multiplying polynomials?
I believe that its easier to understand the multiplication of a radical than that of a polynomial.
How to illustrate the information?In mathematics, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.
A polynomial is an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.
When multiplying radicals with the same index, multiply under the radical, and then multiply in front of the radical. An example is:
= 3✓2 × 4✓2
= 12✓4
= 12 × 2
= 24
The multiplication of a radical is easier.
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-5/12 - (-9/3) what is the answer for this equation
Answer:
2 7/12
Step-by-step explanation:
Simple fraction problem
Question
Each square on the grid represents 1 km2.
What is the approximate area of this park?
about 10 km2 to 20 km2
about 10 km 2 to 20 km 2
about 25 km2 to 35 km2
about 25 km 2 to 35 km 2
about 40 km2 to 50 km2
about 40 km 2 to 50 km 2Question
Each square on the grid represents 1 km2.
What is the approximate area of this park?
about 10 km2 to 20 km2
about 10 km 2 to 20 km 2
about 25 km2 to 35 km2
about 25 km 2 to 35 km 2
about 40 km2 to 50 km2
about 40 km 2 to 50 km 2
The approximate area of the park on the grid is: E. about 40 km² to 50 km².
How to Find the Approximate Area on a Coordinate Grid?The number of square on a coordinate grid that is covered determines the area covered. We can make an estimate by counting how many of this square on the coordinate grid that is covered, then find out the area depending on how much square area each grid represents.
In the coordinate plane given, which shows a park, we are told that each of the square on the grid equals 1 k = square kilometer.
The number of each of these squares we can find that is covered by the park on the grid is: 48 squares.
Therefore, the area of 48 squares on the grid = 48 × 1 = 48 km². Since not all squares are fully covered by the park, we can state that the approximate area of the park on the grid is: E. about 40 km² to 50 km².
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+
Simplify the following expressions by combining the like terms!
3) 4x-7-y+6-2y
4) 6y + 2(y + 1) - 5
5) 3(2+3x) + 4(y + 2x) - 6
Answer:
5) 3(2+3x)+4(y+2x)-6
Step-by-step explanation: its gone be -6 either way
Use the figure to the right to list all of the pairs of angles that fit each description.
The pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Angle DescriptionFrom the question, we are to list the angles that fit the given descriptions
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W;
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Hence, the pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
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What is [tex]\frac{3}{4}[/tex] - [tex]\frac{2}{b}[/tex]
The answer is [tex]\boxed {\frac{3b - 8}{4b}}[/tex].
3/4 - 2/b3(b) - 2(4) / 4(b)3b - 8 / 4b"if i purchase this product for $79.99 and two accessories for $9.99 and $7.00, how much would i owe after the 8.75% tax is applied?" employee: "your total would be __________."
Answer:$96.98
Step-by-step explanation: all you just do is to add it all up to the total amount.
Answer: $105.47
I hope you get the job!!!!!
Which equation represents the explicit formula for a constant velocity arithmetic sequence?
A. xₙ = x₁+(n-1)(v•△t)
B. xₙ = x₁+(n+1)(v/△t)
C. xₙ = x₁+(n+1)(v•△t)
D. xₙ = x₁+(n-1)(v/△t)
The equation which represents the explicit formula for a constant velocity arithmetic sequence is; Choice A; xₙ = x₁+(n-1)(v•△t).
Which equation among the answer choices represents the explicit formula for a constant velocity arithmetic sequence?It follows from convention that an arithmetic sequence is usually defined by an expression of the form;
T(n) = T(1) + (n-1)×d in which case, d = common difference.
Consequently, in the event that the velocity in discuss is constant, it follows that the required expression is; Choice A; xₙ = x₁+(n-1)(v•△t).
Therefore, xₙ = x₁+(n-1)(v•△t) represent the equation for explicit formula for a constant velocity arithmetic sequence.
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A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid.
A solid right pyramid has a square base. The base edge length is 2 centimeters longer than the height of the pyramid. The height of the pyramid is 6 centimeters.
If the height is 6 cm, what is the volume of the pyramid?
24 cm3
48 cm3
128 cm3
144 cm3
Answer: it’s 128 (also what you did on my question was not cool, do better)
Step-by-step explanation:
We know the height is 6 and the length is 2 more than the height then the length is 8 (6+2=8) and then you solve for volume and get 128
The correct answer for the volume of the pyramid is [tex]128[/tex] cm³.
Given:
Square base edge lenght 2 cm than the height of the pyramid.
Height of the pyramid is 6 cm.
Square base edge length = Height of pyramid + 2cm
= 8 cm.
Base area:
Area of the square is calculated as side².
Area of square = 8*8
= 64 cm²
Volume of pyramid is calculated as [tex]\dfrac{1}{3} *basearea*height[/tex]
[tex]\dfrac{1}{3}*64*6\\\\ =128[/tex]
The volume of the pyramid is [tex]128[/tex] cm³.
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A rectangular prism with a square base is cut from the center of a triangular prism. each side of the square base measures 1.7 units.what is the volume of the shaded solid? round to the nearest tenth of a cubic unit.11.6 units345.4 units357.0 units368.6 units3
Rounding to the closest tenth of a cubic unit, the shaded solid's volume is 45.4 cubic units.
What is rectangular prism?The 3D shape of a rectangular prism has six rectangular faces. Multiply a rectangular prism's three dimensions—length, width, and height—to determine its volume. Cubic units are used to measure volume.
According to the given information:The following formula can be used to determine a rectangular prism's volume:
Vr = Height * Width * Length
Triangular prism volume Vt is determined by its base area and height.
concerning the rectangular prism;
Vr = 1.7 × 1.7 × 4
Vr = 11.56 units in 3
Regarding the triangular prism
Vt = 0.5 × 5.7 × 5 × 4
Vt = 57 unit3
Volume of the solid shaded by Vt - Vr
The solid's shaded volume is equal to 57 - 11.56.
The colored solid's volume is 45.44 cubic units.
Due to this, the shaded solid's volume, when rounded to the nearest tenth of a cubic unit, is 45.4 cubic units.
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Select all the ways that express the number 32.148.
A 32 tens + 14 tenths + 8 hundredths
B 32 ones + 14 hundredths + 8 thousandths pauodt er
C 321 tenths + 48 thousandths
D 32,148 hundredths
E 32,148 thousandths
Answer: B, C, E
Step-by-step explanation: a is wrong 32 tens is 320. B is right. 321 tenths is 32.1 and 48 thousandths is 0.048 so C is correct. 32,148 hundredths is too much but 32,148 thousandths is 32.148
At 3:00 PM a man 138 cm tall casts a shadow 149 cm long. At the same time, a tall building nearby casts a shadow 163 m long. How tall is the building?
The building is 151 meters tall
How to determine the height of the building?From the question, we have the following parameters about the building and the man
Man's height = 138 cm
Man's shadow = 149 cm
Building's shadow = 163 m
Based on the above parameters, we have the following equivalent ratio:
Ratio = Height : Shadow
So, we have:
Man's height : Man's shadow = Building's height : Building's shadow
Substitute the known values in the above equation
138 cm : 149 cm = Building's height : 163 m
Remove the units
138 : 149 = Building's height : 163
Express as fraction
138 /149 = Building's height/163
Multiply both sides by 163
Building's height = 163 * 138 /149
Evaluate the product
Building's height = 151 m
Hence, the building is 151 meters tall
So, the complete parameters are:
Man's height = 138 cm
Man's shadow = 149 cm
Building's shadow = 163 m
Building's height = 151 m
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xy =8 inches wy =24 and xz=48 inches height from the ground to the base of the window is?
The height of the ground from the base of the window is 144 inches.
How to find the side of a right angle triangle?One angle of a right angle triangle is equals to 90 degrees.
Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.
tan x = WY / XY
tan x = opposite / adjacent
tan x = 24 / 8
x = tan⁻¹ 3
x = tan⁻¹ 3
x = 71.5650511771
x = 71.60°
tan 71.60 = h / 48
cross multiply
h = 48 tan 71.60
h = 48 × 3
h = 144 inches
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