At (0.958, 0.287, 5) and (0.958, -0.287, -5) points, the helix r(t) = sin(t), cos(t), t intersect the sphere x^2 + y^2 + z^2 = 26.
The sphere x^2 + y^2 + z^2 = 26 is a sphere with center at the origin and radius sqrt(26).
The helix r(t) = sin(t), cos(t), t is parameterized by sine and cosine functions, which oscillate between -1 and 1.
To find the points at which the helix intersects the sphere, we need to find the values of t such that the distance between r(t) and the origin is equal to sqrt(26).
The distance between a point (x, y, z) and the origin is given by the formula:
d = sqrt(x^2 + y^2 + z^2)
So, substituting the values from r(t), we have:
d = sqrt(sin^2(t) + cos^2(t) + t^2)
Setting d equal to sqrt(26), we have:
sqrt(sin^2(t) + cos^2(t) + t^2) = sqrt(26)
Squaring both sides, we have:
sin^2(t) + cos^2(t) + t^2 = 26
Recall that sin^2(t) + cos^2(t) = 1, so we have:
1 + t^2 = 26
Subtracting 1 from both sides, we have:
t^2 = 25
Taking the square root of both sides, we have:
t = ±5
So, the two points of intersection are (sin(5), cos(5), 5) and (sin(-5), cos(-5), -5).
Rounding the results to three decimal places, we have:
(sin(5), cos(5), 5) = (0.958, 0.287, 5)
(sin(-5), cos(-5), -5) = (0.958, -0.287, -5)
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What is the answer to this?
Answer:
$24,000
Step-by-step explanation:
20,000x(1+0.05x4)=20,000x1.2=24,000
What time is 2330 in military time?
The first two digits represent hours, and the last two digits represent minutes. 00:00 is midnight and 12:00 is noon. 0001 to 1159 defaults to "A.M." hour.
11:30 PM in regular time on a 12-hour clock.
1. 23:30 represents afternoon time, so we add 12 hours to the given time.
2. 11 + 12 hours = 23 hours
3. minutes is always the same no matter which time format is used.
4. Remove PM and colon.
5. conversion 11:30 23:30 war time
Step 1
First divide the given time into hours and minutes. For wartime 2330, this is 23 hours and 30 minutes.
Step 2
Then check if the set time is greater than 1300. Since 2330 is greater than 1300, we use the hour subtraction rule (23 - 12 = 11 hours).
Step 3
Military time minutes are the same as standard time, so 30 minutes is still 30 minutes.
Step 4
Add a colon between the calculated hours and minutes, and the result is 11:30.
Step 5
2330 is greater than 1200, so according to the mentioned rules, adding the PM after the expected time gives 23:30 regular time.
The correct answer is 23:30 standard time.
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A swimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t= 0, city water containing 0.003% chlorine is pumped into the pool at a rate of 6 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.006% chlorine? What is the percentage of chlorine in the pool after 1 hour? After 1 hour the pool will be % chlorine. (Round to four decimal places as needed.)
The pool water will be 0.006% chlorine after approximately 236.5 minutes, and the percentage of chlorine in the pool after 1 hour (60 minutes) is approximately 0.674%.
Let C(t) be the amount of chlorine in the pool at time t in minutes, measured in gallons of chlorine. Since the volume of the pool is 10,000 gal and the initial concentration of chlorine is 0.01%, we have:
C(0) = 10,000 gal x 0.01% = 1 gal
As city water containing 0.003% chlorine is pumped into the pool at a rate of 6 gal/min and the pool water flows out at the same rate, the differential equation for C(t) is:
dC/dt = (0.003 - C(t)/10,000) x 6 - C(t)/10,000 x 6
Simplifying the right-hand side and solving the differential equation using separation of variables, we get:
C(t) = 30,000(1 - e^(-t/166.7)) - 180,000e^(-t/166.7)
After 1 hour (60 minutes), we have:
C(60) = 30,000(1 - e^(-60/166.7)) - 180,000e^(-60/166.7) ≈ 0.0674 gal
The percentage of chlorine in the pool after 1 hour is:
0.0674 gal / 10,000 gal x 100% ≈ 0.674%
To find when the pool water is 0.006% chlorine, we set C(t) = 10,000 gal x 0.006% = 0.6 gal and solve for t:
30,000(1 - e^(-t/166.7)) - 180,000e^(-t/166.7) = 0.6
Using numerical methods, we find that t ≈ 236.5 minutes.
After roughly 236.5 minutes, the chlorine content of the pool will be 0.006%, and after an hour (60 minutes), it will be approximately 0.674%.
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find the unit rate!
it would end up by costing $0.55 cents a cup
A customer purchases a pair of jeans and a few shirts. Each shirt costs the same amount. The expression 60 + 20x represents the cost before tax.
What do the different parts of the expression model?
Drag the parts of the expression into the boxes to match each description.
cost of jeans | Total cost of the shirts
60, 20x, 20, x
Answer:
Cost of Jeans: $60
Total cost of shirts: 20x
Number of shirts purchased: x
Total cost of all combined: 20x + 60
Step-by-step explanation:
The expression given is 60 + 20x.
Note that it is stated that the customer purchases only ONE pair of Jeans, which implies that the constant 60 is the price of the said jeans.
"A few [shirts]" implies an unknown amount of the product (shirts). The unknown amount can be denoted as a variable, which in case the question implies as x. Based on the given expression, it is implied that the cost per shirt is $20, as you will multiply the amount of shirt with the base amount for shirts.
In this case:
Cost of Jeans: $60
Total cost of shirts: 20x
Total cost of all combined: 20x + 60
Number of shirts purchased: x
~
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Find the measure of the missing angle
Answer:
Step-by-step explanation:
a= 180-130
= 50 (angles on a straight line)
Factor f(x) into linear factors given that k is a zero of f(x).
11) f(x) = 2x3 - 3x2 - 5x + 6; k = 1
A) f(x) = (x − 1)(x + 1)(2x − 6)
B) f(x) = (x - 1)(x + 2)(2x - 3)
C) f(x) = (x + 1)(x + 2)(2x - 3)
D) f(x) = (x − 1)(x − 2)(2x + 3)
Answer:
Step-by-step explanation:
If k=1 is a zero of f(x), then (x-1) is a factor of f(x) by the factor theorem. We can use polynomial long division or synthetic division to find the quotient when f(x) is divided by (x-1):
2 -3 -5 6
1| 2 -1 -6
2 -3 0
The quotient is 2x^2 - 3x, so we can write f(x) as:
f(x) = (x-1)(2x^2 - 3x) = (x-1)x(2x-3)
Therefore, the correct answer is B) f(x) = (x-1)(x+2)(2x-3).
What is the value of 156 kg in lbs?
The formula for converting kilograms (kg) to pounds (lbs) is to multiply the mass in kilograms by 2.20462262.The calculation for converting 156 kg to lbs is 156 x 2.20462262 = 344.7382612 lbs.
Thus, the value of 156 kg in lbs is 344.7382612 lbs.To better understand, we can break down the formula into steps. We start by multiplying the kilograms (kg) by 2. This results in 312, which is twice the mass in kilograms. We now add 0.20462262 to the result (312). This gives us a total of 312.20462262, which is the equivalent of 156 kg in lbs.The result of the formula is a unit of mass in the imperial system of measurement. The imperial system of measurement is used in the United States and Great Britain, and is based on pounds (lbs).To further illustrate, one kilogram is equal to 2.20462262 pounds. Thus, 156 kg is equal to 156 x 2.20462262 = 344.7382612 lbs.In conclusion, it is possible to convert kilograms (kg) to pounds.
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Write a statement that increases numpeople by 5. Ex: if numpeople is initially 10, the output is: there are 15 people.
A statement that increases numpeople by 5 is
numpeople = numpeople + 5
Here's a statement that increases the value of numpeople by 5:
numpeople = numpeople + 5
After executing this statement, the value of numpeople will be increased by 5. For example, if numpeople was initially 10, the value of numpeople would be 15 after executing this statement.
Here's a complete program that demonstrates the statement:
numpeople = 10
print("There are", numpeople, "people.")
numpeople = numpeople + 5
print("There are", numpeople, "people.")
This program would output the following:
There are 10 people.
There are 15 people.
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What is the solution to the system of equations?{y=−5x+1}{−5x−y=−3}
Answer: [tex](0.2,2)[/tex]
Step-by-step explanation:
[tex]-5x-y=-3[/tex]
add y on both side of the equation
[tex]-5x=y-3[/tex]
add 3 on both side of the equation
[tex]y=-5x+3[/tex]
Then insert [tex]-5x+3[/tex] as y in the equation [tex]y =5x+1[/tex]
[tex]5x+1=-5x+3[/tex]
add 5x on both side of the equation
[tex]10x+1=3[/tex]
minus 1 on both side of the equation
[tex]10x=2[/tex]
divide by 10 on both side of the equation
[tex]x=0.2[/tex]
That is how you get x
To get y, you would sub 0.2 for x in the equation [tex]y=5x+1[/tex] or[tex]-5x-y=-3[/tex], I prefer the first equation
[tex]y=5x+1[/tex]
sub 0.2 for x
[tex]y=5(0.2)+1[/tex]
multiply 5 by 0.2
[tex]y=1+1[/tex]
add them up
[tex]y=2[/tex]
and there you go for y
The solution would be in a [tex](x,y)[/tex] form. So, [tex](0.2, 2)[/tex] would be our answer.
What is the least common multiple between of 5 and 9
The company plans to find the center of the data an give a 5% raise to the employees who have been employee for at least those number of years.Find the mean and median,and explain which will be better from the employees prescriptive.
Number of years of each employed {11,6,32,7,18,4,9,1,15,9,5,27}
The mean is 11.25 and median is 8, and from the employees' perspective, the median would be a better measure of central tendency to use for determining the raise cut-off point.
The mean and medianTo find the mean and median, we can start by arranging the data in ascending order:{1, 4, 5, 6, 7, 9, 9, 11, 15, 18, 27, 32}
Mean:The mean is the average value of the dataset. We can find the mean by summing up all the values and dividing by the total number of values:
mean = (1 + 4 + 5 + 6 + 7 + 9 + 9 + 11 + 15 + 18 + 27 + 32) / 12
= 135 / 12
= 11.25
Therefore, the mean of the dataset is 11.25.
Median:The median is the middle value in the dataset. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
In this case, the dataset has 12 values, so we need to find the average of the 6th and 7th values:
median = (7 + 9) / 2
= 8
Therefore, the median of the dataset is 8.
From the employees' perspective, the median would be a better measure of central tendency to use for determining the raise cutoff point. This is because the median is not affected by outliers as much as the mean.
In this dataset, the value of 32 is much larger than the other values and could skew the mean upward, which would result in a higher cutoff point for the raise. On the other hand, the median is not affected by the outlier and provides a better representation of the central value of the dataset.
A 5% raise for employees who have been employed for at least 8 years (the median) would be more fair and reasonable for all employees.
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The quadrilateral is a trapezoid. What is the value of x?
A. 4
B. 5
C. 48
D. 25
If the quadrilateral is a trapezoid , then the value of x is = (b) 5 .
We know that the Midsegment of a trapezoid is parallel to each of the base and it's length is one half the sum of the lengths of the bases.
From the figure , we can observe that ⇒ side lengths are 21 units, 27 units , and the sides are parallel to each other.
From the given diagram of the trapezoid , the below expression is true:
that means : ⇒ 5x-1 = (21 + 27)/2 ;
⇒ 2(5x - 1) = 21 + 27 ;
⇒ 10x = 48 + 2 ;
⇒ 10x = 50
On Divide both sides by 10 ;
we have ;
⇒ x = 50/10 ;
⇒ x = 5 .
Therefore , for the quadrilateral the value of x is = 5 .
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The given question is incomplete , the complete question is
The quadrilateral in the below figure is a trapezoid. What is the value of x ?
(a) 4
(b) 5
(c) 48
(d) 25
What is the value of x in the triangle?
45° + 45 + 90
12 squared 2 + 12 squared 2 + x
The value of x is 24.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Given is a right angled triangle since one of the angle is 90 degrees.
Length of leg 1 = 12√2
Length of leg 2 = 12√2
Length of hypotenuse = x
By Pythagoras theorem,
Hypotenuse² = (leg 1)² + (leg 2)²
x² = (12√2)² + (12√2)²
x² = 2 × (12√2)²
= 576
x = √576
x = 24
Hence the value of x is 24.
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Your question seems incomplete. Probably, the complete question is as follows.
What is the value of x in the triangle?
a 45-45-90 triangle with a leg of length 12 times the square root of 2 and hypotenuse of length x
What do you call a nine sided polygon?
Answer:
a nonagon
Step-by-step explanation:
The table shows some information about the dress sizes of 100 women.
Dress size Number of women
a) Find the median dress size.
16
38
27
19
(1)
10
12
14
16
10 of the 100 women have a shoe size of 6
Sue says that if you choose at random one of the 100 women, the probability
that she has either a shoe size of 6 or a dress size of 16 is 0.29 because
0.1 +0.19 = 0.29
b) Is Sue correct?
State the answer, Yes or No and give a reason for your answer.
(
The solution is the median dress size = 12.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
here, we have,
given that,
from the given data we get,
dress sizes are, 10, 12 , 14, 16
no. of dresses, 16, 38, 27, 19
Hence, using the formula we get, the median dress size = 12.
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Find the area of a circle with diameter 27.2m, both in terms of r and to the nearest tenth. Use 3.14 for r
We have to find the area of a circle which has a diameter of 27.2 m
We know that the area of the circle is:
A = πr², where A = area of the circle and r = radius
Given Diameter = 27.2 m
We know that Radius = Diameter/2,
So, Radius = [tex]\frac{27.2}{2}[/tex]
Radius = 13.6 m
Now, area of circle = 3.14 * 13.6 * 13.6
Area = 580.77
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Flap Pole A and C are both casting a shadow question
Based on the proportionate ratio, the height of flagpole c is 7.5ft.
From the case, we know that both flagpoles positions created a similar triangle, where:
a = 16.5 ft
x = 12 ft
y = 10 ft
c ?
To find the height of flagpole c, we can use the proportionate ratio as:
a = (x + y)
c y
16.5 = (12 + 10)
c 10
16.5 / c = 22 / 10
22c = 16.5 (10)
22c = 165
c = 7.5
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What is Residual sum of square?
Residual sum of squares (RSS) is a measure of the total amount of variance in a given data set that is not explained by a model.
It is equal to the sum of squared differences between the observed data values and the predicted values from the model. This measure is commonly used in regression analysis to evaluate the performance of a model. The formula for RSS is RSS = Σ(y_i - ȳ)², where y_i is the observed value and ȳ is the predicted value.For example, let's say we have a data set of 10 observations (y_1, y_2, ...,y_10). We fit a linear regression model to the data set which predicts a value ȳ_i for each observation. The RSS for this model is calculated by summing the squared differences between the observed values (y_i) and the predicted values (ȳ_i) for each of the 10 observations. This yields the RSS, which is a measure of how much of the variance of the data set is not explained by the model.
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What is the equation of the new line when the parent equation:y = x , is transformed by reflecting over the y - axis and is translated down 8 units?
A. y = -x - 8
B. y = -x + 8
C. y = -8x
D. y = x - 8
The solution is Option A.
The transformed equation is y = -x - 8
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be represented as A
Now , the value of A is
f ( x ) = x or y = x
Now , when the function is reflected over the y-axis , the x coordinate of the function is changed to its additive inverse
So , reflected function is g ( x ) = -x
Now , when the function is translated down 8 units ,
It is a vertical shift of down by d units: y = f(x) - d
The new transformed function is h ( x ) = -x - 8
Hence , the transformed function is y = -x - 8
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You want to show that KML is similar to FGH using Side-Side-Side Similarity Theorem. Complete the extended proportion that can be used to show such a similarity.
KM/?=?/FH=ML/?
A.) Fill in the blank: KM/?
B.) Fill in the blank: ?/FH
C.) Fill in the blank: ML/?
The extended proportion that can be used to show such a similarity is:
KM/ FG = KL/ FH = ML/ GH
What are similar triangles?Two or more triangles are said to have similar relations if on comparing their corresponding sides and measure of angles, there exist some common relations among them. Similarity of triangles can be expressed by some common terms in relation to their sides and angles.
In the given question, it has been stated that the triangles are similar using Side-Side-Side similarity theorem. Thus on comparison, the extended proportion that can be used to show such a similarity is:
KM/ FG = KL/ FH = ML/ GH
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Greta is a contestant on the kids' game show, Spend or Switch! When she makes it up on stage, host Guy Granger takes out a stack of one hundred-dollar bills. He divides the bills evenly among all 5 contestants on stage. Each contestant receives 4 one hundred-dollar bills. Which equation can you use to find the number of bills b in Guy Granger's stack?
Answer:
Step-by-step explanation:
If Guy Granger's gave each contestant 4 bills and there are 5 contestants, then you would multiply 4x5 which would give you 20. This is the amount of bills in Guy Granger's stack.
2. ALGEBRA LaToya Barnes' credit card uses the average-daily-
method of computing finance
balance-including-purchases
charges. Her card has a monthly periodic rate of 1.76% and
shows a finance charge of $7.64. Find her average daily balance
for the past billing cycle.
If ALGEBRA LaToya Barnes' credit card uses the average-daily-
method of computing finance balance-including-purchases charges. her average daily balance for the past billing cycle is 434.
What is the her average daily balance?The average daily balance can be found by using the formula:
Average Daily Balance = (Finance Charge / Monthly Periodic Rate)
Now we can plug in the values and solve for the average daily balance:
Average Daily Balance = (7.64 / 0.0176)
Average Daily Balance =434
Therefore, LaToya Barnes' average daily balance for the past billing cycle was 434.
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Solve the following inequality.
-8 < 3x+1 <7
Answer:
move all terms not containing x from the center section of the inequality -3<x<2
interval notation
(-3,2)
Step-by-step explanation:
Please help me I’ll give you the best rating nO lie Trust
The distance the cyclist travelled during the time are as follows;
4 meters, 18 m and 45 etc.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
Distance = speed x time
Distance = 5 x 0.8
= 4 meters
Distance = 10 x 1.8
= 18 meters
Distance = 15 x 3
= 45 meters.
Here Segment shows as time is increasing, distance is also increasing. Which means the cyclist is moving forward at a speed.
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The graph of a quadratic function with vertex (0,3) is shown in the figure below find the domain and range
The domain of this quadratic function is {-∞, ∞}.
The range of this quadratic function is {3, ∞}.
How to determine of this quadratic function?In Mathematics, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Generally speaking, the domain of this quadratic function are all the x-values (independent value) that are located on the x-axis of the graph, which include {-∞, ∞} or all real numbers.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞}.
Range = {3, ∞}
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Similar shapes and scale drawings worksheet
Answer:
Step-by-step explanation:
wheres the worksheet...
Allergy Sufferer #1 must take one capsule every 6 hours. Allergy Sufferer #2 must take one capsule every 12 hours. Together, how many hours will it take them to consume 45 capsules?
180 hours will it take them to consume 45 capsules.
What is least common multiple ?
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the given numbers. In other words, it is the smallest number that is divisible by all the given numbers without leaving a remainder.
To find the LCM of two or more numbers, you can list their multiples and look for the smallest number that appears in all the lists. However, this can become time-consuming for large numbers. There are various methods and algorithms to find the LCM efficiently, such as using prime factorization or the Euclidean algorithm.
According to the question:
Allergy Sufferer #1 takes 1 capsule every 6 hours, so in 45 capsules, they will need to take 45 * 6 = 270 hours.
Allergy Sufferer #2 takes 1 capsule every 12 hours, so in 45 capsules, they will need to take 45 * 12 = 540 hours.
To find the total time it will take them together to consume 45 capsules, we need to find the least common multiple (LCM) of 6 and 12.
The prime factors of 6 are 2 and 3.
The prime factors of 12 are 2, 2, and 3.
To find the LCM, we take the highest power of each prime factor that appears in either factorization. In this case, that's 2^2 * 3 = 12.
So, the LCM of 6 and 12 is 12.
This means that every 12 hours, Allergy Sufferer #1 will have taken 2 capsules (since 12/6=2), and Allergy Sufferer #2 will have taken 1 capsule.
Therefore, in 12 hours, they will have taken a total of 2+1=3 capsules.
So, to consume 45 capsules, it will take them 45/3 = 15 lots of 12 hours, which is 180 hours in total.
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whats the missing number?
Answer:180
Step-by-step explanation:
1-------60
2-------120
3-------x
4------240
n-------60*n
so, 3-----60*3=180
TREES From point A,
the angle of elevation to the top of a pine tree is 42°.
From point B,
on the same side of the tree, the angle of elevation to the top of the tree is 50°.
If point A
and point B
are located 12
feet apart and are both at ground level, what is the approximate height of the tree to the nearest foot?
feet
Answer:
44 ft
Step-by-step explanation:
You want to know the height of a tree whose top is at angles of elevation of 42° and 50° from points 12 feet apart.
TangentThe tangent of an angle is related to the side lengths of a right triangle by ...
Tan = Opposite/Adjacent
This tells us the length of the side adjacent to the angle of elevation is ...
Adjacent = Opposite/Tan
ApplicationHere, the height of the tree is the side of the triangle opposite the angle of elevation, and the difference of adjacent sides is 12 ft:
12 = h/tan(42°) -h/tan(50°)
h = 12/(1/tan(42°) -1/tan(50°)) ≈ 12/(1.11061 -0.83910) ≈ 44.197
The approximate height of the tree is 44 feet.