A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. Approximate the length of the pole. Round to the nearest hundredth.
Answers
The length of the pole is 19.15 feet.
What is the angle of elevation?The angle of elevation is the angle created when an observer looks at an object placed above its height in relation to the eye level or the horizontal line. An angle of elevation is, for example, the angle created between the line of sight and the horizontal line when a man on Earth observes the Sun.
Given:
Angle made by straight road = 15°
Angle of elevation of the sun = 57°
Length of the shadow = 75 feet
∠ACB = 90° - 57° = 33°
∠CAB = 57° - 15° = 42°
Using Sine Law to find BC i.e.length of the pole.
[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]
[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]
[tex]BC= \frac{75sin 42}{sin 33}[/tex]
BC ≅ 19.15 feet (to the nearest hundredth.)
Hence, the approximate length of the pole is 19.15 feet.
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Related Questions
HELPPPPP!!!!!!!!!!!!!!!!!!!!!1
Two similar triangles are shown below:
Two triangles are shown. The sides of the triangle on the left are marked 4, 5, 6. The sides of the triangle on the right are marked as 3, 2, and 2.5. For the triangle on the left, the angle between sides marked 6 and 5 is labeled as a, marked by a double arc, and the angle between the sides marked 6 and 4 is labeled as b, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 2 and 3 is labeled as c and the angle between the sides marked 2.5 and 3 is labeled as d, marked by a double arc. The angle between the sides 2 and 2.5 is labeled as e, marked by a triple arc, and it is also the angle on the top vertex of this triangle.
Which two sets of angles are corresponding angles? (4 points)
Group of answer choices
∠a and ∠e; ∠b and ∠c
∠a and ∠c; ∠b and ∠d
∠a and ∠e; ∠b and ∠d
∠a and ∠d; ∠b and ∠c
Answers
Step-by-step explanation:
the 2 triangles are similar.
that means their corresponding angles are equal, and their side lengths (and heights and so on) have all the same constant scaling factor.
so, we see that the side with the length 6 must corresponds to the side with the length 3 (factor 1/2).
as then the side with the length 5 corresponds to the side with the length 2.5, and the side with the length 4 corresponds to the side with the length 2 (all have the same factor 1/2).
a is the angle between 6 and 5 (the 2 longest sides).
the angle between the 2 longest sides in the smaller triangle (3 and 2.5) is d.
so, a and d correspond.
b is the angle between 6 and 4 (the longest and the shortest side).
the angle between the corresponding sides 3 and 2 is c.
so, b and c correspond.
therefore, the 4th and last answer choice is correct.
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $725 per week. How much did she earn last week if she sold $4,500 in electronics merchandise?
Round your intermediate calculations and answer to the nearest cent.
Answers
If Danielle sold $4500 in electronics merchandise last week then she earn a total of $1073.75 .
In the question ,
it is given that
Commission of Danielle on everything she sells at electronic store = 7.75%
Base salary of Danielle = $725
amount of electronics merchandise sold by Danielle last week = $4500
So according to question
money earn = base salary + 7.75% of 4500
substituting the value of base salary as $725
= 725 + 0.0775*4500
= 725 + 348.75
= 1073.75
So, Danielle earns $1073.75 .
Therefore , If Danielle sold $4500 in electronics merchandise last week then she earn a total of $1073.75 .
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HELP URGENT!!!
Find the common ratio of the geometric sequence 19.
38, 76, ...
Answers
The common ratio of the Geometric sequence 19, 38, 76 .... is 2.
What is common ratio of the Geometric sequence ?The distance between each number in a geometric series is known as the common ratio.
The reason it is common to all numbers and also the ratio between two consecutive numbers in the sequence is why it is known as the common ratio.
Divide the nth term by the (n-1)th term in a geometric series to find the common ratio.
The common ratio of the Geometric sequence 19, 38, 76 is
common ratio = (38/19) = 2
or common ratio = 76/38 = 2
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Sun shades are sold in the shape of right isosceles triangles. If the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade?
Answers
The length of the legs of the sun shade is 8√2 feet.
The equation used is option b , y = 1/2x² and y = 64
Isosceles triangle: What is it?
A triangle with two sides that have the same length is said to be isosceles.
Given,
Area of triangle = 64 sq.ft
Here, an isosceles triangle has two equal sides
Let
x is equal to the length side of a right isosceles triangle's leg.
y is the area of a right isosceles triangle at position
Currently, the legs of a right isosceles triangle are equal.
Area of triangle = 1/2 × base × height
y = 1/2 × (x) × (x)
y = x²/2
64 = x²/2
128 = x²
x = √128
x = 8√2
The length of the legs of the sun shade is 8√2 feet.
The equation used is option b , y = 1/2x² and y = 64
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Answer:
Step-by-step explanation:
first part: B.
second part: -11.3 or 11.3, 11.3
Amber wants to put a carpet on the floor of her bedroom. The floor is a square with an area of 7.29 square feet. How long should the piece of carpet on each side
Answers
The piece of carpet on each side of the floor will be 10.8 feet.
How to calculate the value?From the information, Amber wants to put a carpet on the floor of her bedroom and the floor is a square with an area of 7.29 square feet.
It should be noted that the side will be
= ✓7.29
= 2.7 feet.
Therefore, the perimeter will be found and this will be:
= 4 × side
= 4 × 2.7
= 10.8 feet
This illustrates the length.
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Factor 15x³-5x+6x-2 by grouping. What is the resulting expression?
O (5x²+2)(3x-1)
O (5x²-2)(3x+1)
O (15x+2)(x-1)
O (15x²-2)(x+1)
Answers
Answer: Choice A. [tex](5\text{x}^2+2)(3\text{x}-1)[/tex]
==================================================
Work Shown:
[tex]15\text{x}^3-5\text{x}^2+6\text{x}-2\\\\(15\text{x}^3-5\text{x}^2)+(6\text{x}-2)\\\\5\text{x}^2(3\text{x}-1)+2(3\text{x}-1)\\\\(5\text{x}^2+2)(3\text{x}-1)\\\\[/tex]
Explanation:
The idea is to pair up the terms into two groups. Factor each group separately. Then we pull out the overall GCF (3x-1) to finish up the factorization. You can use the FOIL rule to expand out the answer to get the original expression again, which helps confirm the answer.
What is the slope of the line that contains these points? 13 12 14 15 V -4 2. 8 14 y slope:
Answers
ok
Slope = (y2 - y1) / (x2 - x1)
P1 = (12, -4)
P2 = (14, 8)
Substitution
Slope = (8 - - 4) / (14 - 12)
= (8 + 4) / 2
= 12/2
= 6
Result
Slope = 6
Якщо 1 <a<2 i 2<b<4,то:
Answers
Answer:
A
Step-by-step explanation:
a/b;
2/1=2;
5/4=1.25
that's why we can write it this way: 1.25 < a/b < 2
means the answer is A
what are the coordinates of r, the image of r(-4,3) after s reflection in the line y=x
Answers
Answer:
(3, - 4 )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
(- 4, 3 ) → (3, - 4 )
Adam’s house is 12 miles from his house. It takes his older brother 20 minutes to drive him school. What is his brother’s driving speed
Answers
Step-by-step explanation:
I assume we want ca miles/hour answer as speed.
but just formally, any distance per time unit is speed.
in that sense
12 miles / 20 minutes = 3 miles / 5 minutes
is the speed.
but now to convert this to miles/hour.
we want to multiply 3/5 or 12/20 by f/f, so that the denominator is 1 hour.
by multiplying the numerator by the same value we make sure the speed ratio remains the same.
so, what "f" do we need to multiply 20 with to get 60 (1 hour = 60 minutes) ?
right, f = 3
therefore, we get
12/20 × 3/3 = (12×3)/(20×3) = 36/60 = 36 miles / 1 hour
his brother's driving speed was 36 miles/h or 36 mph.
I need help ASAP 50% of my grade this term
Answers
Answer:
The first 4 terms are 3,9,15, and 21
Step-by-step explanation:
The first term in the recursive formula is 3 (it is important because that would be the number we substitute for the second term. This logic also applies to finding the next term with the answer to the previous term) The formula is an = a(n-1) + 6. Because of this formula the nth on the right side is the previous one plus 6. With that in mind let find the mext three terms To find a2 you would first substitute n for 2 making it a2 = a(2-1) +6 which is a2 = a1 + 6. We know that the first term is 3 so we substitute a1 for 3 to get a2 = 3 + 6 which is 9. The second term is 9 To find a3 we do the same steps for solving a2 only this time we use the second term to put in place of a2+ 6 which is 9 + 6 which equals to 15. The third term is 15 Again we are doing the same steps to find a4 but we use the third term to substitute for a3 + 6 which is 15 + 6 which equals to 21. The fourth term is 21.There's a image of all of the work above
The table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched.
a. Complete the table.
b. Describe the scales you could use on the x and y axes of a coordinate grid that would show all the distances and weights in the table.
distance (cm) weight (newtons)
20 28
55
140
1
Answers
a)Table is completed below.
b)The scale should take the coefficient 1.4 into account, therefore the x-axis scale will be 100 with 1-cm intervals and the y-axis scale will be 140 with 1.4-newton intervals.
What is proportional relationship?
Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
Given.
The proportion is: according to the first row of the proportional relationship
y = kx
28 = k*20
k = 28/20 = 1.4
the following is the function:
y = 1.4x
a) Fill in the following table:
Weight and distance (in centimeters) (newtons)
20 | 28
55 | 55*1.4 = 77
140/1.4 = 100 | 140
1 | 1*1.4 = 1.4
b) The scale should take the coefficient 1.4 into account, therefore the x-axis scale will be 100 with 1-cm intervals and the y-axis scale will be 140 with 1.4-newton intervals.
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4р+2=3р-7 what is the answer show work
Answers
Answer:
p = -9
Step-by-step explanation:
4p + 2 = 3p -7 subtract 3p to get p's on the same side
1p + 2 = -7 subtract 2 to get p alone
p = -9
Answer:
p = -9
Step-by-step explanation:
4p + 2 = 3p -7 subtract 3p to get p's on the same side
1p + 2 = -7 subtract 2 to get p alone
p = -9
of the following, which population is most dense? please choose the correct answer from the following choices, and then select the submit answer button. answer choices 100 individuals per 100 square meters 5000 individuals per 200 square meters 100,000 individuals per 20,000 square meters 15,000 individuals per 10,000 square meters
Answers
The population that is most dense is the one for 5000 individuals per 200 square meters
Given the following information:
100 individuals per 100m^2
5000 individuals per200m^2
100,000 individuals per 20,000m^2
15,000 individuals per 10,000m^2
We find the population that is most dense using the formula:
Population density=(No. of people/Land area)
For 100 individuals per 100m^2,
Population density=100/100=1
For 5000 individuals per200m^2
Population density=5000/200=25
For 100,000 individuals per 20,000m^2
Population density=100,000/20,000=5
For 15,000 individuals per 10,000m^2
Population density=15,000/10,000=1.5
Hence, highest population density is 25 for 5000 individuals per200m^2
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A line has a slope of 4/5 and passes through point (-2,6) . Write an equation of the line in slope point form
Answers
Write an equation of the line in slope- point form
[tex]y- 6 = \frac{4}{5} (x+2)[/tex]
How to write the point- slope form of the equation?
We know, the point- slope formula is given by,
[tex]y-y_1=m(x-x_1)[/tex]
Given:
m= 4/5
[tex](x_1,y_1)= (-2,6)[/tex]
So, the equation of the line is,
[tex]y-y_1=m(x-x_1)\\\\y- 6 = \frac{4}{5} (x+2)[/tex]
It can also be written as ,
y- 6 = 0.8 (x+2)
What is point- slope form?
The equation of the straight line that is inclined at a specific angle to the x-axis and passes through a specific point can be found using the point slope form. A line's equation is an equation that each and every point on the line can solve. Thus, a line can be represented by a linear equation with two variables. Only when we are aware of both the slope of the line and a point on the line can we utilize the point slope formula.To learn more about point -slope form, refer:
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water use per day in the summer in phoenix is normally distributed with mean of 310 millions of gallons and standard deviation of 45 millions of gallons. city reservoirs have a combined storage capacity of nearly 350 million gallons. city reservoirs have a combined storage capacity of nearly 350 million gallons. (a) what is the probability that a day requires more water than is stored in city reservoirs?
Answers
The probability that a day requires more water than is stored in city reservoirs will be; 0.965
What is a z- score?The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.
Given that Water use in the summer is normally distributed with a mean of 310 million gallons and a standard deviation of 45 million gallons.
Let X be the random variable that shows the quantity of water required on a particular day.
Z-score :
[tex]Z = \dfrac{X - \mu}{\sigma},[/tex]
Now, the probability that a day requires more water than is stored in city reservoirs will be;
[tex]Z = \dfrac{350 -310}{45},[/tex]
Z = 0.965
We can see that the above value to the given P(X > 350)= 1 - P(Z < b), we get the value of b is; 0.965.
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Dan spent half of his weekly allowance. He then earned $8.90 by completing some chores. What is his weekly allowance if he currently has $14.70 (prior to getting his weekly allowance he had $0)?
Answers
The required allowance that Dan has prior is given as $11.6.
Given that,
Dan spent half of his weekly allowance. He then earned $8.90 by completing some chores. What is his weekly allowance if he currently has $14.70 (prior to getting his weekly allowance he had $0) is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the allowance Dan has be x,
According to the question,
x/2 + 8.90 = 14.70
x = 29.40 - 17.80
x = $11.6
Thus, the required allowance that Dan has prior is given as $11.6.
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which counterexample can be used to show that the following conjecture is false?
Answers
The other conjecture from A to C is true the only false conjecture is the option D.
Adjacent angles
Ming estimated that there would be 21 members in his bicycle club by the end of summer. There were actually 15 members at the end of summer. What is the percent error of Ming’s estimate?
Answers
The percent error of Ming’s estimate is 40%.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
here, it is given that :
Estimated number of members in his bicycle club by the end of summer = 21
Actual number of members in his bicycle club by the end of summer = 15
Now, the percent error of Ming’s estimate :
percent error = {(21-15)/15 } x 100
percent error = (6/15) x 100
percent error = 40%
Therefore, the percent error of Ming’s estimate is 40%.
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A toy company that makes bubbles fills its 8-ounce bottles using a machine. To check that the machine fills the bottles with the proper amount, the company randomly checks bottles off the assembly line. A bottle passes inspection if the percent error of the amount is 2% or less. What is the range of values that a bottle could contain to pass inspection? Round to the nearest hundredth.
oz to
oz???
Answers
The range of values that a bottle could contain to pass inspection will be 7.840 - 8.160 ounces.
How to calculate the value?It was stated that the toy company that makes bubbles fills its 8-ounce bottles using a machine.
The bottle passes inspection if the percent error of the amount is 2% or less. The minimum range will be:
= 8 ounces - (2% × 8 ounces)
= 8 ounces - 0.16 ounces
= 7.84 ounces
The maximum range will be:.
= 8 ounces + (2% × 8 ounces)
= 8 ounces + 0.16 ounces
= 8.16 ounces.
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The allowable range for the toy company is [7.84, 8.16].
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, the allowable percentage error is 2% or less.
Now, 2% of 8 ounces is,
= (2/100)×8.
= 0.16 ounces.
So, the allowable range is from (8 - 0.16) = 7.84 ounces to
(8 + 0.16) = 8.16 ounces.
As it is being given that it is 2% or less we'll use include the least value too.
So, the allowable range of the bottles is [7.84, 8.16].
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three congruent regular hexagons can be drawn in such a way that all of them overlap each other and create more than 6 distinct areas or compartments.
Answers
Yes
By drawing 36 little ones and 1 small one
It rained all week, and it created a leak in the roof! The roof repair was $100.00 for the repairman to come and fix it.
What is the balance after the roof repair$
Answers
Answer:
100.00
Step-by-step explanation:
it's 100.00 because the roof is being repaired and the person will have to pay after
2. Find the missing measure
Answers
Answer: 129
Step-by-step explanation: 180-51
Answer:
129.
Step-by-step explanation:
it's 129 believe me
If B = 2s + s² and A = 3 - 4s², find an expression that equals B + 3A in
standard form
Answers
Answer:
- 11s² + 2s + 9
Step-by-step explanation:
B = 2s + s²
A = 3 - 4s²
then
2s + s² + 3(3 - 4s²)
=2s + s²+ 9 - 12s²
= - 11s² + 2s + 9
A local carnival charges $7.50 for adult admission and $5.25 for child admission. The carnival made $378 in an hour. The carnival
admitted twice as many children as adults.
How many adults and children were admitted in the hour?
Answers
Answer:
21 adults42 childrenStep-by-step explanation:
You want to know how many adults and children were admitted if there were twice as many children who paid $5.25 for admission as there were adults who paid $7.50, and total admission revenue was $378.
SetupLet 'a' represent the number of adults admitted. Then 2a is the number of children. The total revenue is ...
7.50a +5.25(2a) = 378
SolutionCollecting terms, we have ...
18a = 378
a = 21 . . . . . . . divide by 18
2a = 2·21 = 42 . . . . . find the number of children admitted
21 adults and 42 children were admitted.
21 adults were admitted.
42 children were admitted.
Describe algebra.Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.
Due to that,
Carnival earns a total of $378 in one hour.
Adult fees are $7.50.
Children's fees equal $5.25
Suppose that the carnival allows twice as many youngsters as adults.
If there are x adult, then
Children will thereafter be twice as many.
Since,
$378 is the total amount from both adults and children.
Then,
7.50x + 5.25(2x) = 378
7.50x + 10.50x = 378
18x = 378
x = 378 / 18
x = 21
As x was the total number of adults
Then, in an hour, 21 adults were admitted.
Since there were a total of two children,
Next, there were
42 kids were admitted in an hour (2(21)).
As a result, 42 kids and 21 adults were admitted in one hour.
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Given mn, find the value of x.
Answer:
(6x-7)°
(4x-1)⁰
Answers
The value of x after solving the expression is 3.
What is an expression?
An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numerals (constants), variable, operations, equations, brackets, punctuation, and grouping. Many writers differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical things. However, in modern mathematics, and particularly in computer algebra, formulae are considered as expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.
Given expression 6x-7 = 4x-1
or, 6x-4x = -1+7
or, 2x = 6
or, x = 6/2 = 3
Hence, the value of x after solving the expression is 3.
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researchers studying meditation contacted over 1{,}0001,0001, comma, 000 randomly selected adults in 101010 nations. the results showed that those who meditated on a regular basis were less likely to suffer from stress than adults who meditate less regularly or not at all. can we conclude that meditating caused the lower stress? why?
Answers
Not necessarily, because this was not an experiment.
In my opinion, Yet scientific evidence from case studies, surveys of meditator experiences, and historical studies is emerging to show that meditation can be associated with stress, negative effects, and mental health problems. Meditation can induce a state of deep relaxation and a calm mind. During meditation, you focus your attention and eliminate the stream of disorganized thoughts that can fill your mind and cause stress. This process can lead to increased physical and emotional well-being.
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Please help i’m begging due in a bit❗️❗️❗️❗️❗️❗️
Answers
3. 300
4. $180
5. $23.75
6. $102.6
Answer: 1 is 300 2 is 180 3 is 23.75 and the fourth one is 102.6
Step-by-step explanation: dont forget to add your $ signsss
Pls help Me its Due tonight I really struggle and have no time to do this pls help me .
Answers
The factorized polynomial 6x² + 15xy -14x -35y is given as (2x + 5y) (3x - 7)
Factorization of PolynomialsA polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.
To solve this problem, we simply need to factorize the polynomial given.
[tex]6x^2 + 15xy - 14x - 35y[/tex]
Let's look for a common factor and factorize similar or like terms.[tex]6x^2 + 15xy - 14x - 35y\\(2x + 5y) (3x - 7)[/tex]
This is the the reduced or factorized form of the given polynomial.
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Work out the area of this circle.
Take to be 3.142 and write down all the digits given by your calculator.
10 cm
please help !!
Answers
Answer:
Area is 314.2 cm²
Step-by-step explanation:
- Consider a circle whose radius is r, while calculating its area, the formula is derived from its circumference;
[tex]{ \rm{circumference = 2\pi r}}[/tex]
- but area is the integral of circumference;
[tex]{ \rm{area = \int circumference }} \\ \\ { \rm{area = \int2\pi r \: dr}}[/tex]
- Assume area is between the center to the edge from r = 0 to r = r
[tex] { \rm{area = 2\int^{r}_{0}\pi r \: dr}} \\ \\ { \rm{area = 2[\pi ( \frac{ {r}^{2} }{2} )]^{r} _{0} }} \\ \\ { \rm{area = \pi {(r)}^{2} - \pi {(0)}^{2} }} \\ \\ { \boxed{ \rm{area = \pi {r}^{2} }}}[/tex]
- From the question given, the circle has a radius of 10cm
[tex]{ \rm{area = 3.142 \times {10}^{2} }} \\ \\ { \bf{area = 314.2 \: {cm}^{2} }}[/tex]
[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]