Answer:
The relationship between the number of faces, vertices, and edges of a three-dimensional object is described by Euler's formula, which states that for any polyhedron (a solid object bounded by flat faces), the number of faces (F), vertices (V), and edges (E) satisfy the equation F + V - E = 2. This formula is true for any convex polyhedron, such as a cube or a regular tetrahedron.
The formula is based on the fact that every face of a polyhedron is bounded by a closed loop of edges, and each vertex is where three or more edges meet. The total number of edges is the sum of the number of edges around each face, which is equal to twice the number of faces since each edge is shared by two faces, and the number of edges meeting at each vertex, which is equal to the degree of the vertex (the number of edges meeting at the vertex).
Therefore, by knowing the number of faces, vertices, and edges of a three-dimensional object, we can determine if it is a convex polyhedron and use Euler's formula to check if the numbers are consistent with a solid shape.
Alex, Bill, Carl and David shared $168. David received 1/7 of the total amount of money received by Alex, Bill and Carl. Alex received 3/4 of the total amount of money received by Bill and Carl. Bill received 2/5 as much money as Carl. How much did Bill receive?
Bill's share = $56 Therefore, Bill received $56.
Let's start by setting up some equations based on the given information:
David's share = 1/7 * (Alex's share + Bill's share + Carl's share)
Alex's share = 3/4 * (Bill's share + Carl's share)
Bill's share = 2/5 * Carl's share
The sum of all four shares is $168.
We can use the fourth equation to solve for one of the shares in terms of the others:
Alex's share + Bill's share + Carl's share + David's share = $168
Alex's share + Bill's share + Carl's share = $168 - David's share
Substituting the other equations into this expression, we get:
Alex's share + (2/5 * Carl's share) + Carl's share + (1/7 * (Alex's share + (2/5 * Carl's share) + Carl's share)) = $168
Simplifying this equation, we get:
(8/7) * Alex's share + (22/35) * Carl's share = $168
Now we can use the other equations to solve for Carl's share, and then for Bill's share:
From Bill's share = 2/5 * Carl's share, we get Carl's share = (5/2) * Bill's share
From Alex's share = 3/4 * (Bill's share + Carl's share), we get Alex's share = (3/4) * ((7/2) * Bill's share) = (21/8) * Bill's share
Substituting these expressions into the equation we derived earlier, we get:
(8/7) * (21/8) * Bill's share + (22/35) * (5/2) * Bill's share = $168
3 * Bill's share = $168
Bill's share = $56
Therefore, Bill received $56.
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Use a calculator to find the trigonometric ratio. Round your answer to four decimal places
sin 98°~
Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.
How to Find the Trigonometric Ratio?One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.
Using a calculator, we can find the sine of 98 degrees as follows:
sin 98° ≈ 0.9848
Rounding this to four decimal places, we get:
sin 98° ≈ 0.9848
Therefore, sin 98° is approximately equal to 0.9848.
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What is the area of the object above?
14 cm²
62 cm²
24 cm²
84 cm²
The area of the object in the image shown in the attachment below is calculated as: 62 cm².
How to Find the Area of the Object?The area of the object can be found by decomposing the figure into two rectangles - larger rectangle and smaller rectangle.
Area of the larger rectangle = length * width
Length of the larger rectangle = 5 cm
Width of the larger rectangle = 4 cm
Area of the larger rectangle = 5 * 4 = 20 cm²
Area of the smaller rectangle = length * width
Length of the larger rectangle = 7 cm
Width of the larger rectangle = 6 cm
Area of the larger rectangle = 7 * 6 = 42 cm²
Area of the object = 20 + 42 = 62 cm².
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Using L’Hôpital’s Rule, evaluate
heeeeeelp
The value of the given limit expression is 1.
Given is limit expression [tex]\lim _{x\to \infty }\left(x^{\frac{1}{3x}}\right)[/tex], we need to use L’Hôpital’s Rule to solve it,
So,
[tex]\lim _{x\to \infty \:}\left(x^{\frac{1}{3x}}\right)[/tex]
Using the exponent rule,
[tex]=\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right)[/tex]
Applying the chain rule,
[tex]\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right) = 1[/tex]
Hence the value of the given limit expression is 1.
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Question 4
The table below shows the scores of a group of students on a 10-point quiz.
Frequency
Test Score
3
4
5
6
7
8
9
10
4
1
0
3
3
5
1
6
The mean score on this test is:
1 pt194 Details
Enter an integer or decimal number [more..)
The median score on this test is:
Question Help: Video 1 Video 2
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The mean score of the test is 7.13.
The median score of the test is 7.
What is the mean and median score on the test?To get mean score, we have to multiply each test score by its corresponding frequency, sum up products and then divide by the total frequency.
Mean score = EF/ n
Mean score = (34 + 41 + 50 + 63 + 73 + 85 + 91 + 106) / (4 + 1 + 0 + 3 + 3 + 5 + 1 + 6)
= (12 + 4 + 0 + 18 + 21 + 40 + 9 + 60) / 23
= 164 / 23
= 7.13
To find the median score, we will arrange the scores in ascending order: [tex]3, 4, 4, 4, 4, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10.[/tex]
Since there are 23 scores, the median will be the 12th score (in the middle). So, the median score = 7.
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A lorry tank was 4/5 full of petrol. when the Guage indicate 72litres. what is the full capacity of the tank?
The calculated full capacity of the tank is 90 liters
From the question, we have the following parameters that can be used in our computation:
Proportion = 4/5
This is represented as
Size = 72 liters
Using the above as a guide, we have the following:
4/5 * x = 72 liters
Where
x = the full capacity of the tank
So, we have
x = 72 * 5/4
Evaluate
x = 90
Hence, the full capacity of the tank is 90 liters
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Based on proportions, if a lorry tank was ⁴/₅ full of petrol when the gauge indicates 72 liters, the full capacity of the tank is 90 liters.
What is proportion?Proportion refers to the fraction or portion of a whole value, quantity, or number.
Proportions are ratios equated to each other.
We can depict proportions using fractions, decimals, or percentages.
The fraction of the lorry tank of petrol = ⁴/₅ (0.80)
If ⁴/₅ = 72 liters, proportionately, the full tank = 90 liters (72 ÷ 0.80)
Thus, we can conclude that when the lorry tank is full the quantity of petrol in it is 90 liters.
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In a large population, about 70% of families have a pet. A researcher takes a random sample of 6 families and surveys
whether they have a pet.
Use the binomial distribution to compute the probability that exactly 2 of the families have a pet.
Identify the following information required to find the probability of families that have a pet.
If in a large population, about 70% of families have a pet. A researcher takes a random sample of 6 families and surveys whether they have a pet. The probability of families that have a pet is: 0.0595.
How to find the probability?Number of trial= 6
Probability of success = 0.7
Probability of failure = 1 - 0.7 = 0.3
Probability that exactly 2 of the families have a pet
Let make us of binomial distribution formula to determine the probability
P(X = 2) = (6 choose 2) * 0.7² *[tex]0.3^{4}[/tex]
= 15 * 0.49 * 0.0081
= 0.0595
Therefore the probability is 0.0595.
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Learn with an example
Factor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
6c³-9c
The greatest common factor is 3C and GCF form of polynomial is 3c(c² - 3).
The given polynomial is
6c³-9c
We can write it as;
3c(c² - 3)
We know that
The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor (HCF) is another name for it.
Therefore 3c is its GCD.
Divide each term of polynomial 3c,
6c³ ÷ 3c = 2c² and -9c ÷ 3c = -3
Thus,
3c(c² - 3) is the factored version of the polynomial with the highest common factor.
Also if GCD is 1 then after dividing each term by 1 we get same result
thus the polynomial be 3c(c² - 3).
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After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
1: The required table is described below.
2: The range is (0,36)
3: X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)
What is line?A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
We are given that,
y = -x² + 36
The equation of the rainbow is represented by the parabola,
Now, we are required to find a linear equation which cuts the graph of the parabola at two points.
Let us consider the equation joining the points (-6,0) and (0,36), given by .
y = 6x + 36
So, the corresponding table for the linear equation is given by,
x y = 6x + 36
-6 0
0 36
1 42
6 72
Now, we will answer the questions corresponding the functions.
1. Domain and Range of the rainbow.
Since, the equation of the rainbow is
y = -x² + 36
So, from the figure, we get that,
Domain is the set of all real numbers.
Range is the set {y | y ≤ 36}
Here, domain represents the points which are used to plot the path of the rainbow and range represents the points which are form the rainbow.
Not all points make sense in the range as the parabola is opening downwards having maximum point as (0,36).
2. X and Y-intercepts of the rainbow.
As, the 'x and y-intercepts are the points where the graph of the function cuts x-axis and y-axis respectively i.e. where y=0 and x=0 receptively'.
We see that from the figure below,
X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)
Here, these intercepts represents the point where the parabola intersects the individual axis.
3. Is the linear function positive or negative.
As the linear function is represented by the upward flight of the drone.
So, the linear function is a positive function.
y = 6x + 36
4. The solution of the system of equations is the intersection points of their graphs.
So, from the figure, we see that the equations intersect at the points (-6,0) and (0,36).
Thus, the solution represents the position when both the drone and rainbow intersect each other.
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The following is a list of weights, in pounds, of dogs at a bark park. Is the mean, median, or mode likely to be the best
measure of the center for the data set?
35, 39, 37, 37, 38, 34, 35, 37,65
answer :
median or 37
explanation :
median is not influenced by an outlier like 65 in the dataset
steps :
to get the median
arrange the weights in order from smallest to largest:
34, 35, 35, 37, 37, 37, 38, 39, 65
median = middle value = 37
37 has :
four weights before it &
four weights after it
so the median weight is 37 pounds.
VNIHO NI es sequence. c). C 9 is 27 km from R on a bearing of 060° town T is 19km from town R on a aring of 3400 draw a diagram showing the relative position of the towns.
The description of the given bearing with the towns and a similar drawing of bearing is given below:
How to solveThe directions to draw the diagram that shows the relative position of the towns is given below:
Town R is at the center of the coordinate system.
Town C is 27km away on a bearing of 060°. Start at R, move 27km at 060° to find C towards east-southeast.
Town T is 19 km away from R on a ring of 3400.
T is on a circular path of radius of 3400 units.
To plot T, draw a circle at R with a 3400 unit radius. Put T on the circle, 19 km from R. Diagram: R center, C ESE, T on a circular path with a 3400 unit radius around R.
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Could someone help I’m having a hard time with this question
The cost of covering 1 unit² should be $2.477 to be in the budget and the total area to be covered is 3027.22 ft².
Given is a blueprint we need to find area that be covered and then the cost of covering the area,
So, we will find the area by splitting the figure into different shapes,
So the area =
Ar(rectangle) + Ar(semicircle) + Ar(triangle) + Ar(square)
= 9×3 + 3.14×2²/2 + 1/2×3×1 + 3³
= 27 + 6.28 + 1.5 + 27
= 61.78 units²
Since 1 unit = 7 ft
So, 1 unit² = 49 ft²
therefore, 61.78 units² = 61.78 × 49 = 3027.22 ft²
Since our budget is $7500
Costing of covering the area = 3027.22 × x = 7500
x = $2.477
Hence the cost of covering 1 unit² should be $2.477 to be in the budget.
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For the function , find f' (1).
guys pls help me
The derivative of the function is solved and f' ( 1 ) = 0.183
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = sinh⁻¹ ( √ (2x + 3 )
On taking the derivative of the function , we get
f' ( x ) = 1/ ( √2x + 4 ) ( √ ( 2x + 3 ) )
On simplifying , we get
when x = 1
f ( 1 ) = 1 / ( √6 ) ( √5 )
f ( 1 ) = 1/√30
f ( 1 ) = 0.18257
f ( 1 ) = 0.183
Hence , the function is solved
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Write the equation of a line that is perpendicular to y=7/5 x+6 and that passes throght the point (2,-6)
The equation of line that passes through and is perpendicular toy = (7/5)x + 6 is [tex]y = -\frac{5}{7}x - \frac{32}{7}[/tex].
What is the equation of the perpendicular line?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line:
y = (7/5)x + 6
Using the slope intercept, slope m is 5/2
Slope m = 7/5
Note: the equation of a perpendicular line to y = (7/5)x + 6 must have a slope that is the negative reciprocal of the original slope.
Slope of perpendicular line = -1 / ( 7/5 )
Slope of perpendicular line = -5/7
Plug the slope m = -5/7 and point (2,-6) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
[tex]( y - (-6) = -\frac{5}{7}( x - 2 ) \\\\y + 6 = -\frac{5}{7}x + \frac{10}{7} \\\\y = -\frac{5}{7}x + \frac{10}{7} - 6\\\\y = -\frac{5}{7}x - \frac{32}{7}[/tex]
Therefore, the equation of the line is [tex]y = -\frac{5}{7}x - \frac{32}{7}[/tex].
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What is the solution to this system of linear equations?x − 3y = −2x 3y = 16(7, 3)(3, 7)(−2, −3)(−3, −2)
The solution to the system of linear equations is (14, 16/3).
To find the solution to the given system of linear equations, we can use the method of substitution. First, we can solve the second equation for y by dividing both sides by 3, which gives us y = 16/3. .
We can then substitute this value of y into the first equation and solve for x. This gives us x - 3(16/3) = -2, which simplifies to x = 14. This point represents the intersection of the two lines, where they cross over each other on the coordinate plane.
The other answer choices given in the question are not valid solutions to the system of equations.
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Answer:
C
Step-by-step explanation:
Put these four functions in order from smallest to largest : 1/4,2/3,4/7,1/2
Answer:
1/4, 4/7, 2/3, 1/2
Step-by-step explanation:
10. Kristen compared the y-intercept of the graph of the function f(x) = 7x - 5 to the y-intercept of the graph of the linear function that includes the points in the table below. X -5,-2,0,3 g(x) -56,-20,4,40
What is the difference when the y-intercept of g(x) is subtracted from the y-intercept of f(x)?
On a number line, point L is located at -2.5, and point M is at 6.5. If the ratio LK to KM is 6:3, where is point K on the number line?
Point K is located at 3.5 on the number line.
To find point K on the number line, we need to apply the ratio LK to KM, which is 6:3. First, we can simplify this ratio to 2:1.
Next, we will find the total distance between points L and M. The distance LM = 6.5 - (-2.5) = 9 units.
Now, we can divide this distance into 3 equal parts, as per the simplified ratio 2:1. Each part will be 9/3 = 3 units long.
Since LK is 2 parts of the ratio, we will multiply the length of one part (3 units) by 2. LK = 3 * 2 = 6 units.
Finally, we'll find the coordinates of point K by adding the length of LK to the coordinate of point L. So, K = -2.5 + 6 = 3.5.
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Answer:
Point K is at 3.5
Step-by-step explanation:
I just took the test
Explain why the probability of rolling a sum from 2 to 12 is 100%. [C:2]
The probability of rolling a sum from 2 to 12 on 2 dices is 100%
Given the data,
The two dice should be rolled.
Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).
The resultant 36 results are as follows:
1-1, 1-2, 1-3, 1-4, 1-5, 1-6
2-1, 2-2, 2-3, 2-4, 2-5, 2-6
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
4-1, 4-2, 4-3, 4-4, 4-5, 4-6
5-1, 5-2, 5-3, 5-4, 5-5, 5-6
6-1, 6-2, 6-3, 6-4, 6-5, 6-6
When using two dice, there are a total of 36 possibilities that might occur.
As a result, the results' total ranges from 2 to 12.
Hence , the probability is 100 %
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IXL S.10…Geometry…Explain Down Below Please
The area of the shaded region, to the nearest hundredth can be calculated as approximately: 1,195.71 mm².
What is the Area of the Shaded Region?The area of the shaded region can be found using the area of circle, which is: Area = πr²
Therefore, area of the shaded region = area of larger circle - area of smaller circle.
Area of larger circle:
radius (r) = 14 + 6.6 = 20.6 mm
Area of larger circle = 3.14 * 20.6² = 1,332.4904 mm²
Area of smaller circle:
radius (r) = 6.6 mm
Area of larger circle = 3.14 * 6.6² = 136.7784 mm²
Area of the shaded region = 1,332.4904 - 136.7784 = 1,195.71 mm².
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Heather has a combination of dimes and quarters in her piggy bank. If Heather has a total of 43 coins and the value in the piggy bank is $7.60, how many of each coin does she have?
Answer:
Step-by-step explanation:
5.6
Based on the graphs of f (x) and g(x), what is (f ⋅ g)(1)?
The value of the composite function (f . g)(1) when evaluated is 6
Evaluating the composite functionsFrom the question, we have the following parameters that can be used in our computation:
The graph of the function f(x)
Also, we have
The graph of the function g(x)
The composite function (f . g)(1) is calculated as
(f . g)(1) = f(1) * g(1)
From the graph, we have the following values
f(1) = -2
Also, we have
g(1) = 3
So, we have
(f . g)(1) = 2 * 3
Evaluate
(f . g)(1) = 6
Hence, the composite function (f . g)(1) when evaluated is 6
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I don’t understand this one here I need help
Assuming [tex]f(x)=x^2[/tex].
[tex]y=x^2\\x=-\sqrt y \vee x=\sqrt y[/tex]
Since [tex]x\geq0[/tex] only [tex]x=\sqrt y[/tex] is valid.
Therefore
[tex]f^{-1}(x)=\sqrt{x}[/tex]
The classroom had a 16-centimetre-long glue stick, and then Christina used 2.5 centimetres of it. How long is the stick now?
Answer:
[tex]13.5cm[/tex]
Step-by-step explanation:
You just need to subtract to find your answer!
The information we are given:
We have a 16cm glue stick.
Christina used 2.5cm of it.
Subtracting:
16 - 2.5 = 13.5
Now, dont forget your units :D
[tex]13.5 -- > 13.5cm[/tex]
I hope I helped!~~~Harsha~~~
A normal distribution has a mean of 146 and a standard deviation of 4. Find the z-score of the data value of 153
Answer:
To find the z-score of a data value, we use the following formula:
z = (x - μ) / σ
where z is the z-score, x is the data value, μ is the mean of the distribution, and σ is the standard deviation.
Given a normal distribution with a mean (μ) of 146 and a standard deviation (σ) of 4, and a data value (x) of 153, we can plug these values into the formula:
z = (153 - 146) / 4
z = 7 / 4
z = 1.75
Thus, the z-score of the data value 153 is 1.75.
Which statements describe finding the limit shown?
Check all that apply.
O Multiply by √x +2+3
√x+2+3
Getx-1 in the numerator.
Get (x-7)(√x+2-3) in the denominator.
O Divide out a common factor of x- 7.
Calculate the limit as
The correct statements that apply to the given limits are:
Option A: Multiply by (√(x + 2) + 3)/(√(x + 2) + 3)
Option D: "Divide out a common factor of x - 7."
Option E: The limit of the given expression is 1/6.
How to find the limits of the function?Option: We generally multiply by the conjugate of the expression to eliminate square roots in simplification. Thus, option A applies.
Option B: Get x - 1 in the numerator:
This statement is not correct. The expression does not involve x - 1 in the numerator.
Option C: Get (x - 7)(√(x + 2) - 3) in the denominator:
This statement is not correct due to the fact that we want to simplify the expression, and not introduce a more complex denominator.
Option D: Divide out a common factor of x - 7:
This statement is correct because by factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.
Option E: Calculate the limit as 1/6:
After canceling out the common factor of x - 7, the simplified expression becomes:
lim x -> 7 (√(x + 2) - 3)/(x - 7)
= lim x -> 7 1/(√(x + 2) + 3)
To find the limit, we substitute the value x = 7 into the simplified expression:
lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6
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In the circle below, IK is a diameter. Suppose mIJ=78 and mILJ=69 . Find the following.
m
m
Applying the inscribed angle theorem, the indicated measures in the circle are: a) m<JIK = 51°; b) m<KJL = 51°.
How to Find the Measures in the Circle Using the Inscribed Angle Theorem?Recall that the measure of an intercepted arc is equal to twice the measure of an inscribed angle, based on the inscribed angle theorem.
We are given the following:
m(IJ) = 78°
m<IJL = 39°
Therefore, we have:
a. m<JIK = 1/2(m(JK)) [based on the inscribed angle theorem]
m(JK) = 180 - m(IJ)
m(JK) = 180 - 78 = 102°
Thus:
m<JIK = 1/2(102)
m<JIK = 51°
b. m<KJL = 1/2(m(KL) [based on the inscribed angle theorem]
m(IL) = 2(IJL)
m(IL) = 2(39) = 78°
m(KL) = 180 - m(IL) = 180 - 78
m(KL) = 102°
m<KJL = 1/2(m(KL) = 1/2(102)
m<KJL = 51°
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Complete Question:
In the circle below, IK is a diameter. Suppose m(IJ) = 78° and m(IJL) = 39°. Find the following.
a. m<JIK
b. m<KJL
Missing image is attached below.
Helena lost her marbles but then she found them and put them in 4 bags with m marbles in each bag she had 3 marbles left over that didn’t fit in the bags how many marbles did Helena have in all I need help
Find the numerical value of the log expression.
log a = -1
log b = -6
log
a²
64c4
log c = 3
The numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] is 10 when log a = -1, log b = -6 and log c = 3.
Given that,
We have to find the numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] when log a = -1, log b = -6 and log c = 3.
We know that,
The use of a logarithm can be applied to solve issues that cannot be resolved using the concept of exponents simply. A logarithm is simply a different way to define exponents.
So,
Take the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex]
= [tex]log\frac{a^2}{b^4c^4}[/tex]
= log a² - log(b⁴c⁴) [ from [tex]log\frac{x}{y}[/tex] = log x-log y ]
= log a² - (log b⁴ + log c⁴) [ from log (xy) = log x + log y ]
= 2log a - 4log b - 4log c [ from log xⁿ = nlog x ]
= 2( -1) - 4(-6) - 4(3)
= -2 + 24 - 12
= 24 - 14
= 10
Therefore, The numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] is 10.
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find tan s
thank you
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{40}\\ a=\stackrel{adjacent}{ST}\\ o=\stackrel{opposite}{24} \end{cases} \\\\\\ ST=\sqrt{ 40^2 - 24^2}\implies ST=\sqrt{ 1600 - 576 } \implies ST=\sqrt{ 1024 }\implies ST=32 \\\\[-0.35em] ~\dotfill\\\\ \tan(S )=\cfrac{\stackrel{opposite}{24}}{\underset{adjacent}{32}} \implies \tan(S )=\cfrac{3}{4}[/tex]
