Using sine rule the value of angle N in the triangle is 61 degrees.
How to find angle of a triangle using sine rule?Using sine rule
MO / sin N = MN / sin ∠O
Therefore,
MO = 18
MN = 6
∠O = 17°
Hence,
18 / sin N = 6 / sin 17
cross multiply
18 sin 17 = 6 sin N
divide both sides by 6
sin N = 5.26269068501 / 6
sin N = 0.87711511416
N = sin⁻¹ 0.87711511416
N = 61.296295658
∠N ≈ 61°
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PLEASE HELP!! BRAINLIEST AND 10 POINTS !!
Answer:
Give brainliest first then I’ll give the answer
Step-by-step explanation:
At a toy shop, 45 toys were sold in September. A bonus will be given to workers if they can increase sales by 40% in October. How many toys must the sales team sell in October to receive the bonus?
Answer:
First off, we can find the number that has to be increased by multiplying the original amount by 40%:
45×40%
=45×0.4
=18
We can then add the above amount to the original amount to find the toys they must sell:
45+18
=63
They must sell 63 toys to get the bonus.
Alternatively:
The total percenrage of toys need to be sold to get a bonus with the 40% increase:
=100%+40%
=140%
The amount of toys:
=45×1.4
=63
Therefore the answer is 63.
Hope it helps!
Step-by-step explanation:
In finance, we need to do partial observations of data and estimate the data generating process (DGP) -- for example, log-normal returns. Sometimes, we can observe only the data points of a certain process, but we don't know what is the function generating the process. Consider the following graph is a plot of the f ′
(x), of a function f(x) given. What is the underlaying function ( f(x −
i)) that is the generator of the observed points in the plot f ′
(x −
i), for points x −
1=−1,x −
2=−0.9,…,x −
n=1?
The underlying function f(x - i) that generates the observed points f'(x - i) in the plot can be determined by integrating the observed points. By integrating f'(x - i), we can obtain f(x - i) up to a constant of integration.
The constant of integration can be determined by incorporating additional information or constraints related to the problem or by considering the behavior of the function at a specific point.
To find the underlying function f(x - i) that generates the observed points f'(x - i), we need to integrate the observed points.
Integration is the reverse process of differentiation, so by integrating f'(x - i), we can recover f(x - i) up to a constant of integration.
The constant of integration arises because integration does not provide a unique solution.
The constant represents an arbitrary additive term that can vary depending on the specific problem or additional constraints.
To determine the constant of integration, we may need additional information or consider specific conditions related to the problem.
It is also important to note that the accuracy of estimating the underlying function f(x - i) depends on the quality and quantity of the observed data points f'(x - i). More data points and precise measurements can lead to a better estimation of the underlying function.
Additionally, the behavior of the function at a specific point can provide valuable insights for determining the constant of integration and refining the estimation of the underlying function.
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select whether the following numbers are rational or irrational. please help me
1)13/4: Rational (a fraction)
2)√17: Irrational (square root of a non-perfect square)
3)3π: Irrational (product of a rational number and an irrational number)
4)0.1 (1 bar): Rational (repeating decimal)
5)-√2: Irrational (negative square root of a non-perfect square)
6)√24: Irrational (square root of a non-perfect square)
7) -√49: Rational (negative square root of a perfect square)
1)13/4: Rational - This number is a fraction, and any number that can be expressed as a fraction is considered rational. In this case, 13/4 can be simplified to 3.25, which is a rational number.
2)√17: Irrational - The square root of 17 cannot be expressed as a simple fraction or terminating decimal. It is an irrational number, meaning it cannot be expressed as a ratio of two integers.
3)3π: Irrational - π (pi) is an irrational number, and when multiplied by a rational number like 3, the result is still an irrational number. Therefore, 3π is an irrational number.
4)0.1 (1 bar): Rational - This number is a repeating decimal, indicated by the bar over the 1. Although it does not have a finite representation, it can be expressed as the fraction 1/9, which makes it rational.
5)-√2: Irrational - Similar to √17, the square root of 2 is also an irrational number. Multiplying it by -1 does not change its nature, so -√2 remains an irrational number.
6)√24: Irrational - The square root of 24 is an irrational number because it cannot be expressed as a simple fraction or terminating decimal. It can be simplified to √(4 × 6), which further simplifies to 2√6, where √6 is an irrational number.
7)-√49: Rational - The square root of 49 is 7, which is a rational number. Multiplying it by -1 does not change its nature, so -√49 remains a rational number.
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The complete question is :
Select whether the following numbers are rational or irrational.
1. 13/4
2. \sqrt{17}
3. 3 π
4. 0.1 (1 bar)
5. - \sqrt{2}
6. \sqrt{24}
7. - \sqrt{49
I need some help if anybody could help
Answer:
The answer is An intersect
Identify the following as either a Permutation or a combination. Then calculate the answer. a) Sara is setting a new code for her garage. The key pad has the numbers 0-9 to choose from, and she needs to set a 4-digit passcode. How many different codes can she possibly set if no digit is going to be repeated? a. Combination b. Permutation _________passcodes.
a. It is b. Permutation
b. Using permutation, the number of different codes is 3024 passcodes.
What is permutation and combination?Permutation is the total number of ways of arranging n different objects in x ways ⁿPₓ = n!/(n - x)! while combination is the total number of ways of selecting n objects x at a time ⁿCₓ = n!/x!(n - x)!
a. Since Sara is setting a new code for her garage. The key pad has the numbers 0-9 to choose from, and she needs to set a 4-digit passcode. Since no digit is to be repeated, it is a permutation since in permutation, we are looking for differnt arrangemnets of the objects.
So, it is b. Permuation
b. Since Sara the key pad has the numbers 0-9 to choose from, and she needs to set a 4-digit passcode and no digit is to be repeated. We have 9 digits permuted or arranged in 4 ways. So, our permutation is ⁹P₄ = 9 × 8 × 7 × 6
= 3024 passcodes
So, the number of different codes is 3024 passcodes.
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I know the answer but I need help with the work
I WIL GIVE 20 POINTS AND BRAINLIST for ANSWER!!!
Jessica estimated that her family used 30% more water this month compared to last month. They used 12000 gallons of water last month. How much water did they use this month? Use the sketch tool to complete the double number line diagram if it is helpful.
Answer:
Below
Step-by-step explanation:
30% is .3 in decimal
So the family used 100 % of last month PLUS .3 of last month MORE
12 000 = 100 % now add .3 (12 000) more =
12 000 + .3 ( 12 000) = 15600 gallons this month
Which of the following statements about the mean absolute deviation (MAD) is the most accurate? A. It is the square root of the standard deviation. B. It can be a positive number or a negative number. C. It is measured in the same units as the original data. D. It is the arithmetic mean of the squared deviations from the mean.
The most accurate statement about the mean absolute deviation (MAD) is that it is measured in the same units as the original data. MAD is the arithmetic mean of the absolute deviations from the mean, which means that it measures the average distance between each data point and the mean. It is different from standard deviation, which measures the spread of the data around the mean, and is calculated by taking the square root of the arithmetic mean of the squared deviations from the mean. MAD can only be a positive number, as it measures distances. Therefore, the correct answer is C.
C. It is measured in the same units as the original data.
The mean absolute deviation (MAD) is a measure of dispersion or variability in a dataset. It is calculated by finding the arithmetic mean of the absolute deviations from the mean of the dataset. Since the absolute deviations are in the same units as the original data, the MAD is also measured in the same units as the original data.
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HELP WILL MARK BRAINLIEST
The measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, center of dilation is P and scale factor is 1/3.
In the given triangle ABC, AB=12.4 units, AC=6.7 units and BC=12.7 units
Now, A'B'=12.4/3
A'B'= 4.1 units
A'C'=6.7/3
A'C'= 2.2 units
B'C'=12.7/3
B'C'= 4.2 units
Therefore, the measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.
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T/F The analysts at the casino try to choose the spread so that there is a 50% chance that the outcome will be below that amount, and a 50% chance that the outcome will be above that amount.
"The analysts at the casino try to choose the spread so that there is a 50% chance that the outcome will be below that amount, and a 50% chance that the outcome will be above that amount" is TRUE.
The analysts at the casino do not try to choose the spread so that there is a 50% chance of the outcome being below or above that amount. The spread is chosen based on factors such as the teams playing, their past performances, and other relevant statistics.
The goal of the casino is to balance the amount of money bet on each side, not to ensure a 50/50 chance of winning for either side. The spread is simply a tool used to even out the betting and ensure a profit for the casino.
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Write a recursive formula for the nth term of the sequence 5,12,19,26,....
Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.
what is sequence ?A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.
given
The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).
The following is a definition of a recursive formula for the nth element of the sequence:
a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)
For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.
Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have
a_2 = a_1 + 7 = 5 + 7 = 12
a_3 = a_2 + 7 = 12 + 7 = 19
a_4 = a_3 + 7 = 19 + 7 = 26
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For the function
f
(
x
)
=
5
(
x
+
10
)
f(x)=5(x+10), find
f
−
1
(
x
)
f
−1
(x).
Answer:
45
Step-by-step explanation:
A survey found that 37 of 77 randomly selected women and 44 of 85 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program. Please check assumptions and interpret the interval.
To proceed with this analysis, we assume that the individuals in the sample were randomly selected and that the samples are independent.
Additionally, the sample sizes are large enough to apply the normal approximation to the sampling distribution of the difference in proportions.Using these assumptions, we can calculate the confidence in is 37/77 ≈ 0.481. The proportion of men who follow a regular exercise program is 44/85 ≈ 0.518. The difference between these proportions is 0.518 - 0.481 ≈ 0.037.
The 95% confidence interval for the difference in proportions can be calculated using the formula: difference ± (critical value) * sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)] where p1 and p2 are the proportions of women and men, n1 and n2 are the respective sample sizes, and the critical value corresponds to a 95% confidence level. Performing the calculations, the 95% confidence interval for the difference in proportions is approximately 0.037 ± 0.129, which gives us a range from -0.092 to 0.166.
Interpreting this interval, we can say that with 95% confidence, the true difference between the proportions of women and men who follow a regular exercise program lies within the range of -0.092 to 0.166. This means that there is insufficient evidence to conclude that there is a significant difference in the proportions of women and men who follow a regular exercise program. The interval includes zero, indicating that the difference could be negligible or non-existent.
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A group of friends wants to go to the amusement park. They have $89.50 to spend on parking and admission. Parking is $7.75, and tickets cost $27.25 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
The number of people who can go to the amusement park is 3 people
EquationTotal amount with the group of friends = $89.50Cost of parking = $7.75Cost of tickets per person =$27.25Number of people who can go to the amusement park = p89.50 = 7.75 + 27.25p
subtract 7.75 from both sides89.50 - 7.75 = 27.25p
81.75 = 27.25p
divide both sides by 27.25p = 81.75 / 27.25
p = 3
Therefore, the number of people who can go to the amusement park is 3 people.
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How to Write XIX in Numbers?
14 + 5 equals a value of 19. Roman numeral 19 is hence XIX.
What are Roman Numerals?Roman numerals are a set of numbers that was first used in ancient Rome and remained to be widely used in European until the Late Middle Ages.
The fixed positive numbers are represented by alphabets in roman numerals. I, II, III, IV, V, VI, VII, VIII, IX, and X are roman numerals that stand for the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 respectively.
The roman numbers XI for 11, XII for 12, XII for 13,... to XX for 20 come after 10.
So, roman numerals require that the number be written in extended form, i.e:
19 = 20 – 1
19 = XX – I
19 = XIX
Therefore, 14 + 5 equals a value of 19. Roman numeral 19 is hence XIX.
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y=−4x−3 y=−2x+1 solve by graphing
Answer: (-2,5)
Step-by-step explanation: just graph both equations they are already set up in the form and find the point where they intersect
What value of z should we use when making a 93% confidence interval for p?.
The crucial value (z) relies on the desired level of confidence and is predicated on a normal distribution when creating a confidence interval for a proportion (p) with a confidence level of 93%.
A 93% confidence level in this instance translates to an alpha level of 0.07 (1 - 0.93 = 0.07) that is split evenly between the two tails. In the usual normal distribution table, we search for the value that falls within the range of 0.07 to find the proper z-value. A 93% confidence level corresponds to a z-value of roughly 1.81. The confidence interval for the proportion p may be calculated using this number and provides a range where the genuine proportion is like to fall.
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here are 10 Superscript 9 bytes in a gigabyte. There are 10 Superscript 6 bytes in a megabyte. How many times greater is the storage capacity of a 1-gigabyte flash drive than a 1-megabyte flash drive?
3 times greater
10 times greater
1,000 times greater
3,000 times greater
The storage capacity of a 1-GB flash drive is 10^3 (or 1,000) times greater than that of a 1-MB flash drive.
To calculate the storage capacity of a 1-gigabyte (GB) flash drive and compare it to a 1-megabyte (MB) flash drive, we need to convert the units to bytes.
Given that there are 10^9 bytes in a gigabyte and 10^6 bytes in a megabyte, we can calculate the storage capacity of each drive as follows:
1 GB = 10^9 bytes
1 MB = 10^6 bytes
Now, to determine how many times greater the storage capacity of a 1-GB flash drive is compared to a 1-MB flash drive, we divide the storage capacity of the 1-GB drive by the storage capacity of the 1-MB drive:
(1 GB) / (1 MB) = (10^9 bytes) / (10^6 bytes) = 10^3
The storage capacity of a 1-GB flash drive is 10^3 (or 1,000) times greater than that of a 1-MB flash drive.
In summary, the storage capacity of a 1-GB flash drive is 1,000 times greater than that of a 1-MB flash drive.
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3. solve - 7 - 6 = k
1
-13
13
-1
Answer:
k=-13...............
reid took seven tests. on the first five tests that he took, he averaged $86$ points. on the last three tests, he averaged $95$ points. if he averaged $88$ points on all seven tests, how many points did he average on the last two tests?
The points that he average on the last two tests will be 93 points.
What is mean?A mean is the average of the set of numbers that are given.
On the first five tests that he took, he averaged 86 points. The total points will be:
= 86 × 5
= 430 points
He averaged 88 points on all seven tests. The total will be:
= (88 × 7)
= 616 points
The point average on the last two tests will be:
= (616 - 430)/2
= 186/2
= 93 points
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Liam bought a plant and planted it in a pot near a window in his house. Let H represent the height of the plant, in inches, t months since Liam bought the plant. A graph of H is shown below. Write an equation for H then state the y-intercept of the graph and determine its interpretation in the context of the problem.
The equation of the function is: H = 4t + 10.
The y-intercept of the function is 10, which is the height of the plant when Liam initially bought it.
How to Write the Equation of a Function?To write the equation of a function, first, find the slope (m) = rise / run. You can pick any two points on the line to find the slope. Next, find the y-intercept (b) which is the point where the line intercepts the vertical axis of the graph.
Find the slope using the two points from the given graph, (5, 30) and (10, 50):
Slope (m) = change in H / change in t = (50 - 30) / (10 - 5) = 20/5
m = 4
The y-intercept is b = 10 [in this context, it is the height of the plant when Liam initially bought it]
To write the equation of the function, substitute m = 4 and b = 10 into H = mt + b:
H = 4t + 10
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100 POINT QUESTION
Compound Interest: Determine the
amount of the investment if the original
$1000 were invested at a rate of 8%
compounded quarterly for 6 years
the sum of two numbers is 45. the greater number is 9 more than the other number. Find each number. use a system of linear equations to justify your answer
Answer:
18 and 27
Step-by-step explanation:
Let x = first (smaller) number
Let y = second (larger) number
Sum of two numbers is 45:
⇒ x + y = 45
The greater number is 9 more than the other number:
⇒ y = x + 9
Substitute y = x + 9 into x + y = 45 and solve for x:
⇒ x + (x + 9) = 45
⇒ 2x + 9 = 45
⇒ 2x = 36
⇒ x = 18
Substitute found value for x into y = x + 9 and solve for y:
⇒ y = 18 + 9
⇒ y = 27
Therefore, the two numbers are 18 and 27
Solution:
Let x and y be the numbers that sum up to 45.
Note that:
x + y = 45y + 9 = xSimplify the second equation such that the constant is the subject.
y + 9 = x=> -x + y = -9Use system of equations to solve for both variables.
x + y = 45-x + y = -9
=> 2y = 36=> y = 18Substitute the value of y into the second equation to find x.
y + 9 = x=> 18 + 9 = x=> 27 = xThe value of x and y is 27 and 18 respectively.
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.)
f(x) = 3x2/3 − 2x
I keep getting stuck at taking the first derivative and solving for critical points. So please show all work and even some of the tedious algebra bits included so I can see where I'm messing up?
The function f(x) = 3x²/3 - 2x has no intercepts, a relative minimum at (1, -1), no points of inflection, and no asymptotes.
Intercepts: To find the x-intercepts, we set f(x) equal to zero and solve for x:
0 = 3x²/3 - 2x
0 = x² - 2x
0 = x(x - 2)
x = 0 or x = 2
Therefore, both x = 0 and x = 2 are not actual x-intercepts, but rather double roots.
Relative Extrema: To find the relative extrema, we take the derivative of f(x) and set it equal to zero,
f'(x) = 2x - 2
0 = 2x - 2
2 = 2x
x = 1
Substituting x = 1 back into the original function, we find f(1) = -1. Therefore, the relative minimum occurs at (1, -1).
f''(x) = 2
Since the second derivative is a constant, it never equals zero. Therefore, there are no points of inflection for this function.
Asymptotes: To determine if there are any asymptotes, we examine the behavior of the function as x approaches positive or negative infinity. Since the highest power of x in the function is 2, the graph does not approach any vertical asymptotes.
For horizontal asymptotes, we look at the limits as x approaches positive or negative infinity:
lim(x→∞) f(x) = lim(x→∞) (3x²/3 - 2x) = ∞
The limits approach positive infinity in both cases, indicating that there are no horizontal asymptotes. Graphically, the function represents a parabola that opens upwards, with a relative minimum at (1, -1).
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1. Josiah's checking account was at $104,24 on Monday. One of his checks was cashed on Tuesday and his
account went down to - $23.99. What was the value of the check that was cashed? Show all work
necessary to justify your answer.
Step-by-step explanation:
mondey balance 104.24$
Tuesday balancs -23.99$
value = 104.24+23.99=128.23$
Which of the following is the square of a binomial?
A. 4m^2 - 6mn + 9n^2, B. 16x^2 + 24xy + 9y^2, C. c^2 - 2cd - d^2, D. a^2 + b^2.
All options except Option D , a² + b² , is the square of the binomial.
What is a Binomial ?A polynomial that contains only two term is called a Binomial.
The sum of square of a binomial is the sum of square of the first term , square of second term and twice of the product of the first and second term.
(a+b)² = a² +b² +2ab
(a-b)² = a² +b²-2ab
The options have to be broken down into this form to check whether they are square of a binomial
Option A : 4m² - 6mn + 9n² = (2m -3n)²
Option B: 16x² + 24xy + 9y²=(4x+3y)²
Option C : c²- 2cd - d²=(c-d)²
Option D : a² + b² cannot be written as the square of binomial.
All options except Option D is the square of the binomial.
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Write f(x) = 2x2 – 44x 185 in vertex form. to write f(x) = 2x2 – 44x 185, factor out from the first two terms. next, form a perfect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 – 22x 121) 185 – 242 the function written in vertex form is f(x) = (x – )2 .
The quadratic function given when converted to vertex form will be: \(f(x) = 2(x-11)^2 -57\)
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
\(y=a(x-h)^2 + k\)
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.
For this case, the given quadratic function is:
\(f(x) =2x^2 -44x + 185\\\)
Converting this to the vertex form, we get:
\(f(x) =2x^2 -44x + 185\\\\f(x) = 2(x^2 -22x) + 185\\f(x) = 2(x^2 -2 \times 11 \times x + 11^2 - 11^2) + 185\\f(x) = 2((x-11)^2 -121) + 185\\f(x) = 2(x-11)^2 -242 + 185\\f(x) = 2(x-11)^2 -57\)
Thus, the quadratic function given when converted to vertex form will be: \(f(x) = 2(x-11)^2 -57\)
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find the slope of a secant line with the intervals of [0,1]
Answer:
m = N/A
Step-by-step explanation:
Can you give me a curve or something?
9+10 is is 21 0or 19 teeeelll meeeee
Answer:
19
Step-by-step explanation:
9
+ 10
19
hope this helps
Answer:
9 + 10 = 19 in real life. but when it comes to the vine, 9 + 10 = 21
Please answer either or all of them and please show me how you solve it
Answer:
Step-by-step explanation:
using pythagoras theorem
a^2 + b^2 = c^2
4^2 + y^2 = 21^2
16 + y^2 = 441
y^2 = 441 - 16
y^2 = 425
\(y = \sqrt{425}\)
\(y = 5\sqrt{17}\)
y = 13.2
a^2 + b^2 = c^2
4^2 + x^2 = 7^2
16 + x^2 = 49
x^2 = 40 - 16
x^2 = 33
x = \(\sqrt{33}\)
x = 5.7 m