El mastil de un velero se halla unido a la proa y a la popa por dos cables que forman con la cubierta, angulo de 45 grados y 60 grados, respectivamente. si el barco tiene una longitud de 25m, ¿cual es la altura del mastil?
Answers
La altura del mástil es de aproximadamente 20.87 metros.
How to find mast height?Para resolver el problema, se puede utilizar la ley de cosenos para encontrar la longitud del mástil:
c² = a² + b² - 2ab cos C
Donde:
c es la longitud del mástil (lo que se busca)
a es la longitud de la parte delantera del barco (25m)
b es la longitud de la parte trasera del barco (también 25m)
C es el ángulo entre a y b, que se puede calcular utilizando la tangente: tan C = 1.5 (pues tan 60° = √3, y tan 45° = 1)
Resolviendo para c:
c² = 25² + 25² - 2(25)(25)cos(arctan 1.5)
c = √(25² + 25² - 2(25)(25)(1/√(1+(1.5)²)))
c ≈ 31.08 m
Por lo tanto, la altura del mástil es de aproximadamente 31.08 metros.
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Related Questions
Hi I need to know with equation is a one solution , no solution anf a infinite solution
Answers
The equation of a line in Slope-Intercept form is:
\(y=mx+b\)Where "m" is the slope and "b" is the y-intercept.
Let's write each equation given in the exercise as a System of equations and then let's write each equation in Slope-Intercept form. Then:
Equation 1 as a System of equations
\(\begin{cases}y=2(x-1)+6\Rightarrow y=2x-2+6\Rightarrow y=2x+4 \\ y=4x-22\end{cases}\)You can identify that the slope and the y-intercept of the first equation are:
\(\begin{gathered} m_1=2_{} \\ b_1=4 \end{gathered}\)And the slope and the y-intercept of the second equation are:
\(\begin{gathered} m_2=4 \\ b_2=-22 \end{gathered}\)Since:
\(\begin{gathered} m_1\ne m_2 \\ b_1\ne b_2 \end{gathered}\)The lines intersect each other and the System of equations has one solution.
Equation 2 as a System of equations
\(\begin{cases}y=6(2x+1)-2\Rightarrow y=12x+6-2\Rightarrow y=12x+4 \\ y=12x+4\end{cases}\)You can see that:
\(\begin{gathered} m_1=m_2 \\ b_1=b_2 \end{gathered}\)Therefore, since they are the same line, the system has infinite solutions.
Equation 3 as a System of equations
\(\begin{cases}y=2(4-x)\Rightarrow y=-2x+8 \\ y=-2(1+x)-2\Rightarrow y=-2-2x-2\Rightarrow y=-2x-4\end{cases}\)Since:
\(\begin{gathered} m_1=m_2 \\ b_1\ne b_2 \end{gathered}\)You can determine that the lines are parallel. Therefore, the System of equations has no solution.
The anwer is:
- The first equation has one solution.
- The second equation has infinite solutions.
- The third equation has no solution.
Given the definitions of f(x) and g(x) below, find the value of g(f(-3)).
Answers
Answer:
-11
Step-by-step explanation:
f(x) = 5x + 11
g(x) = x^2 + 4x - 11
g(f(-3)) = ?
f(-3) = 5(-3) + 11
= -15 + 11 = -4
g(f(-3)) = g(-4) = -(4)^2 + 4(-4) - 11
= 16 - 16 - 11 = -11
A function assigns the value of each element of one set to the other specific element of another set. The value of g(f(-3)) is -11.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given f(x)=5x+11 and g(x)=x²+4x-11, therefore, we can write the value of g(f(x)) as,
g(f(x)) = (5x + 11)² + 4(5x + 11) - 11
= 25x² + 121 + 110x + 20x + 44 - 11
= 25x² + 130x + 154
Now, substitute the value of x as -3 in the function g(f(x)), therefore, we can write,
g(f(-3)) = 25x² + 130x + 154
= 25(3)² + 130(-3) + 154
= 225 - 390 + 154
= -11
Hence, the value of g(f(-3)) is -11.
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Jabari wants to save $66. He earns
$9 every week, walking his
neighbor's dog for 2 hours. He
saves all of his money. How many
weeks will it take him to save $66?
Answers
Answer:
n = 7 1/3 weeks
Step-by-step explanation:
Amount Jabari wants to save = $66
Amount he earns per week = $9
Hours worked per week = 2 hours
How many weeks will it take him to save $66?
Let
n = number of weeks will it take him to save $66
66 = 9n
n = 66/9
n = 7 3/9
n = 7 1/3 weeks
Or
n = 7.33 weeks
Find the area of the unshaded region.
multiple choice group answers
565
555
530
560
Answers
the distance between town A and town B is 123 km. Two buses begin their journey and move directly toward each other. From town A, the bus is moving at a speed of 45 km/hr and from town B, the bus is moving at a speed of 67 km/hr. Assuming the buses started at the same time, find how far is their meeting point from town A?
Answers
Answer:
Speed of slower bus = 50mph and
speed of faster bus = 60 mph
Step-by-step explanation:
Let speed of first bus be x mph
Then speed of second bus = x+10 mph.
Let A and B have a distance d.
Then given that faster bus reached in 3.5 hours.
i.e. ... i
THe other bus was away from B by 1/6 times d.
Distance travelled by slower bus = 1-1/6 = 5d/6
Time taken = 3.5 hours
i.e. ... ii
Divide i by ii to eliminate d.
ie Speed of slower bus = 50mph and
speed of faster bus = 60 mph
Use ii equation
miles
one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. what is the area of the parallelogram? express your answer in simplest radical form.
Answers
The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².
What is parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.
Here,
A parallelogram has adjacent angles that add up to 180 degrees.
Since one angle of parallelogram is 120°.
240+2x=360
2x=120
x=60
The other will be 60°
The area of parallelogram= lh
l=15 inch
h=b(sin 60°)
=8*√3/2
h=4√3 inch
area of parallelogram= 15*4√3
= 60√3 inch²
The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."
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CAN ANYONE help me need it
Answers
Below are some authorial techniques that can be used to create mystery, tension, or surprise in literature.
What are authorial techniques that can be used to create mystery?Order of events: The order in which events are presented can create a sense of mystery or suspense.
Pacing: The pace of a story can also be used to create suspense. A slow-paced story can build tension by allowing the reader to dwell on the details of a situation, while a fast-paced story can create excitement and surprise by keeping the reader guessing what will happen next.
Structure: The structure of a story can also be used to create mystery, tension, or surprise. For example, a story that is told in flashback can create a sense of mystery by revealing information about the past that is relevant to the present.
Time manipulation: The manipulation of time can also be used to create suspense.
Language: The language that an author uses can also be used to create mystery, tension, or surprise. For example, an author might use vague or ambiguous language to create a sense of mystery, or use strong language to create a sense of tension or surprise.
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A factory makes 23 fear of rope
per minute. How mary text of rope
will the factory make in 7 minutes,
Answers
Answer: 2346
Step-by-step explanation:
HW 3: Problem 9 Previous Problem List Next (1 point) Suppose that X is normally distributed with mean 110 and standard deviation 21. A. What is the probability that X is greater than 145.28? Probabili
Answers
The probability that X is greater than 145.28 is approximately 0.0465.
Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 16 using fertilizer A, and 17 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results of the experiment are shown below.[table]Which of the following statements best describes the conclusion that can be drawn from this experiment?A. There is no statistical evidence of difference in the yields between fertilizer A and fertilizer B (p > 0.15).B. There is a borderline statistically significant difference in the yields between fertilizer A and fertilizer B (0.10 < p < 0.15).C. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10).D. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).E. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (p < 0.01).
Answers
Answer:
There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).
Step-by-step explanation:
Which of the following pair of linear equations is inconsistent?
A. x - 2y = 6; 2x + 3y = 4
B. 9x - 8y = 17; 18x -16y = 34
C. 2x + 3y = 7; 4x + 6y = 5
D. 5x - 3y =11; 7x + 2y =13
Answers
Substituting the first equation into the second equation, we get: 4(2x + 3y) + 6y = 5
Expanding the left side gives: 8x + 12y + 6y = 5
Combining like terms gives: 8x + 18y = 5
Subtracting 5 from both sides gives: 8x + 18y - 5 = 0
Combining like terms gives: 8x + 18y = -5
This equation represents a line in the xy-plane. The original equation 2x + 3y = 7 represents a different line in the xy-plane. These lines do not intersect, so this system of equations has no solutions and is inconsistent.
A shop sells bagels for $5 per dozen. You can use the table to answer the questions. Explain your reasoning. Number of Bagels Price in Dollars 12 5 At this rate, how much would 6 bagels cost? How many bagels can you buy for $50?
Answers
Answer:
For 6 bagels it would be $2.50, and you can buy 120 bagels for $50
Step-by-step explanation:
Use a software program or graphing utility with matrix capabilities to decode the cryptogram. 3 2 6
A= 1 1 3
1 1 4
24 24 77 73 57 176 46 33 104 74 56 188 29 21 63 32 27 86 85 63 203 68 48 144 74 51 153 90 67 213 37 25 76 60 48 145 94 69 207 72 54 175 30 25 77 33 28 84 SEMPTEMBER THE ELEVENTH WILL ALWAYS REMEMBER
Answers
To decode the cryptogram, we need to multiply the matrix A by the column vector [3, 2, 6] using matrix multiplication.
Each entry in the resulting vector corresponds to a letter in the decoded message.
Let's perform the matrix multiplication:
A =
[1 1 3]
[1 1 4]
Column vector: [3, 2, 6]
A * [3, 2, 6] = [24, 24, 77, 73, 57, 176, 46, 33, 104, 74, 56, 188, 29, 21, 63, 32, 27, 86, 85, 63, 203, 68, 48, 144, 74, 51, 153, 90, 67, 213, 37, 25, 76, 60, 48, 145, 94, 69, 207, 72, 54, 175, 30, 25, 77, 33, 28, 84]
The resulting vector represents the ASCII values of the characters in the decoded message. Converting these ASCII values back to their corresponding letters, we obtain the decoded message:
"SEMPTEMBER THE ELEVENTH WILL ALWAYS REMEMBER"
Please note that the decoded message may contain additional spaces or punctuation marks that are not present in the original matrix representation.
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Draw the graph of f(x)=3x^4+4x^3−12x^2+12 and enter all extreme points. Also state whether they are minimum or maximum points.please show a figure and detailed answer
Answers
The draw is:
Now, to find the extreme points we need to calculate the derivative and solve it for equal zero.
\(\begin{gathered} f(x)=3x^4+4x^3−12x^2+12 \\ f^{\prime}(x)=12x^3+12x^2−24x \end{gathered}\)Let's solve = 0:
\(\begin{gathered} f^{\prime}(x)=12x^3+12x^2−24x^=0 \\ 12x^3+12x^2−24x=0 \\ 12x(x^2+x-2)=0 \\ x^2+x-2=0 \\ (x+2)(x-1)=0 \\ x=-2 \\ x=1 \\ x=0 \end{gathered}\)We have the extreme points: x= -2, x=1, x=0. To compute what point is minimal or maximal we have to evaluate each point. For x= -2
\(\begin{gathered} f(x)=3x^4+4x^3−12x^2+12 \\ f(-2)=3(-2)^4+4(-2)^3−12(-2)^2+12 \\ f(-2)=48-32-48+12=-20 \end{gathered}\)Now for x=1:
\(f(1)=3(1)^4+4(1)^3-12*1^2+12=3+4-12+12=7\)Now for x=0:
\(f(0)=3*0+4*0-12*0+12=12\)Comparing these 3 points, we have local minimals at -2 and 1, and a local maximal at 0.
there are 618 cookies and they're going to be split between three people
Answers
Answer:
206.
Step-by-step explanation:
Each person will receive 618 / 3
= 206 cookies.
So basically, this is a division problem. The question is 618 divided by 3. The answer is 206. You can always check by saying, what is 206 times 3?
20 girls And 28 boys volunteer to plant trees at a school the principle divides the girls and boys into identical groups, that have girls and boys in each group what is the greatest number of groups the principle can make'
Answers
Answer:
4 groups
Step-by-step explanation:
Find the Greatest Common Factor.
Plz give me brainliest!!!
What should be done to both sides of the equation in order to solve y + 8.5 = 17.2?
Add 8.5.
Subtract 17.2.
Add 17.2.
Subtract 8.5.
Answers
Answer:
subtract 8.5
Step-by-step explanation:
this will isolate y
The area of this polygon is 228 square meters
What is the length of the side labeled with a question mark
Enter your answer in the box
Answers
Answer: 7
Step-by-step explanation:
Let the unknown length be x
Cut the polygon into 2 pieces
6 * 24 + x * (18 - 6) = 228
144 + 12x = 228
12x = 84
x = 7
The length of the side labeled with a question mark in the given polygon is 7 meters.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, the area of this polygon is 228 square meters.
We know that, the area of a rectangle is Length×Breadth
Area of a large rectangle = 24×6
= 144 square meters
Let the length of unknown side be x.
Area of a small rectangle = 12×x
Total area = Area of a large rectangle+Area of a small rectangle
228=144+12x
12x=228-144
12x=84
x=84/12
x=7 meters
Therefore, the length of the side labeled with a question mark is 7 meters.
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The function f(x) = 4e^x when evaluated for f(2) is:
Answers
Using a calculator, you should get
f(x) = 4*e^x
f(2) = 4*e^2 .... replacing every x with 2
f(2) = 29.5562243957433
This is an approximate value. Round this however you need to.
The value of f(2) = 29.5562243957433
Approximate value of function -A method for approximating the value of a function near a known value. The method uses the tangent line at the known value of the function to approximate the function's graph.For eveluate for f(x) we put x = 2,
f(x) = 4*e^x
f(2) = 4*e^2 .... replacing every x with 2
f(2) = 29.5562243957433
Therefore, This is an approximate value f(2) = 29.5562243957433.
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" X is at least 2" can be represented by x > 2.
True
False
Answers
Answer: False, as you see there's the word "Least" so x can be equate to one. So therefore it's false.
If a figure is dilated by a factor of 5/6, the area of the figure will change by a factor of ?
Answers
Answer:
5/6
Step-by-step explanation:
WORTH 60 POINTS PLS
HELP N B HONEST
Answers
A statement that correctly compares the two functions include the following: C. they have the same x-intercept and the same end behavior as x approaches ∞.
What is the x-intercept?In Mathematics, the x-intercept of is sometimes referred to as horizontal intercept and the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).
By critically observing the table representing function g and the graph representing function f, we can reasonably infer and logically deduce that they both have different y-intercept.
However, both function g and function f have the same x-intercept of 1 and the same end behavior as x approaches infinity (∞).
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Phythagorean theorem help plsss
Answers
Answer:
95cm
Step-by-step explanation:
c²=76²+57²
c²=5776+3249
√c²=√9025
c=95
I hope this helps
I'll mark brainliest!
Answers
Answer:
im answering so he can have it :D
Step-by-step explanation:
If the variance of a distribution is 16, the mean is 12, and the number of cases is 24, what is the standard deviation?
Answers
Answer:
To calculate the standard deviation we use the following equation:
The symbol "o" is used to represent the standard deviation of a population.
\(o=\sqrt{o2} \\o=\sqrt{16}\\ o=4\)
So standard deviation is 4.
what is the area of a circle when the radius is 5ft
Answers
Answer:
78.54 ft²
Step-by-step explanation:
Hello!
The formula for the area of a circle is A = πr², where r is the radius.
Given r is 5, find the area:
A = πr²A = π*5²A = 25πA = 78.5398163397 ≈ 78.54The area is 78.54 ft²
(1.) Find the volume of a cube if an edge of the cube has a
length of 6 feet.
(2.) A right circular cylinder has the radius of 4 meters and
the height of 10 meters. Find the volume of the cylinder.
Answers
The volume of the cube with an edge length of 6 feet is 216 cubic feet, and the volume of the cylinder with a radius of 4 meters and height of 10 meters is 160π cubic meters.
Volume of a cube: The volume of a cube is given by the formula V = \(s^{3} ,\) where s represents the length of one side of the cube. In this case, the edge length is 6 feet, so we substitute s = 6 into the formula: V = \(6^{3}\) = 6 * 6 * 6 = 216 cubic feet. Therefore, the volume of the cube is 216 cubic feet.
Volume of a cylinder: The volume of a right circular cylinder is calculated using the formula V = π\(r^{2}\)h, where r represents the radius and h represents the height of the cylinder.
Given that the radius is 4 meters and the height is 10 meters, we substitute these values into the formula: V = π(\(4^{2}\))(10) = π * 16 * 10 = 160π cubic meters. Thus, the volume of the cylinder is 160π cubic meters.
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Is this statement true or false?Why?Researchers conducted a study and obtained a p-value of 0.30. Because the p-value is quite high, there is evidence to accept the null hypothesis.
Answers
Researchers conducted a study and obtained the p-value is 0.30, which is higher than the common significance level of 0.05. This means that there is not enough evidence to reject the null hypothesis, but it does not mean that the null hypothesis is accepted.
Hence this statement is false.
When researchers conduct a study and obtain a p-value, they use it to make a decision regarding the null hypothesis.
However, a high p-value does not provide evidence to accept the null hypothesis.
Instead, it indicates that there is not enough evidence to reject the null hypothesis.
1. Researchers start with a null hypothesis (H0), which is a statement that there is no effect or relationship between variables being studied.
They also have an alternative hypothesis (H1), which is a statement that there is an effect or relationship between variables.
2. They collect data and perform statistical tests to calculate the p-value, which represents the probability of observing the test results (or more extreme results) assuming the null hypothesis is true.
3. The p-value is then compared to a pre-determined significance level (alpha), commonly set at 0.05 or 5%.
If the p-value is less than the significance level, researchers reject the null hypothesis in favor of the alternative hypothesis.
4. In this case, the p-value is 0.30, which is higher than the common significance level of 0.05.
This means that there is not enough evidence to reject the null hypothesis, but it does not mean that the null hypothesis is accepted.
5. Instead, researchers should say that they "fail to reject" the null hypothesis, meaning they cannot confidently conclude that the alternative hypothesis is true based on the data and analysis.
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if i write 2 1/3 pages in 6 minutes how many can I write in 18 minutes
Answers
Answer:
7 pages
Step-by-step explanation:
21/3=7/3
18÷6=3
7/3×3=7
plz help will give brainliest
Answers
Step-by-step explanation:
Hey there!!!!
Your required answer is option A.
The reason is.
When we solve it through elimination method we need to multiply second equation by "2" and then subtract to get "-4y" in 1st equation and "+4y" in 2nd equation cancelled.(As when we multiply equation 2 by 2 and subtract we get "-2y" as "+4y".)
So, it the equation seems like,
\(12 {x}^{2} + 4 {y}^{2} = 22\)
Now, this equation is made after multiplying it by 2 and subtracting the 1st and 2nd equation to solve the equation s.
So, the answer is option A.
Hope it helps...