Therefore, the correct answer is option D: "The wire is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell. "Option E, "the wire does not carry any current," is not correct because the wire is in a region with a magnetic field, and therefore will have an induced current.
we are asked to determine the position and direction of the wire that is parallel to the cylinder axis in the hollow region. The long straight cylindrical shell has an inner radius R and an outer radius Ro, and carries a current i that is uniformly distributed over its cross section. The wire is located in the hollow region, which is defined as r > R and r < Ro.
Based on this information, we can determine the position and direction of the wire.To begin, we know that the wire must be on the cylinder axis since it is parallel to the axis. This eliminates options A, B, and C. Additionally, we know that the current in the wire must be in the opposite direction to the current in the shell. This is because the magnetic field created by the current in the shell will induce a current in the wire that is opposite in direction in order to create a repulsive force.
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Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if
The distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
Describe Distance?Distance can be calculated using a variety of methods, depending on the context. For example, the distance between two points in a straight line can be calculated using the Pythagorean theorem in two dimensions or the distance formula in three dimensions. In more complex situations, such as when the two points are not in a straight line, distance may be calculated using other mathematical methods or by estimating the distance based on contextual information.
Distance is often used in everyday life to describe how far apart objects or locations are from each other, such as the distance between two cities, the distance from home to work, or the distance between two landmarks. It is also used in many scientific fields to describe the separation between celestial objects, the distances traveled by particles in a chemical reaction, or the distances between neurons in the brain.
We can solve this problem using the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:
a/sin A = b/sin B = c/sin C
Let's label the distance from point A to the boat as a, the distance from point B to the boat as b, and the distance from point C to the opposite bank as c. We are given that AB = 50 meters, angle ABC = 68 degrees, and angle BCA = 73 degrees. We want to find a and b.
First, we can find the measure of angle ACB by using the fact that the sum of angles in a triangle is 180 degrees:
angle ACB = 180 - angle ABC - angle BCA
angle ACB = 180 - 68 - 73
angle ACB = 39 degrees
Next, we can use the Law of Sines to find a and b:
a/sin 68 = c/sin 39
b/sin 73 = c/sin 39
Solving for c in both equations gives:
c = a sin 39 / sin 68
c = b sin 39 / sin 73
We can set these two equations equal to each other and solve for b:
a sin 39 / sin 68 = b sin 39 / sin 73
b = a (sin 39 / sin 73) * (sin 68 / sin 39)
b = a (sin 68 / sin 73)
We know that a + b = 50, so we can substitute the expression for b into this equation:
a + a (sin 68 / sin 73) = 50
Solving for a gives:
a = 50 / (1 + sin 68 / sin 73)
a ≈ 23.3 meters
Substituting this value of a into the expression for b gives:
b ≈ 26.7 meters
So the distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
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The complete question is
Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if angle ABC=68 degree and angle BCA=73 degree. Round to the nearest foot.
(HELP PLS)
Milwaukee's average high temperature in the summer is four
degrees lower than other cities in its same latitude.
Which option best describes the reason for that change?
OSioux Falls is near mountains.
O Milwaukee is beside a lake.
OSioux Falls is closer to a desert.
O Milwaukee has more mountains.
We can claim that after answering the above question, the As a result, equation the correct answer is "Milwaukee is near a lake."
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the sentence "2x + 3" equals the value "9". The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complex equations, regular or nonlinear, with one or more factors are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
Milwaukee's average high temperature in the summer is four degrees lower than other cities in its latitude since it is located next to a lake. The lake (Lake Michigan) cools the surrounding areas, notably Milwaukee, which is located on the lake's western shore. This is referred to as the "lake breeze" effect, and it is a regular occurrence in cities located near major bodies of water. As a result, the correct answer is "Milwaukee is near a lake."
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If $4,323 was withheld during the year and taxes owed were $4,576:
a. Would the person owe an additional amount or receive a refund?
b. What is the amount? [Make sure to show your work]
Answer:
a. Since taxes owed ($4,576) are greater than the amount withheld ($4,323), the person would owe an additional amount.
b. The additional amount owed can be calculated by subtracting the amount withheld from the taxes owed:
Additional amount owed = Taxes owed - Amount withheld
= $4,576 - $4,323
= $253
Therefore, the person would owe an additional $253.
Please mark my answer as brainliest!
an apple falls from a tree 100 km to the ground. if the acceleration due to gravity is 9,8 m/s² and the mass of the apple is 0,2 gram. what is the potential energy of the apple?
Answer: 196 Joules (J)
Step-by-step explanation:
To calculate the potential energy of the apple, we can use the formula:
Potential Energy = Mass x Gravity x Height
First, let's convert the height from kilometers to meters:
100 km = 100,000 meters
Now, let's convert the mass of the apple from grams to kilograms:
0.2 gram = 0.0002 kilograms
Using these values, we can calculate the potential energy:
Potential Energy = 0.0002 kg x 9.8 m/s^2 x 100,000 m
Potential Energy = 196 Joules (J)
Therefore, the potential energy of the apple is 196 Joules (J).
PLEASE HELP ME SOLVING THIS CHART PLEASEEE I TRIED BUT I DON'T FEEL IT RIGHT
Rewrite the following equation in slope-intercept form. Y + 5 = 1 7 ( x + 7 )
Answer: y = 17x + 114
Step-by-step explanation:
The equation for the slope-intercept form is y = mx + b.
Arrange the equation so that it resembles y = mx + b.
You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.
y + 5 = 17(x + 7)
y + 5 = 17x + 119
y + 5 - 5 = 17x + 119 - 5
y = 17x + 114
Answer:
Y = 17x + 114
Step-by-step explanation:
1. Y + 5 = 17 (x+7)
2. Y + 5 = 17x + 119 [Multiply the numbers in parenthesis by 17.]
3. Y = 17x + 114. [To keep the balance and move the 5 over, subtract it from 119.]
One - third of a number y is 14.
Answer:
42
Step-by-step explanation:
Answer:
Step-by-step explanation:
If one-third of a number y is 14, we can express this mathematically as:
1/3 y = 14
To solve for y, we can isolate y on one side of the equation by multiplying both sides by 3:
1/3 y * 3 = 14 * 3
Simplifying, we get:
y = 42
Therefore, the number is 42.
what is the area of the trapizoid. not draw to scale
a. 8 cm2
b. 62 cm2
c. 84 cm2
d. 125 cm2
Evaluate. 547+233×5−142 whats this answer
The answer to the expression 547 + 233 × 5 - 142 is 1752. To solve the expression, we must follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication, and Division (performed left to right), and Addition and Subtraction (performed left to right).
Since there are no parentheses or exponents in this expression, we start with multiplication and division. In this case, we have to multiply 233 by 5, which gives us 1165. Then, we add 547 to 1165, which gives us 1712. Finally, we subtract 142 from 1712, which gives us the final answer of 1752. Therefore, the result of the expression 547 + 233 × 5 - 142 is 1752, which can be obtained by following the order of operations and performing the arithmetic operations in the correct order.
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the student body of a large university consists of 60% female students. a random sample of 8 students is selected. what is the probability that among
The probability of selecting 8 female students from a sample of 8 students from a student body with 60% female students is 0.2187, or 21.87%.
The probability of selecting a sample of 8 students from a student body of 60% female students is calculated using binomial probability. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of independent trials. In this case, the probability of selecting 8 students, with 60% being female students, can be calculated using the binomial probability formula.
The probability can be calculated using the following equation:
[tex]P(x=8) = (n!/((n-x)!x!)) * p^x * q^{(n-x)}[/tex]
Where:
In this case, n = 8, x = 8, p = 0.6, and q = 0.4. Plugging these values into the equation gives us a probability of 0.2187. This means that there is a 21.87% chance of selecting 8 female students out of a sample of 8 students from a student body with 60% female students.
It is important to remember that binomial probability is only used when there are two possible outcomes in each trial (i.e. success or failure). Additionally, it is important to remember that the equation only applies when the trials are independent of each other.
In conclusion, the probability of selecting 8 female students from a sample of 8 students from a student body with 60% female students is 0.2187, or 21.87%.
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The angle turns through 5/6 of the circle The angle measures of 5/6 of the circle the answer is?
Answer:
A circle has 360 degrees, so 5/6 of the circle can be found by multiplying 360 by 5/6:
5/6 of 360 = (5/6) × 360 = 300
Therefore, the angle measures of 5/6 of the circle is 300 degrees.
how many driving lessons do you need to do with a professioanl instructor before my parents could teach me
The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.
In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.
The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.
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HELP ME PLEASE PLEASE!!! URGENT
This equation fits the given data: Oy = -2x + 10. The equation creates a linear relationship between the x and y values, with each x value increasing by 1 resulting in a decrease in the y value by 2.
What is linear ?Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.
The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.
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This equation fits the given data: y = 1/3x + 2. The equation creates a linear relationship between the x and y values. Hence the correct option is b.
What is linear relationship?Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.
The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.
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find a basis for the subspace of consisting of all vectors such that . hint: notice that this single equation counts as a system of linear equations; find and describe the solutions. answer:
A basis for the subspace of all vectors satisfying the equation x + y + z = 0 is {(-1, 0, 1), (0, 1, -1)}.
SOLUTION:
A basis for the subspace of all vectors (x, y, z) satisfying the single equation x + y + z = 0 can be found by solving this system of linear equations.
Step 1: Choose two variables to express in terms of the remaining variable.
Let's express x and y in terms of z. From the given equation, we get:
x = -y - z
y = -x - z
Step 2: Choose two independent vectors that satisfy the equations.
We can choose two independent vectors by setting z = 1 and z = -1:
When z = 1:
x = -y - 1
y = -x - 1
Let y = 0, then x = -1, so one vector is (-1, 0, 1).
When z = -1:
x = -y + 1
y = -x + 1
Let x = 0, then y = 1, so the other vector is (0, 1, -1).
Therefore, a basis for the subspace of all vectors satisfying the equation x + y + z = 0 is {(-1, 0, 1), (0, 1, -1)}.
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valencia theater sold 487 tickets for a play. tickets cost $14 per student with valid valencia identification and $25 per non-student. if total receipts were $8391, how many valencia student tickets and non-student tickets were sold?
354 Valencia student tickets and 133 non-student tickets were sold.
Let's use algebra to solve the problem. Let
x be the number of Valencia student tickets sold
y be the number of non-student tickets sold
We know that
x + y = 487 (the total number of tickets sold is 487)
14x + 25y = 8391 (the total receipts from ticket sales is $8391)
We can use the first equation to express one of the variables in terms of the other. For example, we can solve for y
y = 487 - x
Here we have to use the substitution method, we can then substitute this expression for y into the second equation
14x + 25(487 - x) = 8391
Simplifying and solving for x
14x + 12275 - 25x = 8391
-11x = -3884
x = 354
So, 354 Valencia student tickets were sold. We can use the first equation to find y
x + y = 487
354 + y = 487
y = 133
So, 133 non-student tickets were sold.
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jenny places a total of red easter eggs in several green baskets and a total of orange easter eggs in some blue baskets. each basket contains the same number of eggs and there are at least eggs in each basket. how many eggs did jenny put in each basket?
If each basket contains the same number of eggs and there are at least 4 eggs in each basket, Jenny put 3 red eggs in each of 6 baskets, and 4 orange eggs in each of 6 baskets.
Let's call the number of eggs in each basket "x." We know that Jenny placed a total of 18 red eggs, so the number of baskets with red eggs can be represented as 18/x. Similarly, the number of baskets with orange eggs can be represented as 24/x.
Since we know that each basket contains at least 4 eggs, we can set up the inequality 4 ≤ x.
Now we can use this information to set up an equation:
18/x + 24/x = total number of baskets
Simplifying this equation, we get:
42/x = total number of baskets
But we also know that the total number of baskets is an integer (you can't have a fraction of a basket), so x must be a factor of 42.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. But we also know that each basket must contain at least 4 eggs, so we can eliminate 1, 2, and 3 as possible values of x.
Therefore, the possible values of x are 6, 7, 14, 21, and 42. But we also know that there are 18 red eggs and 24 orange eggs, so x must be a factor of both 18 and 24.
The common factors of 18 and 24 are 1, 2, 3, and 6. Therefore, the only possible value of x is 6.
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Complete question is:
Jenny places a total of 18 red Easter eggs in several green baskets and a total of 24 orange Easter eggs in some blue baskets. Each basket contains the same number of eggs and there are at least 4 eggs in each basket. How many eggs did Jenny put in each basket?
-2(-3)+27÷(-3)+3?
Please help
Answer:
0
Step-by-step explanation:
-2(-3)+27÷(-3)+3
6-9+3
0
Given:-
[tex] \tt \: -2 ( - 3 )+27 ÷ ( - 3 ) + 3 = ?[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: -2 ( - 3 )+27 ÷ ( - 3 ) + 3 = ?[/tex][tex] \: [/tex]
[tex] \tt \: [-2 ( - 3 ) + 27 ÷ ( - 3 )] + 3 [/tex][tex] \: [/tex]
[tex] \tt \: 6 - 9 + 3[/tex][tex] \: [/tex]
[tex] \tt \: -3 + 3[/tex][tex] \: [/tex]
[tex] \boxed{ \tt {\purple{ \: \:0 \: \: }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
jordan wants to create an equiangular octagon whose side lengths are exactly the first 8 positive integers, so that each side has a differetn length. how many such octagons can jordan create
There is only one equiangular octagon that Jordan can create with side lengths as the first 8 positive integers.
To create an equiangular octagon with side lengths as the first 8 positive integers, each side must have a different length. The sum of the interior angles of an octagon is 1080 degrees, so each angle in the octagon must measure 135 degrees.
If we arrange the 8 integers in decreasing order, we can label the longest side as a and the remaining sides as b1, b2, b3, b4, b5, b6, in descending order. Then, we must have:
a + b1 + b2 = a + b2 + b3 = a + b3 + b4 = a + b4 + b5 = a + b5 + b6 = a + b6 + b1 = 135 degrees
Simplify each equation, we get:
b1 - b3 = b2 - b4 = b3 - b5 = b4 - b6 = b5 - b1 = b6 - a
Since all the side lengths are different, we can use these equations to find all possible combinations of side lengths. By inspection, we can see that there is only one set of side lengths that satisfies these conditions, namely:
a = 8
b1 = 7
b2 = 6
b3 = 5
b4 = 4
b5 = 3
b6 = 2
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PLEASE HELP FAST (giving brainliest)
First one is 6
second one is 12
third one is -8
hope this helps
Answer:
Step-by-step explanation:
x=6
x=12
x=-8
Find the slope of the line that passes through the points A( 2, -4 ) and B( 3, 4 ).
The slope of AB =
Answer: slope=4
Step-by-step explanation:
[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]
[tex]Slope=\frac{4- - 4}{3-2}[/tex]
[tex]Slope=\frac{4+4}{3-2}[/tex]
[tex]Slope=4[/tex]
The area of a circle is 36л ft². What is the circumference, in feet? Express
your answer in terms of pie
Answer:
12π feet
Step-by-step explanation:
The formula for the area of a circle is A = πr², where A is the area and r is the radius. We are given that the area is 36π ft², so we can set up an equation:
36π = πr²
To solve for the radius, we can divide both sides by π:
36 = r²
Taking the square root of both sides, we get:
r = 6
Now that we know the radius is 6 feet, we can use the formula for the circumference of a circle, C = 2πr:
C = 2π(6)
Simplifying, we get:
C = 12π
Therefore, the circumference of the circle is 12π feet.
assume that you want to construct a 95% ci for the mean of a normal distribution with population variance 30. the sample average is 10 and the sample size is 20. what is the lower limit of the ci? approximate your answer using only one decimal.
By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.
To construct a 95% CI for the population mean of a normal distribution, we can use the formula:
CI = sample mean ± z* (standard error)
Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:
standard error = population standard deviation / √sample size
In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:
standard error = 5.48 / √20 = 1.226
Now, we can use the formula for the CI:
CI = 10 ± 1.96 x 1.22
Simplifying this expression gives us:
CI = (7.59, 12.41)
This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.
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the probability is approximately 0.6 that in a randomly selected week, they will make a combined total less than what amount?
There is a probability of around 60% that during a week picked randomly, the combined sum of their earnings will be below $0.2533.
The given probability is a measure of the chances that the occurrence of an event will happen. In the context of the question, we want to calculate the combined total of earnings that are less than a certain amount. We know that the probability is approximately 0.6. Therefore, the answer is given by the value that satisfies this condition.
That is, P(X < a) = 0.6where X represents the combined total earnings of a randomly selected week, and a is the required amount.
To solve for a, we can use the cumulative distribution function (CDF) of X. The CDF gives the probability that X is less than or equal to a. Therefore, CDF(a) = P(X ≤ a)
The complement of this probability isP(X > a) = 1 - CDF(a)
We know that P(X < a) = 0.6, which is equivalent to (X ≤ a) = P(X < a) + P(X = a) = 0.6 + 0 = 0.6
Therefore, P(X > a) = 1 - CDF(a) = 1 - P(X ≤ a) = 1 - 0.6 = 0.4
Now we can use a calculator to find the value of a that corresponds to P(X > a) = 0.4.
For example, if we use a calculator, we get a value of a = 0.2533 (rounded to four decimal places).
Therefore, the probability is approximately 0.6 that in a randomly selected week, they will make a combined total of less than $0.2533.
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calculate the amount of heat produced, in kj, when 52.40 g of methane, ch4, burns in an excess of air, according to the following equation.
Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ
The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:
[tex]Q = mcΔT[/tex]
Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).
Using the equation, the amount of heat produced can be calculated as follows:
Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
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is the number of linearly independent columns in a matrix a equal to the number of linearly independent rows in a? why?
Yes, the number of linearly independent columns in a matrix A is equal to the number of linearly independent rows in A.
This is because the definition of linear independence states that no linear combination of a set of vectors can equal the zero vector, so if one set of vectors is linearly independent, the other set of vectors must also be linearly independent.
To explain further, the number of linearly independent vectors in a matrix A is determined by the rank of the matrix. The rank of a matrix is the number of linearly independent rows and columns in the matrix.
So if the rank of A is n, then the number of linearly independent columns and rows of A must be n. This is because if there are n linearly independent columns in the matrix, the number of linearly independent rows must also be n.
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suppose a recessive genetic disorder occurs in 9 percent of the population whst id the percentage of the populaation that is hetero
The percentage is 42% of the population is heterozygous for the recessive genetic disorder.
To determine the percentage of the population that is heterozygous for a recessive genetic disorder occurring in 9 percent of the population,
follow these steps:
1. Identify the frequency of the recessive allele (q) by taking the square root of the 9 percent occurrence (0.09). The square root of 0.09 is 0.3.
2. Calculate the frequency of the dominant allele (p) using the equation p = 1 - q. In this case, p = 1 - 0.3 = 0.7.
3. Determine the percentage of the population that is heterozygous using the equation 2pq. In this case, 2(0.7)(0.3) = 0.42 or 42%.
So, 42% of the population is heterozygous for the recessive genetic disorder.
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PLS HELPPPPPP
Work out the missing side x. Give your answers to 1 d.p. or better.
Therefore, the length of the perpendicular is 1 cm. Therefore, the length of the perpendicular is approximately 1.335 cm (rounded to three decimal places).
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle.
Here,
a. Given that the hypotenuse is 2 cm and the angle is 30 degrees, we can use trigonometry to find the length of the perpendicular. Let's call the length of the perpendicular x. Using the trigonometric ratio for sine (sin), we have:
sin(30°) = opposite/hypotenuse
sin(30°) = x/2
Multiplying both sides by 2:
2*sin(30°) = x
We know that sin(30°) is equal to 0.5, so we can substitute that in:
2*0.5 = x
x = 1
b. Given that the base is 3 cm and the angle is 24 degrees, we can use trigonometry to find the length of the perpendicular.
Let's call the length of the perpendicular x.
Using the trigonometric ratio for tangent (tan), we have:
tan(24°) = opposite/adjacent
tan(24°) = x/3
Multiplying both sides by 3:
3*tan(24°) = x
We may use a calculator to find the value of tan(24°), which is approximately 0.445:
3*0.445 = 1.335
c. cos 72°=x/9
0.3091*9=x
x=2.78 units
d. cos 23°=5.9/x
x=5.9/0.9205
x=6.409 units
e. sin 36°=3.6/x
x=3.6/0.5877
x=6.1255 units
f. cos 48°=4.3/x
x=4.3/0.6691
x=6.4226 units
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Write the equation of the parabola which has its vertex at (0, 5) and passes through the point (1, 0)
y = -5x² + 5 is the equation of the parabola which has its vertex at (0, 5) and passes through the point (1, 0)
We know that the vertex of the parabola is (0, 5), which means that the equation for the parabola has the form:
y = a(x - 0)² + 5
where 'a' is a constant that determines the shape of the parabola. Since the parabola passes through the point (1, 0), we can substitute these values into the equation and solve for 'a':
0 = a(1 - 0)² + 5
0 = a + 5
a = -5
Therefore, the equation of the parabola is: y = -5x² + 5
This equation represents a parabola that opens downwards (since the coefficient of x² is negative), has a vertex at (0, 5), and passes through the point (1, 0).
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Rotate the figure 180 degrees
The coordinates of the image after rotating the figure 180 degrees about the origin are T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Calculating the coordinates of the imageGiven that
T'(-4, 3). V'(-5, 5), W'(-2, 5). X(-1, 3)
Rotating a figure by 180 degrees is equivalent to flipping it over the horizontal and vertical axes simultaneously.
This means that the x-coordinate of each point will be negated, and the y-coordinate will be negated as well.
Therefore, to find the coordinates of the image of a point after rotating it by 180 degrees, you can use the following formula:
(x', y') = (-x, -y)
Using the above, the image is
T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Hence, the image is T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
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Complete question
Rotate the figure 180 degrees about the origin
T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
T'(3, 4). V'(5, 5), W'(5, 2), X '(3. 1) (Th
T'(-3, 4) V(-5. 5), W'(-5, 2). X'(-3, 1)
T'(-3, -4), V'(-5, -5). W(-5, -2), X '(-3, -1)
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Ms. Leon will have a total of $840 in her savings account by the end of 4 years.
To calculate the total amount that Ms. Leon will have in her account at the end of 4 years with simple interest, we can use the following formula:
A = P(1 + rt)
where:
A = the total amount in the account at the end of the time period
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
t = the time period (in years)
Putting in the given values, we get:
A = 750(1 + 0.03 × 4)
A = 750(1.12)
A = $840
Therefore, at the end of 4 years, Ms. Leon will have a total of $840 in her savings account.
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