Compute the orthogonal projection of v⃗ =[−7−9]
onto the line L
through [26]
and the origin
Answers
The orthogonal projection of \(\vec{V}\) =[−7−9] onto the line L through [26] and the origin is given by the vector [-69/10 -207/10].
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To find the orthogonal projection of a vector \(\vec{V}\) onto a line L, we need to follow these steps:
Find a vector \(\vec{n}\) that is orthogonal to the line L.
Find the projection of \(\vec{v}\) onto \(\vec{n}\) . This projection will be a scalar.
The orthogonal projection of \(\vec{v}\) onto L is the vector that is obtained by multiplying the scalar projection of \(\vec{v}\) onto \(\vec{n}\) by the unit vector in the direction of L.
Let's apply these steps to the problem at hand:
Step 1: Find a vector \(\vec{n}\) that is orthogonal to the line L.
The line L passes through [2 6] and the origin, so we can find the direction vector of the line by subtracting the two points:
\(\vec{d}\) = [2 6]−[0 0]=[2 6].
To find a vector that is orthogonal to \(\vec{d}\), we can take the cross product of \(\vec{d}\)with the vector [0 0 1]:
\(\vec{n}\) = \(\vec{d}\) × [0 0 1] = [−6 2 0].
Step 2: Find the projection of \(\vec{v}\)onto \(\vec{n}\) .
The projection of \(\vec{v}\) onto \(\vec{n}\) is given by the formula:
proj n v = ( \(\vec{v}\) · \(\vec{n}\) ) / || \(\vec{n}\) ||² * \(\vec{n}\)
where · denotes the dot product and || \(\vec{n}\) || is the magnitude of \(\vec{n}\) .
Substituting the values we have:
proj n v = ([-7 -9] · [-6 2 0]) / ||[-6 2 0]||² * [-6 2 0]
= (-54 + (-18)) / (36 + 4) × [-6 2 0]
= -72/40 × [-6 2 0]
= [-27 9 0]/5
Step 3: The orthogonal projection \(\vec{v}\) onto L is given by:
proj L v = (proj n v · \(\vec{d}\) / || \(\vec{d}\) ||²) × \(\vec{d}\) / || \(\vec{d}\) ||
where || \(\vec{d}\) || is the magnitude of \(\vec{d}\) .
Substituting the values we have:
proj L v = ([−27 9 0]/5 · [2 6]/(2² + 6²)) * [2 6]/(2² + 6²)
= -207/40 * [2 6]
= [-69/10 -207/10]
Therefore, the orthogonal projection of \(\vec{v}\) =[−7−9] onto the line L through [26] and the origin is given by the vector [-69/10 -207/10].
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Related Questions
What is the x-intercept of a line
Answers
Answer:
The x-intercept is the point where a line crosses the x-axis
Step-by-step explanation:
Igor, whose eye height is 4. 5 ft. , wishes to find the height of an oak tree out in front of his castle. He places a mirror on the ground between himself and the tree. He is now 5. 5 feet away from the center of the mirror and the mirrors is 70 feet from the tree. What is the height of the oak tree in front of Igor´s castle?
Answers
The height of the oak tree in front of Igor's castle is approximately 57.27 ft. To find the height of the oak tree, we can use the principle of similar triangles.
The height of the tree can be determined by comparing the ratio of the height of Igor to the distance between Igor and the mirror with the ratio of the height of the tree to the distance between the mirror and the tree.
Let's represent the height of the oak tree as 'h'. According to the problem, Igor's eye height is 4.5 ft, and he is 5.5 ft away from the center of the mirror. The mirror is placed 70 ft from the tree.
Using the similar triangles concept, we can set up the following proportion:
(height of Igor) / (distance between Igor and mirror) = (height of tree) / (distance between mirror and tree)
Plugging in the given values, we have:
4.5 ft / 5.5 ft = h / 70 ft
Solving this proportion, we find:
(4.5 ft * 70 ft) / 5.5 ft = h.
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At 6 a.m., a meteorologist records the temperature as −3.2°F . Seven hours later, the meteorologist records the temperature as 11.7°F.
Which expression represents the total temperature change, in degrees Fahrenheit, over the seven hours?
11.7+(−3.2)
−3.2+11.7
|11.7+(−3.2)|
|11.7−(−3.2)|
Answers
The correct expression in this case is |11.7−(−3.2)|.
Negative numbersGiven that at 6 am, a meteorologist records the temperature as −3.2°F, and seven hours later, the meteorologist records the temperature as 11.7°F, to determine which expression represents the total temperature change, in degrees Fahrenheit, over the seven hours, the following reasoning must be carried out:
A negative number is a value that is below 0, that is, the inverse of said negative number is required in positive values to equate to 0.So, -3.2 requires 3.2 to get to 0. If we add 11.7 to that, the total required values will be 14.9 (3.2 + 11.7).In turn, in mathematics, subtracting a negative number from a positive number implies adding that number (1 - (-1) = 2).Therefore, the correct expression in this case is |11.7−(−3.2)|.
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Write a olution that contain ax2=y and ha no olution when a=4 and one olution otherwie
Answers
The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.
We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.
According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by
x = (-b +/- √(b² - 4ac)) / (2a)
In this formula, if we add "ax² = y," we obtain
x = (-0 +/- √(0² - 4ay)) / (2a)
which simplifies to
x = √(-4ay) / (2a)
If a = 4, the equation becomes
x = √(-16y) / 8
The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.
The equation has a single solution provided by any other value of a.
x = √(-4ay) / (2a)
For example, if a = 3, the equation becomes
x = √(-12y) / 6
Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.
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please help factorise 7ab+a
Answers
Answer:
= a(7b + 1)
Step-by-step explanation:
7ab + a
a(7b + 1).
Find the distance between the following two points:
(4,-1) and (7,-3)
Answers
Answer:
\(d = \sqrt{13}\)
Step-by-step explanation:
Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Simply plug in the 2 coordinates into the distance formula to find distance d:
\(d = \sqrt{(7-4)^2+(-3-(-1))^2}\)
\(d = \sqrt{(3)^2+(-3+1)^2}\)
\(d = \sqrt{9+(-2)^2}\)
\(d = \sqrt{9+4}\)
\(d = \sqrt{13}\)
HELP YALLL
I’m not good at math
Answers
Answer:
7x^2−19x+10
Step-by-step explanation:
3 x 2 − 14 x + 16 + 4 x 2 − 5x − 6
A simple difference is also called a.an interaction effect. b.a marginal means difference. c.a factorial design. d.a main effect.
Answers
A simple difference is also called a marginal means difference. Option B
In experimental design and statistical analysis, a simple difference refers to the comparison of means between two groups or conditions. It represents the difference in average scores or values between the groups being compared. It is often used to assess the impact of an independent variable on a dependent variable by examining the variation in means between different levels of the independent variable.
The term "marginal means difference" emphasizes that the comparison is based on the average or marginal means of the groups being compared. It helps to distinguish it from other types of differences, such as interaction effects or main effects, which involve more complex comparisons or analyses in factorial designs.
Overall, a simple difference or marginal means difference is a straightforward way to evaluate the effect of an independent variable on a dependent variable by comparing the average values between different groups or conditions.
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Each of the 14 students in the art club needs 4One-fourth ounces of paint for a project. The art store sells paint only in 8-ounce bottles.
How many bottles of paint does the art club president need to buy for the project?
3
4
7
8
PLEASE AWNSER ASAP WILL GIVE BRAINLIEST
Answers
Answer:
4
Step-by-step explanation:
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve. The sum of two numbers is -5. Three times the first number equals 4 times the second number. Find the two numbers. -(20)/(7 )and -(15)/(7) -5 and 12 (20)/(7 ) and (15)/(7) -20 and -15
Answers
The two numbers are x = -23/4 and y = 18/1, which can be simplified to x = -5 3/4 and y = 18. The correct ans is option A.
The sum of two numbers is -5. Three times the first number equals 4 times the second number. We have to find the two numbers. Let's assume the first number to be x and the second number to be y, The sum of two numbers is -5.x + y = -5
(i)Three times the first number equals 4 times the second number3x = 4y
(ii)We can use either substitution or elimination method to find the value of x and y. Let's solve the equations by the elimination method,
Multiplying equation (i) by 4 and subtracting it from equation (ii) eliminates the variable x3x - 4y = 0 -20y = -15y = 3/4Substituting the value of y in equation (i),x + 3/4 = -5x = -(20/4 + 3/4)x = -23/4Therefore, the two numbers are x = -23/4 and y = 3/4.The correct option is (A) -(20)/(7) and -(15)/(7).
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Look over Chuck's work What is incorrect about the way Chuck interpreted his problem? What should have been a clue to Chuck that something was wrong?
Answers
The probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.
To find the probability that a random student will be taking both Algebra 2 and Chemistry, we need to use the concept of conditional probability.
Let's denote the event of taking Algebra 2 as A and the event of taking Chemistry as C. We are given that P(A) = 0.08 (8% probability of taking Algebra 2) and P(C|A) = 0.17 (17% probability of taking Chemistry given that the student is taking Algebra 2).
The probability of taking both Algebra 2 and Chemistry can be calculated using the formula for conditional probability:
P(A and C) = P(C|A) * P(A)
Substituting the given values:
P(A and C) = 0.17 * 0.08
P(A and C) = 0.0136
Therefore, the probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.
It is important to note that the probability of taking both Algebra 2 and Chemistry is determined by the intersection of the two events, which means students who are taking both courses. In this case, the probability is relatively low, as it depends on the individual probabilities of each course and the conditional probability given that a student is taking Algebra 2.
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Solve the following Linear Programming Problem by Graphical Method:
Max z = 15x1 + 20 xz x₁ + 4x₂ ≥ 12 x₁ + x₂ ≤ 6 s.t., and x₁, x₂ ≥ 0
Answers
The solution to the linear programming problem is:
Maximum value of z = 120
x₁ = 0, x₂ = 6
To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.
The constraints are:
x₁ + x₂ ≥ 12
x₁ + x₂ ≤ 6
x₁, x₂ ≥ 0
Let's plot these constraints on a graph:
The line x₁ + x₂ = 12:
Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.
The line x₁ + x₂ = 6:
Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.
The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):
Shade the region in the first quadrant of the graph.
The feasible region is the overlapping shaded region determined by all the constraints.
Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).
Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:
For (6, 0): z = 15(6) + 20(0) = 90
For (4, 2): z = 15(4) + 20(2) = 100
For (0, 6): z = 15(0) + 20(6) = 120
For (0, 0): z = 15(0) + 20(0) = 0
From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).
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49. Group Anagrams
Given an array of strings, group anagrams together.
For example, given: ["eat", "tea", "tan", "ate", "nat", "bat"], Return:
[
["ate", "eat","tea"],
["nat","tan"],
["bat"]
]
Note: All inputs will be in lower-case.
Answers
The problem requires grouping anagrams from a given array of strings. This can be achieved by using a hash table with sorted strings as keys and corresponding anagrams as values.
To group anagrams together, we can use a hash table where the keys are sorted strings and the values are lists of strings that are anagrams of the corresponding key. Here's a Python implementation:
```
def group_anagrams(strs):
# Create a hash table
anagrams = {}
# Iterate over each string in the input array
for s in strs:
# Sort the string and use it as a key in the hash table
sorted_s = ''.join(sorted(s))
if sorted_s in anagrams:
# If the key already exists, append the string to the corresponding value
anagrams[sorted_s].append(s)
else:
# If the key doesn't exist yet, create a new key-value pair
anagrams[sorted_s] = [s]
# Return the values of the hash table as a list
return list(anagrams.values())
```
For the input `["eat", "tea", "tan", "ate", "nat", "bat"]`, this function would return `[['eat', 'tea', 'ate'], ['tan', 'nat'], ['bat']]`. Note that the order of the groups and the order of the strings within each group may be different from the example output in the prompt, but the groups themselves are the same.
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we find t=2.73 with 5 degrees of freedom. what is the appropriate p-value.
Answers
The appropriate p-value for a t-value of 2.73 with 5 degrees of freedom is approximately 0.05. This indicates that there is a 5% chance of observing a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true.
In statistics, the p-value measures the strength of evidence against the null hypothesis. The null hypothesis states that there is no significant difference or effect in the population being studied. The p-value is calculated by determining the probability of obtaining a test statistic (in this case, the t-value) as extreme as or more extreme than the observed value, assuming the null hypothesis is true.
To determine the appropriate p-value for a t-value, we typically consult a t-distribution table or use statistical software. In this case, with 5 degrees of freedom and a t-value of 2.73, we look up the critical value or use software to find the corresponding p-value. The p-value associated with a t-value of 2.73 and 5 degrees of freedom is approximately 0.05.
The p-value of 0.05 indicates that there is a 5% chance of obtaining a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true. Generally, a p-value of 0.05 or lower is considered statistically significant, implying that the observed result is unlikely to have occurred by chance alone. If the p-value is below a predetermined significance level (often denoted as α, commonly set at 0.05), we reject the null hypothesis in favor of an alternative hypothesis. If the p-value is above the significance level, we fail to reject the null hypothesis.
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I need help on these long division questions
Answers
Answer:
2480, 2444, 30073, 4761, 117660
Step-by-step explanation:
what do you expect to observe when a pre-1982 penny is placed in hydrochloric acid? explain your reasoning.
Answers
When a pre-1982 penny is placed in hydrochloric acid, it will undergo a chemical reaction that will cause the penny to dissolve due to the presence of copper in it.
Hydrochloric acid is a strong, colorless, and highly corrosive solution that is made up of hydrogen chloride and water. It is a mineral acid that is often used in various chemical and industrial processes.
When a pre-1982 penny is placed in hydrochloric acid, it undergoes a chemical reaction with the hydrochloric acid. This reaction will cause the penny to dissolve due to the presence of copper in it.Copper reacts with hydrochloric acid to produce copper chloride (CuCl2) and hydrogen gas
(H2).2HCl(aq) + Cu(s) → CuCl2(aq) + H2(g)
This reaction will cause the penny to lose its copper content and dissolve in the hydrochloric acid, leaving only the zinc content behind. Therefore, if a pre-1982 penny is placed in hydrochloric acid, you would expect to observe the penny dissolving, which indicates that the penny is made of copper.
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: Factorize: 4x4 + y4
Answers
Answer:
4 ( x ) + ( y )
Step-by-step explanation:
.........
hmm yeah
Answer:
4*(4 + y)
Step-by-step explanation:
4*4 + 4y
16 + 4y
highest common factor is 4
4*(4+y)
yo is arjun du.mb
csCsscasxsCSc
Answers
Answer:
ok kapoor
Step-by-step explanation:
A laptop has 2 year warranty. The moon lifespan of the laptop is 3.8 years, with a standart deviation of 0.58 years.
If a store sells 5000 laptops. How many of these players will fail before warranty expires?
Please someone help me
Answers
We can use the normal distribution to estimate the number of laptops that will fail before the warranty expires. We can assume that the laptop lifespan follows a normal distribution with a mean of 3.8 years and a standard deviation of 0.58 years.
First, we need to calculate the z-score for the value x = 2 years:
z = (x - mu) / sigma = (2 - 3.8) / 0.58 = -3.10
where mu is the mean lifespan of the laptop and sigma is the standard deviation.
We can then use a standard normal distribution table or a calculator to find the probability that a normal random variable is less than or equal to the z-score of -3.10. This probability is approximately 0.001.
Therefore, the proportion of laptops that will fail before the warranty expires is approximately 0.001.
To find the number of laptops that will fail before the warranty expires out of 5000 laptops sold, we can multiply the proportion by the total number of laptops:
Number of laptops that will fail before the warranty expires = 0.001 * 5000 = 5
Therefore, we can expect that 5 laptops out of 5000 sold will fail before the warranty expires.
Mortgage companies usually charge interest semi-annually. What would be the effective rate of interest on a mortgage at 8.15 percent compounded semi-annually? O a. 8.23 percent O b. 8.32 percent O c. 8.46 percent O d. 8.40 percent If you want to save $1,000,000 for retirement with $200 monthly deposits (end-of-month) at 6 percent interest compounded monthly, how long will it take? O a. 54.4 years O b. 55.9 years O c. 52.8 years O d. 57.2 years
Answers
a) The effective rate of interest on a mortgage at 8.15 percent compounded semi-annually is 8.23 percent.
b) It will take approximately 54.4 years to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly.
a) To find the effective rate of interest, we use the formula: Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1.
For a mortgage at 8.15 percent compounded semi-annually, the nominal rate is 8.15 percent and the number of compounding periods is 2 per year.
Plugging these values into the formula, we get Effective Rate = (1 + (0.0815 / 2))^2 - 1 ≈ 0.0823, or 8.23 percent. Therefore, the effective rate of interest on the mortgage is 8.23 percent.
b) To determine how long it will take to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly, we can use the formula for the future value of an ordinary annuity: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of periods.
Rearranging the formula to solve for n, we have n = log(FV * r / P + 1) / log(1 + r). Plugging in the values $1,000,000 for FV, $200 for P, and 6 percent divided by 12 for r, we get n = log(1,000,000 * (0.06/12) / 200 + 1) / log(1 + (0.06/12)) ≈ 54.4 years.
Therefore, it will take approximately 54.4 years to save $1,000,000 for retirement under these conditions.
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Suppose a central angle is inscribed inside of a circle. The angle measures 36 degrees and the minor arc is 15 cm. Calculate the area of the circle and round your answer to two decimal places.
Answers
The area of the circle is 1790.49 centimeters square
To calculate the area of the circle, we shall need the radius of the circle
We can get the radius from the arc length
Mathematically, the length of an arc is;
\(\frac{\theta}{360\text{ }}\text{ }\times\text{ 2}\pi r\)From the question, the length is 15 cm while the central angle is 36
Thus we have;
\(\begin{gathered} 15\text{ = }\frac{36}{360}\text{ }\times\text{ 2}\pi r \\ \\ 150\text{ = 2}\pi r \\ \\ \pi r\text{ = 75} \\ \\ r\text{ = }\frac{75}{\pi} \end{gathered}\)Mathematically, the area of the circle will be;
\(\begin{gathered} A\text{ =}\pi\text{ }\times r^{2^{}} \\ \\ A\text{ = }\pi\text{ }\times\text{ }\frac{75}{\pi}\text{ }\times\text{ }\frac{75}{\pi} \\ \\ A\text{ = }\frac{75^2}{\pi}\text{ = 1,790.49 cm} \end{gathered}\)question 11(multiple choice worth 1 points) (01.02 mc) there are (42)3 ⋅ 40 horses at a stud farm. what is the total number of horses in the farm? 0 46 47 424
Answers
The total number of horses at the stud farm is (B) 4⁶.
To find the total number of horses at the stud farm, we can simplify the expression (4²)³ ⋅ 4⁰.
Let's break it down step by step:
(4²)³ = 4²ˣ³ = 4⁶
Since any number raised to the power of 0 is equal to 1, we have:
4⁰ = 1
Now, we can substitute these values back into the expression:
(4²)³ ⋅ 4⁰ = 4⁶ˣ¹ = 4⁶
Therefore, the total number of horses at the stud farm is 4⁶.
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3. for a population with a standard deviation of 8 and mean of 40, draw a bell shaped curve, marking location of the mean and the numbers that correspond with all the standard deviations
4. Using the graph and info from question 3, what is the z-score for X = 48? (you should be able to answer this question by looking at your graph, and do not have the need to use the equation to solve)
Answers
The z-score for X = 48, given a population with a standard deviation of 8 and a mean of 40, is 1.
A bell-shaped curve, also known as a normal distribution, is a symmetric curve with a single peak resembling a bell. It is commonly used to represent data that follows a normal distribution pattern.
In the provided graph, the location of the mean (μ) is marked on the bell-shaped curve. Additionally, the numbers corresponding to each standard deviation, which are -1, -2, +1, and +2, are also indicated. These values represent the distance from the mean in terms of standard deviations.
To calculate the z-score for X = 48, we can use the z-score formula: $z = \frac{X - \mu}{\sigma}$, where X is the raw score, μ is the population mean, and σ is the population standard deviation.
Applying the formula to the given values, we have:
$z = \frac{48 - 40}{8} = 1$
Therefore, the z-score for X = 48 is 1.
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(an intermediate algebra review exercise) use polynomial long division to perform the indicated division. write the polynomial in the form p(x)
Answers
Required polynomial in the form p(x) is: \(\[f(x)=\boxed{x^3-2x^2+4x-3+\frac{5}{x-1}}\]\)
We are given the following polynomial: \(\[f(x)=\frac{x^4-3x^3+2x^2-7x-2}{x-1}\]\)
To perform polynomial long division we divide the highest degree terms of the numerator and denominator. Then we write the quotient and remainder on top of each other and multiply the denominator of the original problem with the quotient to check if the answer is correct.
Let's start with the highest degree terms.
\(\[\begin{array}{r r c r r} &x^3 &-2x^2 &+4x &-3\\ \cline{2-5} x-1 & x^4 &-3x^3&+2x^2&-7x&-2 \\ & \underline{x^4} &-\underline{x^3} & & & \\ & & -2x^3 & +2x^2 & & \\ & & \underline{-2x^3} & +\underline{2x^2} & & \\ & & & 0x^2 & -7x & \\ & & & & -7x & +7 \\ & & & & \underline{-7x} & +\underline{7} \\ & & & & & \boxed{5} \\ \end{array}\]\)
Therefore, the required polynomial in the form p(x) is:\(\[f(x)=\boxed{x^3-2x^2+4x-3+\frac{5}{x-1}}\]\)
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In a game, Mateo earned 180 points for collecting stars. He earned 270 points for
lestroying ships. Plus, he earned 5 points for each prisoner he saved. If he finished
he game with 500 points, how many prisoners did he save?
A
50
B 10
C) 15
D 250
ht©Swun Math
6.EE.6
SWUN MATH
6.EE.7
Grade 6 Unit 5 Mid-Unit Assessment VB, Page 1
Answers
Answer:
B. 10
Step-by-step explanation:
We can solve this fast by adding the points from the stars and ships together, then subtracting that number from the total 500 points Mateo earnd.
So it would look like this:
180+270=450
500-450=50
So if Mateo scored 50 points from saving prisoners and save is worth 5 points each, we can do 50÷5=10.
WORTH 100 POINTS!!! BRAINLIEST TO ANYONE WHO CAN HELP ME UNDERSTAND THIS PROBLEM!
Hi, I need help with the following algebra 1 question regarding scatter plots. If someone can help me, that would be greatly appreciated! I've been to several tutors, and they couldn't help me with the problem.
Answers
Answer:
answer is b need help?
Step-by-step explanation:
The area of a sector is 30 m2 in a circle with radius 4 m. What is the arc length of the sector?
Answers
Answer:
15 m
Step-by-step explanation:
The area of the circle is
A =pi r^2
A = pi 4^2 = 16 pi
The area of the sector is 30
The fraction is
30/16 pi
Take this time 2pi which are the radians of a circle
30 /16 pi * 2 pi = 15/4
This is the number of radians the angle is
The arc length is s = r * theta where theta is in radians
s = r theta
= 4 * 15/4
= 15
Which expressions are equivalent to x+x+x+2
Choose 2 answers:
Answers
Answer: I don't know the options but from this situation it is 3x+2 or x=3/2
Step-by-step explanation:
You add all the x together and that's the first option second divide it so x us all by itself
What expression shows 0.5 ( x +3) written as a sum
Answers
The expression 0.5 (x + 3) written as a sum is 0.5x + 1.5
How to determine the expression written as a sum?From the question, we have the following parameters that can be used in our computation:
0.5 ( x +3)
Write the expression properly
So, we have the following representation
0.5 (x + 3)
Express the brackets as products
So, we have the following representation
0.5 (x + 3) = 0.5 * (x + 3)
Open the brackets using products i.e. distributive property
So, we have the following representation
0.5 (x + 3) = 0.5 * x + 0.5 * 3
Evaluate the products
So, we have the following representation
0.5 (x + 3) = 0.5x + 1.5
Hence, the expression as a sum is 0.5x + 1.5
Read more about expressions at
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Answer:
1. 0.5x + 1.5
2. are not
Help Please ASAP!!!!!!!!!!
Answers
Answer:8(B)
Step-by-step explanation: