Use the identity (x^2+y^2)^2=(x^2−y^2)^2+(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6.
Answers
Answer:
Step-by-step explanation:
(x^2+y^2)^2=(x^2)^2+2x^2y^2+(y^2)^2
Adding and substracting 2x^2y^2
We get
(x^2+y^2)^2=(x^2)^2+2x^2y^2+(y^2)^2 +2x^2y^2-2x^2y^2
And we know a^2-2ab+b^2=(a-b)^2
So we identify (x^2)^2 as a^2 ,(y^2)^2 as b^2 and -2x^2y^2 as - 2ab. So we can rewrite (x^2+y^2)^2=(x^2 - y^2)^2 + 2x^2y^2 + 2x^2y^2= (x^2 - y^2)^2+4x^2y^2= (x^2 - y^2)^2+2^2x^2y^2
Moreever we know (a·b·c)^2=a^2·b^2·c^2 than means 2^2x^2y^2=(2x·y)^2
And (x^2+y^2)^2=(x^2 - y^2)^2 + (2x·y)^2
Related Questions
132÷1716 show your work
Answers
We will investigate the process of division and express a fraction in its simplest form.
We are given the following operation of division to be performed:
\(132\text{ / 1716}\)We can express the above operation in a form of a fraction as follows:
\(\frac{132}{1716}\)Whenever we are looking at the simplification process we try to determine the divisibility of both numerator an denominator with a common integer.
We see that both numerator and denominator are divisible by integer ( 3 ). Hence, we can go ahead and write down the divisibility of both numerator and denominator by 3 in the fraction form:
\(\begin{gathered} \frac{132}{1716}=\frac{44}{572}\ldots\text{ Divisibility of ( 3 )} \\ \\ \frac{44}{572} \end{gathered}\)We see that both numerator and denominator are divisible by integer ( 11 ). Hence, we can go ahead and write down the divisibility of both numerator and denominator by 11 in the fraction form:
\(\begin{gathered} \frac{44}{572}\text{ = }\frac{4}{52}\ldots\text{ Divisibility of ( 11 )} \\ \\ \frac{4}{52} \end{gathered}\)Next we see that we can further perform the divisibility operation by dividing both numerator and denominator by ( 4 ) and express in fraction in its simplest form:
\(\begin{gathered} \frac{4}{52}\text{ = }\frac{1}{13}\ldots\text{ Divisibility of ( 4 ) } \\ \\ \frac{1}{13} \end{gathered}\)The above result is expressed in its most simplest form. This means the numerator and denominator can not be further divided or divisible by any common integer other than ( 1 ). Hence, we have arrived at the simplest answer to the division operation:
\(\frac{1}{13}\ldots Answer\)According to a recent survey. T3Yh of all tamilies in Canada participatod in a Hviloween party. 14 families are seiected at random. What is the probabity that wix tamilies participated in a Halloween paty? (Round the resut to five decimal places if needed)
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The probability that six families participated in a Halloween party is 0.16859
As per the given statement, "T3Yh of all families in Canada participated in a Halloween party."This implies that the probability of families participating in a Halloween party is 30%.
Now, if we select 14 families randomly, the probability of selecting 6 families from the selected 14 families is determined by the probability mass function as follows:
`P(x) = (14Cx) * 0.3^x * (1 - 0.3)^(14 - x)`
where P(x) represents the probability of selecting x families that participated in a Halloween party.
Here, x = 6
Thus, `P(6) = (14C6) * 0.3^6 * (1 - 0.3)^(14 - 6)``
P(6) = 0.16859`
Hence, the probability that six families participated in a Halloween party is 0.16859.
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The three sides of a triangle of lengths 4, 5, and 7. The triangle is obtuce
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Answer:
Let's check this!
Obtuse triangle formula:
c² < b² + a²
Next fill in the formula:
7² < 5² + 4²
Then simplify:
49 < 25 + 16
Then add:
49 < 41
^^49 is not greater than 41 so therefore the triangle is not obtuse.
When the hypotenuse is bigger than the legs of the triangle it is an acute triangle.
Acute triangle formula:
c² > b² + a²
7² > 5² + 4²
49 > 25 + 16
49 > 41 ✔
You're Welcome and Mark me Brainliest please.
The three sides of a triangle of lengths 4, 5, and 7 are not obtuse triangles.
What is the obtuse triangle?The triangle is an obtuse triangle if the sum of the squares of the smaller sides is less than the square of the largest side.
The three sides of a triangle of lengths 4, 5, and 7.
An obtuse triangle is a triangle in which one of the interior angles is greater than 90°.
The sides of a triangle are not an obtuse triangle as determined in the fooling step given below.
Obtuse triangle formula:
c² < b² + a²
7² < 5² + 4²
49 < 25 + 16
49 < 41
Here; 49 is not greater than 41 so therefore the triangle is not obtuse.
Hence, the three sides of a triangle of lengths 4, 5, and 7 are not obtuse triangles.
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Help me answer the following question.
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Answer:
160 m
Step-by-step explanation:
you can approach this question with the thinking of simple math. First, you have the value of -85 rose by 30 means +30 and descending 105 means -105.
So, the calculation you will get is -85+30-105=-160. The negative means going down as the direction.
Which expression is equivalent to 2^7 x 2^-5
ANSWER CHOICES:
1.) 1/2^-35
2.)1/2^-3
3.)2^-35
4.) 1/2^2
Answers
Using the product rule of exponents we will get:
2⁷*2⁻⁵= 2² = (1/2)⁻²
That is the correct option.
Which expression is equivalent to 2⁷*2⁻⁵?Remember the rule for product of powers:
xᵃ*xᵇ = x⁽ᵃ⁺ᵇ⁾
So here we can use that rule to rewrite our expression as:
2⁷*2⁻⁵ = 2⁽⁷⁻⁵⁾ = 2²
The options are written as (1/2) instead of 2 with the base, so can rewrite this as:
(1/2)⁻²
That is the correct option.
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Find the diameter of a cone that has a volume of 83.74 cubic inches and a height of 5 inches
Answers
Answer:
V = πr²(h/3)
Step-by-step explanation:
83.74 = πr²(5/3)
R = 4.00 in
Diamater = 2r = 2 x 4.00 = 8 inches
mariela took out a mortgage and purchased a house located in the v zone of an nfip participating community. what does that mean for mariela?
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Mariela's purchase of a house located in the V Zone of an NFIP participating community means that the house is located in a high amount of risk flood zone and that she is required to purchase flood insurance if she has a mortgage. This insurance will help to protect her investment in the event of a flood.
Mariela must purchase flood insurance if she has a mortgage on her house, which is located in a high amount of risk flood zone in an NFIP participating community. This insurance will help to protect her investment in the event of a flood.
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If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is: 2
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If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two
When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.
Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .
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a real number between √13 and √14
Answers
Answer:
3.7
Step-by-step explanation:
Consider the following sample data values. 7 4 6 12 8 15 1 9 13 a) Calculate the range. b) Calculate the sample variance. c) Calculate the sample standard deviation. a) The range is 14 b) The sample variance is (Round to two decimal places as needed.) c) The sample standard deviation is (Round to two decimal places as needed.)
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a) The range is 14.
b) The sample variance is 20.78.
c) The sample standard deviation is 4.56.
a) Range
The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:
Range = maximum value - minimum value
Range = 15 - 1
Range = 14
b) Sample variance
To calculate the sample variance, follow these steps:
1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:
n = 9
∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75
X = ∑x/n = 75/9 = 8.33
2. Subtract the sample mean from each data value, square the result, and add up all of the squares:
(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23
3. Divide the sum of squares by one less than the total number of values to get the sample variance:
s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78
Therefore, the sample variance is 20.78 (rounded to two decimal places).
c) Sample standard deviation
To calculate the sample standard deviation, take the square root of the sample variance:
s = √s² = √20.78 = 4.56
Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).
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Solve u^2= -25, where u is a real number.
Simplify your answer as much as possible.
If there is more than one colution
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the answer is ±5i :)
(-7)·(-7)·5·5·5·5 rewrite it with exponents please
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Consider two normal distributions, one with mean -2 and standard deviation 3.7, and the other with mean 6 and standard deviation 3.7 Answer true or falso to each statement and explain your answers. a. The two normal distributions have the same spread. b. The two normal distributions are centered at the same place a. Choose the correct answer below. O A False because the distributions have different standard deviations B. True because the distributions have the same mean OC. False because the distributions have different means OD. True because the distributions have the same standard deviation
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so we can say that statement b is also False.The mean of the first distribution is -2, while the mean of the second distribution is 6. As a result, the two normal distributions are not centered at the same place.
'
The statement "The two normal distributions have the same spread" is false, and the statement "The two normal distributions are centered at the same place" is false as well.Explanation:Normal Distribution: A normal distribution is a statistical distribution that is symmetric about its mean, showing that data near the mean is more frequent in occurrence than data far from the mean. To describe the distribution of data, it is frequently utilized, and it is frequently utilized in inferential statistics.A normal distribution is defined by two parameters: its mean (μ) and its standard deviation (σ). The mean (μ) is the center of the distribution, while the standard deviation (σ) indicates how spread out the data is from the mean of the distribution.The spread of a distribution is determined by its standard deviation (σ). The standard deviation is the measure of dispersion, which shows how much the data deviates from the mean. As a result, the standard deviation (σ) determines the spread of the normal distribution.Here are the given parameters of the two normal distributions:Distribution 1:Mean = -2Standard deviation = 3.7Distribution 2:Mean = 6Standard deviation = 3.7According to the parameters of the two normal distributions mentioned above, we may deduce that the two normal distributions have the same standard deviation. The spread of the distributions is measured by the standard deviation (σ), therefore we can say that statement a is False.However, the mean of the two normal distributions is not the same, so we can say that statement b is also False.The mean of the first distribution is -2, while the mean of the second distribution is 6. As a result, the two normal distributions are not centered at the same place.
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Zoey read a novel in 30 days she made it a habit to read 13 pages everyday for the first 20 days. if in the last 10 days she reads 6 pages everyday how many pages are in the book?
Answers
Explanation:
20 days times 13 pages= 260pages
10 days times 6 pages = 60pages
Total for the 30 days:
260+60= 320 pages total
Answer:
320 pages.
Step-by-step explanation:
We can simply multiply and add to find how many pages are in the book.
So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.
Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:
\(\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320\)
The quantities X and Y are proportional
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The quantities X and Y are proportional as y = rx then the constant of proportionality r is 1/9.
What is constant of proportionality?Firstly, there is proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called constant of proportionality.
WE have been given quantities X and Y are proportional
y = rx
Where r is constant of proportionality.
Then x = 45 and y = 5
Thus,
y = rx
5 = 45r
Now divide by 45 on both side;
r = 5/45
r = 1/9
Therefore, the constant of proportionality r is 1/9.
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Help with this plzzzzzzzzzzzzzz
Answers
Answer: \(4^0\)
Step-by-step explanation:
\(4^5*4^-^7/4^-^2\)
Rewriting this;
\(\frac{4^5*4^-^7}{4^-^2}\)
When you multiply by the same base, you add exponents.
\(\frac{4^5^+^(^-^7^)}{4^-^2}\)
\(\frac{4^5^-^7}{4^-^2}\)
\(\frac{4^-^2}{4^-^2}\)
When you divide by the same base, you subtract exponents.
\(4^-^2^-^(^-^2^)\)
\(4^-^2^+^2\\4^0\)
yoonie is a personnel manager in a large corporation. each month she must review 16 of the employees. the time that takes to do a review has a bell shaped distribution with a mean of four hours and a standard deviation of 1.2 hours. what is the probability that the average time of 16 reviews will take yoonie from 3.5 to 4.25 hours?
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The probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hours is 0.7492.
The random variable X is defined as the time it takes her to complete one review.
The random variable X follows a Normal distribution with parameters μ = 4 hours and σ = 1.2 hours.
A random sample of n = 16 reviews are selected as a set.
Compute the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hours as follows:
P(3.5 < X < 4.25) = P(3.5-4/1.2√16 < x- μ /σ/√n < 4.25-4/1.2/√16)
=P(-1.67 < Z < 0.83)
= P(Z < 0.83) - (P(Z < -1.67)
= 0.7967 - 0.0475
= 0.7492
Thus, the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hours is 0.7492.
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Given a mean and standard deviation of 3,500 and 2,000 cfs, respectively, find the 2-, 10-, and 100-year peak floods for a normal distribution.
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The 2-, 10-, and 100-year peak floods for a normal distribution are 5500 cfs.
Given a mean and standard deviation of 3,500 and 2,000 cfs, respectively, the 2-, 10-, and 100-year peak floods for a normal distribution can be found as follows:
Formula used in finding the peak flood is as follows:
Q_T= Q_m + K_T
σ
Where Q_T is the flow for a given period,
Q_m is the mean flow, K_T is the coefficient of skewness, and σ is the standard deviation of the flows.
For a normal distribution, K_T= frac{\text{duration of period in years}-1}{2}\times\frac{\text{duration of period in years}+1}{2}
Substitute the mean and standard deviation to the formula above:
When the period of interest is 2 years, the coefficient of skewness is calculated below:
[{{K}_{T}}=\frac{\text{(2-1)(2+1)}}{2}=1\]
Also, K_{T} is 1 for the 10-year and 100-year flood.
When these values are computed, we get the following values:
Q_{2}=3500+1(2000)=5500 \text{ cfs}
Q_{10}=3500+1(2000)=5500 \text{ cfs}
Q_{100}=3500+1(2000)=5500 \text{ cfs}
Therefore, the 2-, 10-, and 100-year peak floods for a normal distribution are 5500 cfs.
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Ha sry I know I am asking a lot from y’all but I really need help
Answers
Answer:
33333333333333333333333333333333333333333333333333333333333333333
Step-by-step explanation:
Answer:
the first one has positive quotient
two integers between -32
Answers
-2 and 1
Show that the characteristic equation for the complement output of a JK flip-flop is: Q(t+1) = JQ+KQ =
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The complement output of a JK flip-flop is given by the Boolean expression JQ + KQ is the same as the characteristic equation for the regular output Q(t+1).
The characteristic equation for the complement output of a JK flip-flop can use the following steps:
Start with the excitation table for a JK flip-flop:
J K Q(t) Q(t+1)
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
The expression for the complement output Q'(t+1) in terms of J, K, Q(t), and Q'(t):
Q'(t+1) = not(Q(t+1))
= not(JQ(t) + K'Q'(t)) // since Q(t+1) = JQ(t) + K'Q'(t)
= not(JQ(t)) × not(K'Q'(t)) // De Morgan's Law
= (not(J) + Q(t)) × KQ'(t) // since not(JQ)
= not(J) + not(Q)
Simplify the expression using Boolean algebra:
Q'(t+1) = (not(J) + Q(t)) × KQ'(t)
= not(J)KQ'(t) + Q(t)KQ'(t) // Distributive Law
= J'K'Q'(t) + JKQ'(t) // De Morgan's Law
= (J'K' + JK)Q'(t)
The characteristic equation for the complement output of a JK flip-flop is:
Q'(t+1) = J'K'Q'(t) + JKQ'(t)
= JQ + KQ
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The ability for nike to manufacture its own shoes and then build stores for distribution is an example of?
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The ability for Nike to manufacture its own shoes and then build stores for distribution is an example of Forward Integration.
What is forward integration ?
In order to lower manufacturing costs and increase efficiency, a sort of vertical integration known as "forward integration" moves up the supply chain.
An operational competency is what?
Functional competences are determined by the tasks and commitments employees make to a certain position. An average of three to five functional skills are ascribed to a given job, depending on the complexity and level of responsibility of the position as well as the seniority of the occupational role.Learn more about Forward Integration
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Três garçons trabalham em um restaurante. No final de um dia de trabalho, um deles recebeu R$
24,00 de gorjeta, o segundo recebeu R$ 57,00 e o terceiro recebeu R$ 39,00. Como eles sempre
dividem por igual toda a gorjeta, quantos reais cada um recebeu nesse dia?
Answers
Step-by-step explanation:
70 Reis espero ter ajudado
Two students are reading a novel. Ashley reads 10 pages per day. Carly reads 8 pages per day, but she starts early and is already on page 40.Part ADrag numbers to complete a system of equations to represent the situation, using d for days and p for pages. Numbers may be used once, more than once, or not at all.
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To represent the situation of Ashley and Carly reading a novel, a system of equations can be formed using variables for days (d) and pages (p). The equations are: Ashley's progress - 10d = p and Carly's progress - 8d = p - 40.
Let's denote the number of days as d and the number of pages read as p. For Ashley, she reads 10 pages per day, so her progress can be represented as 10d = p.
For Carly, she starts early and is already on page 40. This means her progress can be represented as 8d = p - 40. Since she starts on page 40, her progress will be p - 40.
Therefore, the system of equations that represents the situation is:
Ashley's progress: 10d = p
Carly's progress: 8d = p - 40
In these equations, the left side represents the progress of each student in terms of days (d), while the right side represents the progress in terms of pages (p) read.
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Jea need $140 to buy a bicycle. He ave $10 each week. He ha already aved $60. How many week from now can jea buy the bicycle
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If Jea has $60, he will need 80 more dollars to afford the bicycle. If he gets paid $10 a week, it will take him 8 weeks
CC.3 Solve a system of equations by graphing: word problems W9J or For her parents' anniversary party, Kira is considering using one of two venues. A hotel in Stamford will cost $200 for a reservation, plus $50 per person. A restaurant in the same city will cost $75 per person, in addition to $150 for the reservation. In order to make the best decision, Kira figures out how many attendees it would take to have the venues cost the same amount. How many attendees would that be? Write a system of equations, graph them, and type the solution.
Answers
(Y is the total cost and x is the number of people)
the restaurant is $100 plus $40 per person so the equation would be
y = 40x + 100
What we want to know is which x value would make the y values equal to each other. So you can just replace the "y" in one equation with the other equation:
25x + 250 = 40x + 100
and then solve...
1. subtract 100 from both sides
25x + 150 = 40x
2. subtract 25x from both sides
150 = 15 x
3. divide both sides by 15
10 = x
you can check by plugging 10 into the original equations
25(10) + 250
250 + 250 = 500
and
40(10) + 100
400 + 100 = 500
they both cost $500 when you invite 10 people
Determine whether the series converges or diverges. (n+4)! a) 4!n!4" b) 1 \n(n+1)(n+2) =
Answers
We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.
The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.
`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`
As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `
lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`
Since the limit of the ratio test is less than one, the given series converges.
The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).
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n the library of a small town, the mean cost of new books is the same as the median cost of new books. the distribution of book costs is: multiple choice question. negatively skewed symmetrically distributed positively skewed
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If the mean cost of new books is the same as the median cost of new books, then the distribution of book costs is symmetrically distributed.
This means that the data is evenly distributed around the mean and median, and there are an equal number of values on both sides of the central point. In a symmetric distribution, the mean and median are the same, and the data is evenly spread out around them.
A negatively skewed distribution would have a longer tail on the left side, indicating that the majority of the values are higher. A positively skewed distribution would have a longer tail on the right side, indicating that the majority of the values are lower.
A symmetric distribution, on the other hand, has no long tail on either side, and the majority of the values cluster around the central point. Therefore, the distribution of book costs is symmetrically distributed.
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Please help! 30 points!
Use the Law of Cosines to solve the problem.
A ship travels due west for 83 miles. It then travels in a northwest direction for 111 miles and ends up 165 miles from its original position. To the nearest tenth of a degree, how many degrees north of west did it turn when it changed direction? Show your work.
Answers
Answer: \(64.2^{\circ}\)
Step-by-step explanation:
According to the cosine rule
\(\cos C=\dfrac{a^2+b^2-c^2}{2ab}\)
Here, \(a=83, b=111, c=165,\ C=180^{\circ}-\theta\)
Putting values
\(\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}\)
So, the ship turns by \(64.2^{\circ}\) north of west
The ship turned an at angle of 64.2 degrees north of west
Represent the angle, the ship turned due north of west with theta.
From the figure, we have the following equation
\(\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}\)
So, we have:
\(\cos(A) = \frac{83^2 + 111^2 - 165^2}{2 * 83 *111}\)
Evaluate the expression on the right-hand side
\(\cos(A) = -0.4350\)
Take the arc cos of both sides
\(A = \cos^{-1}(0.4350)\)
\(A =115.8^o\)
The value of theta is then calculated as:
\(\theta = 180 -A\)
This gives
\(\theta = 180 -115.8^o\)
\(\theta = 64.2^o\)
Hence, the ship turned an at angle of 64.2 degrees north of west
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Determine the solutions of the equation |x – 3| = 11. 1. Rewrite for two solutions: (x – 3) = 11, –(x – 3) = 11 Solve for x in each equation. What are the solutions to the equation? x = –14, –8 x = –14, 8 x = –8, 14 x = 8, 14
Answers
Answer: C. x=-8,14
Step-by-step explanation:
C
Answer:
x = 14, –8Step-by-step explanation:
|x – 3| = 11
(x - 3) = 11 - (x - 3) = 11
x - 3 = 11 - x + 3 = 11
x = 11 + 3 -x = 11 - 3
x = 14 -x = 8
x = -8