Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.
What is EQUATIONS?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
Equations come in two varieties: identities and conditional equations.
According to our question-
Given line: 2x+5y−7=0
the mid - point of the line segment joining point (2,7) and (−4,1) is
( 2(2−4 )2(7+1))=(−1,4)
the equation of the line will be
y−y 1=m(x−x 1)y−4=( 5−2 )(x+1)
5y−20=−2x−2
2x+5y=18
Hence, Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.
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What would be the net annual cost of the following checking accounts? a. Monthly fee, $2.50: processing fee, 20 cents per check; checks written, an average of 18 a month.
On solving the provided question, we can say that net annual cost of the given account is 18
What is an equation?equation: a statement stating the equality of two expressions having variable- and/or number-filled expressions. Since equations are essentially questions, finding a way to answer them has spurred the development of mathematics.
Net annual cost is that monthly fee X 12 + fee per check X number of checks per month X 12
[tex]= ($3.75 X 12) + ($0.25 X22 X 12)\\ = $111[/tex]
Net annual cost is service charges - Interest earnings
[tex]= ($15 X 3) - (0.06 X $600 X 9 / 12)= $18[/tex]
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Prove Statement 5.38: Let T be the relation on Z defined by (m,n) ∈T iff m−n is divisible by 3 . Prove T is an equivalence relation.
If n is devisible by 3 then n^2 is devisible by 3 it easy.
n=3k so n^2=9k so 9 is devisible by 3.
In the other way, if n^2 is devisible by 3we have n^2=3k wher k is integer number which has to be devisible by 3. If k is not devisible by 3, then n=/sqrt3*r , r^2=k. So n is not integer, contradiction.
This proof show us that iff doesnt work.
If n is devisile by 4 then n^2 is also devisible by 4. But if we have that n^2 is devisibke by 4 then n hasn’t be devisible by 4. Example: n^2=36 is dev by 4 but n=6 is not dev by4.
Its allow because /sqrt 4 is 2.
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what are the first six terms for a₁ = -9, d=8?
a₁ = -9
a₂ = -9 + (2 - 1) * 8 = -9 + 8 = -1
a₃ = -9 + (3 - 1) * 8 = -9 + 16 = 7
a₄ = -9 + (4 - 1) * 8 = -9 + 24 = 15
a₅ = -9 + (5 - 1) * 8 = -9 + 32 = 23
a₆ = -9 + (6 - 1) * 8 = -9 + 40 = 31
1.
(03.03 MC)
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 5(1.07)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 9.19 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 1 to m = 9, and what does it represent? (4 points)
The answers are A) Reasonable domain to plot the growth function = [0, 9] B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm and C) average rate of change of the function f(m) from m
is (3.84/8)
What is function?A function is defined as a relation between a set of inputs having one output each.
Given that, A marine biologist is studying the growth of a particular species of fish when the marine biologist concluded her study, the length of the fish was approximately 9.19 cm
A) For m = 0
f(0) = 5(1.07)⁰ = 5 cm
The length of the fish was approximately 9.19 cm.
m = 9
Domain = [0, 9]
Reasonable domain to plot the growth function = [0, 9]
B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm
C) average rate of change of the function f(m) from m = 1 to m = 9
For m = 1
f(1) = 5(1.07) = 5.35 cm
For m = 9
f(9) = 5(1.07)⁹ = 9.19 cm
Change in 9 - 1 = 8 months = 9.19 - 5.35 = 3.84 cm
average rate of change of the function f(m) from m = 1 to m = 9,
= (3.84/8)
= 0.48 cm per month
Hence, The answers are A) Reasonable domain to plot the growth function = [0, 9] B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm and C) average rate of change of the function f(m) from m is (3.84/8)
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TRUE/FLASE. It's easier to come up with the correctness proof of the divide and conquer algorithm compared to the greedy algorithm.
It's easier to come up with the correctness proof of the divide and conquer algorithm compared to the greedy algorithm is False statement.
It is not easier to come up with a correctness proof of the divide and conquer algorithm compared to the greedy algorithm. The correctness proof of a divide and conquer algorithm is more difficult than a greedy algorithm since it involves breaking down an algorithm into multiple sub-problems and then proving the correctness of the algorithm with respect to each sub-problem. On the other hand, the correctness proof of a greedy algorithm is relatively simple and involves determining if a given solution is optimal. Additionally, the correctness proof of a divide and conquer algorithm requires more complex mathematical analysis such as induction, recurrence relations, or complexity analysis. This makes it more difficult to come up with the correctness proof of the divide and conquer algorithm than the greedy algorithm.
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A spherical balloon is inflated so that its volume is increasing at the rate of 3 cubic feet per minute. How fast is the radius of the balloon increasing when the radius is 2 feet?
The rate at which the spherical balloon's radius is increasing is
3/16π ft/min when the volume is increasing at the rate of 3 ft³/min.
Given, a spherical balloon is inflated so that its volume is increasing at the rate of 3 cubic feet per minute.
we have to find that how fast is the radius of the balloon increasing when the radius is 2 feet.
as, we know the volume of the balloon be,
V = 4/3πr³
now we have to find the rate of change of radius,
On differentiating both the sides with respect to time, we get
V' = 4/3π(3r²)dr/dt
V' = 4πr²dr/dt
as, the rate of change of volume of the balloon be, 3 ft³/min
V' = 3
3 = 4πr²dr/dt
dr/dt = 3/4πr²
Now, on putting r = 2, we get
dr/dt = 3/4π(2)²
dr/dt = 3/16π
so, the radius of the balloon increase at the rate of 3/16π.
Hence, the radius of the balloon increase at the rate of 3/16π.
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Show that Sin3xCos3x is the same as Sin 6x
The solution to the trigonometric equation is sin( 6x ) = 2sin(3x)cos(3x)
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the equation be represented as A
Now , the value of A is
A = sin (6x)
From the trigonometric relations ,
The value of sin( 2x ) = 2sin(x)cos(x)
Now , when x is replaced by 6x
Substituting the values in the equation , we get
sin ( 6x ) = 2 sin ( 6x/2 ) cos ( 6x/2 )
On simplifying the equation , we get
sin ( 6x ) = 2 sin ( 3x ) cos ( 3x )
So , the value of the trigonometric relation is
sin(6x) = 2sin(3x)cos(3x)
Hence , the equation is sin(6x) = 2sin(3x)cos(3x)
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What do you understand by homework and work?
We can say that duties are obligations that one has, while work is an activity that is carried out and that depends on a profession.
Analysis of the concepts: duties and workThe concepts homework and work are related because they are often linked in many contexts. Regarding these terms, we have to:
Duties come being different obligations that one has, for example, a duty can be to clean our room.Work has been an activity that has a dependency on a profession and where payment is received.¡Hope this helped!
The pet shop has 6,157 dog treats. They packed the treats into bags with 7 pieces in each bag. Any treats that did not fit into a bag of 7 were given to Groomer to use to reward animals getting bathed. How many bags of treats did they fill? How many treats were given to the groomer?
They filled bags that total 879 and the treats that did not fit are 4
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given here, total treats = 6157, and group them in bags with 7 each
now, we can write 6157 = 879×7+4
thus, on dividing 6157 by 7 we get the remainder as 4 and the quotient as 879
Hence, the bags of treats they filled is 879, and 4 treats were given to the groomer
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A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to Minitab with the following results: Analysis of Variance Source Factor df Ss MS F 3 28.17 9.39 5.37 0.133 15 26.26 1.75 18 54.43 Total What is the decision rule? (Round your answer to 2 decimal places.) eject H0 if F> At the 0.01 level of significance, is there a difference in the mean number of months before a raise was granted among the four CPA firms? Do not reject O Reject
In this one, We reject the null hypothesis and accept the alternative hypothesis. The z score of -0.07 is in the rejection area
What is the process of doing the hypothesis test?
In math, the ANOVA output is given in tabular format with headers like source, that consists of error sources and these error sources can be unexplained or explained ones. Then the evaluation of these helps to account for the F-statistic is accounted for two terms, known as degrees of freedom which can found against the factor and the error value.
Here we have given that senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary.
And we need to find the difference in the mean number of months before a raise was granted among the four CPA firms
While we looking into given question, we have the sample data as,
=> 3, 28.17, 9.39, 5.37, 0.133, 15, 26.26, 1.75, 18, 54.43
By using the sample data, we have identified the value of the following
Standard Deviation, σ: 15.860418305013
Count, N: 10
Sum, Σx: 161.503
Mean, μ: 16.1503
Variance, σ2: 251.55286881
Now, the hypothesis testing result is written as,
The critical value (cutoff point) is 1.833. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since -0.07 is less than 1.833, we reject the null hypothesis. We accept the alternative hypothesis.
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Fill in a value for angle A and B where A and B is restricted 0 < A < 2n and 0 < B < 21 and A ≠ 13pi/11
Find The related acute angle i
and the quadrant of the principle angle given below.
csc 13pi/11 = cscA = secB
Answer:
Since csc 13pi/11 is undefined, it is impossible to fill in a value for angle A and B that satisfies the given restrictions. Additionally, it is impossible to find the related acute angle or the quadrant of the principle angle without a defined value for angle A and B.
Step-by-step explanation:
A system of two linear equations in two variables x and y is rewritten as the following augmented matrix:
[ 6 6 | -18 ]
[ -4 -2 | 2 ]
Use the Gauss-Jordan Elimination Method to solve for x and y.
x = _________
y = _________
Answer:
x = -10
y = 1
Step-by-step explanation:
To use the Gauss-Jordan Elimination Method to solve for x and y, we need to put the augmented matrix in row-echelon form. The first step is to eliminate the x-coefficient in the second row by adding 4 times the first row to the second row. This gives us the following matrix:
[ 6 6 | -18 ]
[ 0 -10 | -10 ]
Next, we need to eliminate the y-coefficient in the second row. We can do this by adding 5 times the second row to the first row, which gives us the following matrix:
[ 1 -10 | -10 ]
[ 0 -10 | -10 ]
Now, the matrix is already in row-echelon form, so we can read the solution directly from the matrix. The solution is x = -10 and y = 1. Therefore, the solutions to the system of linear equations are:
x = -10
y = 1
Note that there may be other solutions to the system of equations, depending on the specific equations that the matrix represents. The Gauss-Jordan Elimination Method will always give us one possible solution, but there may be other solutions as well.
The median of a discrete random variable is the smallest value for which the cumulative probability equals or exceeds 0.5.
The median can be calculated by ordering the possible values of the random variable from smallest to largest and then finding the value for which the cumulative probability equals or exceeds 0.5.
Firstly, list out all the possible values of the random variable.Secondly, order the values from smallest to largest. Thirdly, calculate the cumulative probability for each value. Fourthly, find the value for which the cumulative probability equals or exceeds 0.5 Finally, this value is the median of the discrete random variable.The median of a discrete random variable can be found by arranging the possible values of the random variable from smallest to largest, and then calculating the cumulative probability for each value. Once the cumulative probability reaches or exceeds 0.5, the corresponding value of the random variable is the median.
Let the random variable X have values {1, 2, 3, 4, 5}.
Ordered from smallest to largest, X has the values {1, 2, 3, 4, 5}.
The cumulative probability for each value of X is calculated as follows:
P(X ≤ 1) = 0
P(X ≤ 2) = 0.2
P(X ≤ 3) = 0.6
P(X ≤ 4) = 0.9
P(X ≤ 5) = 1
The median of X is 3, since it is the smallest value for which the cumulative probability equals or exceeds 0.5.
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In addition to limit theorems that deal with sums, there are limit theorems that deal withextreme values such as maxima or minima. Here is an example. Let U1, . . . , Un be independent random variables distributed uniformly on [0, 1], and let U(n) be their maximum. Findthe cdf of U(n) and a standardized U(n), and show that the standardized variable tends to alimiting value.
cdf of U(n) = Var(Sn)=1
what is standard function?A standard function is one that is defined on an interval of R and is acquired by a finite series of standard operations beginning with any three fundamental functions.
What are the fundamental duties?f(x) = x is the identity function. f(x) = exp, an exponential function (x)
given
let U1, . . . ],
U(n) be their maximum
so cdf of U(n) =does not have a limiting distribution.
Why will a pub and up be equal to zero when Y is less than and one win in is less than the other.
There isn't a standard distribution function that can match this limit everywhere.
hence cdf of U(n) = Var(Sn)=1
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30 POINTS HELP PLEASE
A boat is tied to a dock using two ropes.
what is the length of rope A
Step-by-step explanation:
Using Trigonometry
Cos ø = Adj ÷ Hyp
ø = 35°
Hyp side=15ft
A is the Adj side
Adj = Cos ø × Hyp
Adj = Cos 35° × 15
Adj = 0.8192 × 15 = 12.29
Adj = 12ft approximately
Answer: 12.3
Step-by-step explanation: Based off the quiz I did it said 12.3
A recipe calls for 3 cups of milk to accommodate 8 people. However,
you are preparing food for 20 people. What are the number of
of milk you will need for 20 people?
cups
7.5
Step-by-step explanation:
3:8=×:20 so x=20×3÷8=7.5
Show hint
T
S
.
4 = 64
Review of logarithms (logs)
Solve the equation and show all your work. In
addition, label the base, argument, and exponent.
Enter your answer below.
Pro Tip: Use a calculator to evaluate your logarithm.
Unfortunately the in-screen Desmos calculator can only
evaluate logs with base 10.
Submit
M
Answer:
x=3.
Step-by-step explanation:
[tex]way1) \ 4^x=64;\\x=log_4[64];\\x=3;\\\\way2) \ 4^x=64; \ < = > \ 4^x=4^3; \ < = > \ x=3.[/tex]
Could I have some help with the question below:
A ship is sailing due north. At a certain point the bearing of a lighthouse is N39.8˚E and the distance is 11.5. After a while, the captain notices that the bearing of the lighthouse is now S43.5˚E. How far did the ship travel between the two observations of the lighthouse.
The distance ship travelled 7.4 units between the two observations of the lighthouse.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, a ship is sailing due north. At a certain point the bearing of a lighthouse is N39.8˚E and the distance is 11.5.
P is the ship, R is the light house and Q is the bearing.
PR is the distance between the ship and the light house, PR = 11.5
∠P = 43.5°, ∠Q =39.8°
Thus, ∠R = 180° -∠P-∠Q
= 180°-43.5°-39.8°
= 96.7°
By using sin rule we get
PR/sinR =PQ/sinQ
11.5/sin96.7° =PQ/sin39.8°
11.5/0.9931 =PQ/0.6401
PQ/0.6401=11.55
PQ=7.4 units
Therefore, the distance ship travelled 7.4 units between the two observations of the lighthouse.
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The graph of a function is shown below. What is true about the function on the interval -5< x < -2?
[x|-5<x<-2]
Write the inequality in set-builder notation as the set of all real numbers x such that x is greater than -5 and x is less than - 2
Which of the following is an example of a function with a domain (-∞,+) and a range (-∞,+∞)?
Answer:
Signum function
Step-by-step explanation:
Hope this helps uuuu
What the answer to Energy and mass are related by the formula e=mc2
Answer:
e = mc^2
m = e/c^2
Step-by-step explanation:
An organization needs to reach out to a specific target audience, and has decided that it wants to use social media advertising to do so. It wants to buy specific keywords to accurately target the audience who would want to see these ads. The aim is to get a high effective exposure rate and engagement rate without invading consumer privacy. Which of the following advertising revenue models would best suit the organizations' needs? a. Bidding for ad words b. Pay-per-click c. I-Traffic Index d. Pop-under ads e. Bidding for ad space
The advertising revenue models would best suit the organization needs is option (A) Bidding for ad words
Here the organization wants to buy specific keywords to accurately target the audience who would want to see these ads
The aim of the organization is to get a high effective exposure rate and engagement rate without invading consumer privacy
Bidding for ad words states that the amount of money you are willing to spend for a single click on a given keyword.
Here they will get high effective exposure rate and engagement rate without invading consumer privacy
Therefore, the best advertising revenue model is option (A) Bidding for ad words
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Enter the ordered pair for the vertices for Rx-axis(QRST).
I need help with this please help me
Answer:
Hello! Rx-axis means that they want the coordinates after they are reflected over the x-axis.
The original coordinates are as follows:
Q (1, 5)
R (3, -1)
S (0, 0)
T (-2, 3)
Reflecting a coordinate (x, y) over the x-axis results in the new coordinates being (x, -y).
Performing this translation over the 4 given points, we obtain:
Q' (1, -5)
R' (3, 1)
S' (0, 0)
T' (-2, -3)
hope this helps :)
nonlinear solver methods can find different final values that depend on the starting values of your decision variables.
Nonlinear solver method used in the slope of the objective function as the input values changes. It determines that it reached at the optimum solution when the initial value is equals to zero.
In the nonlinear solver method, the initial values used within one of the nonlinear equation. By default the initial value chosen for all variables is zero or the lower bound. zero is in many cases is a bad initial value for a nonlinear variable. For example, if the variable appears in a product term since the initial derivative becomes zero, and it appears as if the function does not depend on the variable. When the equation is simple, the value of x can be determined analytically. This is used in the case when x can be written explicitly by applying mathematical operations or when a known formula such as the formula for solving a quadratic equation can be used to determine the exact value of x.
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A restaurant customer left $0.70 as a tip. The tax was 5% and the tip was 10% of the cost including tax. a. What piece of information is not needed to compute the bill after tax and tip? b. What was the total bill? a. What information is not needed to solve this problem? OA. The customer left a 10% tip. B. The tax was 5%. OC. The customer left $0.70 as a tip. O D. All of this information is needed to solve the problem. b. The total bill is...
Answer:
1-a. The tax was 5%
b. The total bill is 7$
Step-by-step explanation:
a. We need the 10% tip of bill after tip and tax to get bill.
b. 0.7 = 10%
x = 100% (x is total bill)
x = (0.7*1)/0.1 (divide percentage by 100)
= 0.7/0.1
= 7
Help guys my computer is abt to die it’s due today
Answer:
24
Step-by-step explanation:
Perimeter are the side measures added up.
15 x 0.4 = 6
ΔLMN = 60
60 x 0.4 = 24
Using synthetic division, what is the quotient for (3 x³+5 x²-18 x+39) /(x+4) ?
If the remainder is non-zero, express the remainder term as a fraction using the divisor as the denominator.
Provide your answer below:
quotient___
The quotient is [tex]3x^2 - 7x + 10[/tex].
"Information available from the question"
In the question:
Using synthetic division,
What is the quotient for (3 x³+5 x²-18 x+39) /(x+4)
Now, According to the question:
Let's know:
Synthetic Method: The synthetic division method is a special method of dividing polynomials. This method is a special case of dividing a polynomial expression by a linear factor, in which the leading coefficient should be equal to 1.
(3 x³+5 x²-18 x+39) /(x+4)
[tex]3x^2 - 7x + 10[/tex]
x + 4 [tex]\sqrt{3 x^3+5 x^2-18 x+39}[/tex]
[tex]3x^3 + 12x^2[/tex]
- -
___________________
[tex]-7x^2[/tex] - 18x
[tex]-7x^2[/tex] - 28x
+ +
_____________________
10x + 39
10x + 40
- -
________________________
-1
The quotient is [tex]3x^2 - 7x + 10[/tex].
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27. evaluate yyye xex 21y21z2 dv, where e is the portion of the unit ball x 2 1 y 2 1 z 2 < 1 that lies in the first octant.
Therefore ,E = xex2 + y2 + z2 dv, where e is the portion of the unit ball x2 + y2 + z2 ≤ 1 that lies in the first octant whose value is π/8
What is Volume?The volume of an inhabited three-dimensional space is calculated. It is commonly measured in a variety of imperial, US-standard, and SI-derived units. Volume and the notion of length are interconnected.
Here,
Given :
portion of unit ball = [tex]xe^{x^{2}+y^{2} +z^{2} }[/tex]
and x2 + y2 + z2 ≤ 1
So, using this
We find the triple integral or the volume integral of the expression = [tex]xe^{x^{2}+y^{2} +z^{2} }[/tex]
=> [tex]\int\int\int_{e} xe^{x^{2}+y^{2} +z^{2} }[/tex]dV
=> [tex]\int\limits^{\alpha = \pi /2}_{\alpha =0}\int\limits^{\beta = \pi /2}_{\beta =0} \int\limits^{p= 1}_{p=0}[/tex] pcos[tex]\beta[/tex]sin[tex]\alpha[/tex][tex]e^{{p}^{2}[/tex] [tex]p^{2}[/tex]sin[tex]\alpha[/tex] dpd[tex]\alpha[/tex]d[tex]\beta[/tex]
=>[tex]\int\limits^{\alpha = \pi /2}_{\alpha =0}[/tex][tex]sin^{2}\alpha[/tex] d[tex]\alpha[/tex] + [tex]\int\limits^{\beta = \pi /2}_{\beta =0}[/tex]cos[tex]\beta[/tex] d[tex]\beta[/tex] + [tex]\int\limits^{p= 1}_{p=0} p^{2} e^{p^{2}}[/tex] dp
=>π/8
Therefore ,E xex2 + y2 + z2 dv, where e is the portion of the unit ball x2 + y2 + z2 ≤ 1 that lies in the first octant whose value is π/8
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A group of tourists are on a 3-day long trip. They hike 1/8 of the trail on the first day. On the second day, they hike 4/7 of the remaining distance. On the third day, they hike 1/3 of the remaining distance, plus the final 8 km. How many kilometers long is the trail?
Answer: 32 km (I believe)
Explanation: So, on the first day the tourists walked x/8 km.
Then the remaining distance after the first day is (x- x/8) = 7x/8 km.
On the second day, the tourists walked 4/7 of the REMAINING path, so now we multiply 4/7 by 7x/8 to get x/2 km.
So, the remaining path to travel after 2nd day is (7x/8-x/2) = 3x/8
Remember, on the third day they walked 1/3 of the remaining trail and the last 8 km.
So now, we do (3x/8 - 3x/8 x 1/3) = 8
Now, x/4 =8 ; to find x, we do 8 x 4 to get 32
So, our answer is 32
I hoped this helped!
2x + y ≤8
Please graph this cot me in need it asap