The probability that Bela and Jenn pick the same part is; 0.006944
What is the probability of selection?In maps, it is pertinent to note that parallels are the lines that run from east to west and never intersect with each other while meridians run from north to south and intersect at the north and south poles.
Now, since bella's globe has 12 parallels and 12 great meridians, then it means that the total number of parts in this globe will be 12 * 12 = 144 parts.
Thus, probability that they both pick the same part is;
P(same part picked) = (12/144) * (12/144)
= 0.006944
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NO LINKS!!
Find a logarithmic equation that relates y and x. (Round any numeric values to 3 decimal places.)
ln(y)=
x y
1 1.250
2 1.051
3 0.950
4 0.884
5 0.836
6 0.799
Answer:
[tex]\ln (y) = -0.250 \ln (x)+0.223[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12}x & y\\\cline{1-2} \vphantom{\dfrac12} 1 & 1.250\\\cline{1-2} \vphantom{\dfrac12} 2 & 1.051\\\cline{1-2} \vphantom{\dfrac12} 3& 0.950\\\cline{1-2} \vphantom{\dfrac12} 4& 0.884\\\cline{1-2} \vphantom{\dfrac12} 5& 0.836\\\cline{1-2} \vphantom{\dfrac12} 6& 0.799\\\cline{1-2} \end{array}[/tex]
To convert y = axⁿ to linear form, take natural logs of both sides and rearrange:
[tex]\begin{aligned}y=ax^n \implies \ln y &= \ln ax^n\\\implies \ln y &= \ln a + \ln x^n\\\implies \ln y &= \ln a + n \ln x\\\implies \ln y &=n \ln x+ \ln a\end{aligned}[/tex]
This is in the straight-line form y = mx + c.
Substitute the first values of x and y from the table into the natural log formula and solve for ln(a):
[tex]\implies \ln 1.250= n \ln 1+\ln a[/tex]
[tex]\implies \ln 1.250= n (0)+\ln a[/tex]
[tex]\implies \ln a = \ln 1.250[/tex]
[tex]\implies \ln a = 0.223\; \sf (3 \; d.p.)[/tex]
Substitute the found value of ln(a) and the last values of x and y from the table into the natural log formula and solve for n:
[tex]\implies \ln 0.799= n \ln 6+\ln 1.250[/tex]
[tex]\implies n \ln 6=\ln 0.799-\ln 1.250[/tex]
[tex]\implies n =\dfrac{\ln 0.799-\ln 1.250}{\ln 6}[/tex]
[tex]\implies n =-0.250\;\sf (3 \; d.p.)[/tex]
Substitute the found values of n and ln(a) into the formula to create an equation for ln(y):
[tex]\boxed{\ln (y) = -0.250 \ln (x)+0.223}[/tex]
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At a meeting for math enthusiasts, two entrance fees are charged. Anyone who knows the code word “algemath” only pays 2 euros. Those who are unlucky and do not know the code word pay three euros more. You know that 7338 people were present and that the cashier received 17487 euros. How many people knew the password?
Number of People who knows the Code are 6401
What is Linear Equation in Two Variable?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Let, Number of People who kows the Code be x
Number of Peoplee who do not know the Code be y
According to the Question:
x + y = 7338 ----------(i)
2x + 5y = 17487 ----------(ii)
Multiplying Equation (i) by 2
2x + 2y = 14676 ---------(iii)
Substracting Equation (iii) from Equation (ii)
3y = 2811
y = 937
This means x = 6401
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Marcus saved money to buy camping equipment.
He used 58 of his savings to buy a tent.
He used 14 of his savings to buy a sleeping bag.
How much of his savings does Marcus have left?
Answer:
1/8 savings left
Step-by-step explanation:
add 5/8+1/4 which is 7/8 8/8-7/8= 1/8
Answer:
Marcus has 1/8 of savings left----------------------------
Marcus used:
5/8 + 1/4 = 5/8 + 2/8 = (5 + 2)/8 = 7/8 of savingsRemaining part of savings:
1 - 7/8 = 8/8 - 7/8 = (8 - 7)/8 = 1/8Point A is located at (5, 6). Find the coordinates of the image A' after the
point is reflected across the x-axis.
(5,-6)
(-5,6)
(-5, -6)
(5,6)
Answer:
Step-by-step explanation:
Point A = (5, 6) is reflected across the x axis which is y =0.
When the point is reflected across the x axis, the x coordinate
remains positive, but the y coordinate becomes negative.
The 6 becomes negative (-6).
So the coordinates of A' are (5, -6) which is the first answer.
Find the value of x.
Answer:
x=142
Step-by-step explanation:
47+95=x
x=142
the two angles equal x
a quiz consists of 6 multiple-choice questions with 4 possible responses to each one. in how many different ways can the quiz be answered? (see example 7.)
His chances of correctly predicting an answer are 1/4.
He has a 3/4 chance of getting an answer incorrectly.
Binomial probability is defined.A random variable is distributed binomially with parameters n, p more precisely if
It is the number of successes over n separate* trials, each of which has a chance of success of p.
What distinguishes possibility from probability?Technically, the answer to whether an occurrence is possible is always "yes" or "no," or 1 or 0. Probability is the measure of how probable an event is to occur given the circumstances, assuming that it is feasible.
For instance, the likelihood of the number 5 appearing when we roll the dice is "Yes" (or 1), but the likelihood of the number 8 appearing is "No" (or 0).
Case 1: Guessing exactly 3 correct:
Choosing exactly 3 to get correct = Choosing exactly
3 to get wrong = 6C3 = (6*5*4)/(3*2*1) = 20 ways.
Guess the wrong answer for the first wrong one 3 ways.
Guess the wrong answer for the second wrong one 3 ways.
Guess the wrong answer for the third wrong one 3 ways.
That's 20*3*3*3 = 540 ways
Case 2: Guessing exactly 4 correct:
Choosing exactly 4 to get correct = Choosing exactly
2 to get wrong = 6C2 = (6*5)/(2*1) = 15 ways.
Guess the wrong answer for the first wrong one 3 ways.
Guess the wrong answer for the second wrong one 3 ways.
That's 15*3*3 = 135 ways
Case 3: Guessing exactly 5 correct:
Choosing exactly 5 to get correct = Choosing exactly
1 wrong = 6C1 = 6 ways.
Guess the wrong answer for the wrong one 3 ways.
That's 6*3 = 18 ways
Case 4: Guessing all 6 correct
There is only 1 way to guess them all correct
Total number of ways to pass: 540+135+18+1 = 694 ways to pass
Total number of ways to answer:
(4 ways to answer question 1) times
(4 ways to answer question 2) times
(4 ways to answer question 3) times
(4 ways to answer question 4) times
(4 ways to answer question 5) times
(4 ways to answer question 6) equals 4*4*4*4*4*4 = 46 = 4096
Probability of passing = 694/4096 = 347/2048 = 0.1694335938
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10. The study of the relationships among thermal energy, heat, and work is called dynamics.
True or false
Answer:
False.
Step-by-step explanation:
False. The study of the relationships among thermal energy, heat, and work is called thermodynamics, not dynamics. Dynamics is a branch of mechanics that deals with the motion of objects and the forces that cause that motion. Thermodynamics, on the other hand, is the study of the relationships between heat, work, and other forms of energy, and how these relationships can be used to understand the behavior of systems. It is a branch of physics that is concerned with the study of heat and its effects on matter.
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 60 child bikes and 6 adult bikes in a week? a No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 b No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 c Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 d Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
The correct solution to the given inequalities is;
a No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
How to solve Inequality word Problems?Let the number of child bikes be denoted as c.
Let the number of adult bikes be denoted as a.
For the building time of bikes, the inequality equation would be;
4c + 6a ≤ 120
For the testing time of bikes, the inequality equation would be;
4c + 4a ≤ 100
Checking the equations, for given 60 child bikes and 6 adult bikes in the week.
For the building of bikes,
( 4 × 60) + ( 6 × 6) ≤ 120
240 + 36 ≤ 120
276 ≥ 120 (Inequality not satisfied)
For the testing of bikes,
( 4 × 60 ) + ( 4 × 6 ) ≤ 100
240 + 24 ≤ 100
264 ≥ 100 (Inequality not satisfied)
Hence, the correct option is A.
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II. Given that cos A = 0.42 and sin B = 0.73, evaluate
i. sin (A – B)
ii. cos (A – B)
iii. tan (A + B)
The trigonometric identities values are;
i. sin (A – B) = -0.15
ii. cos (A – B) = 0.5368
iii. tan (A + B) = -3.536
How to solve trigonometric Identity?
We are given;
cos A = 0.42
sin B = 0.73
Since cos A = 0.42 , then sin A = 0.58
Since sin B = 0.73, then cos B = 0.27
i) sin (A – B)
By trigonometric identities, we know that;
sin (A – B) = sinA cos B - cosA sinB
Thus;
sin (A – B) = (0.58 * 0.27) - (0.42 * 0.73)
sin (A – B) = -0.15
ii) cos (A – B)
By trigonometric identities, we know that;
cos (A – B) = cosA cosB + sinA sinB
cos (A – B) = (0.42 * 0.27) + (0.58 * 0.73)
cos (A – B) = 0.5368
iii) tan (A + B)
By trigonometric identities, we know that;
(tan A + tan B)/(1 - tanAtanB)
tan A = sinA/cosA = 0.58/0.42 = 1.389
tan B = sinB/cosB = 0.73/0.58 = 1.259
Thus;
tan (A + B) = (1.389 + 1.259)/(1 - (1.389 * 1.259))
tan (A + B) = -3.536
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find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 2-i, /3 f(x) =
The polynomial function is the product of three terms, each of which is a linear factor with a zero of 2-i, 1/3 respectively.
A polynomial function is a mathematical expression composed of constants and variables, and is used to model a wide variety of phenomena. The polynomial function can be expressed in terms of the factors of its zeros. In this case, the polynomial function of lowest degree with rational coefficients that has the given numbers 2-i, 1/3 as some of its zeros is (x+2)(x-i)(x-1/3). This polynomial can be expressed as the product of three terms, each of which is a linear factor with a zero of 2-i, 1/3 respectively. This means that when x is equal to 2-i or 1/3, the value of the polynomial function is zero. The linear factors are multiplied together to give the polynomial, and this is the simplest form of a polynomial that satisfies the given criteria. The polynomial can then be used to model a variety of phenomena by taking into account the different factors and their effects on the system.
f(x) = (x+2)(x-i)(x-1/3)
f(2-i) = (2-i+2)(2-i-i)(2-i-1/3)
f(2-i) = 0
f(1/3) = (1/3+2)(1/3-i)(1/3-1/3)
f(1/3) = 0
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find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 2-i, /3 f(x) = (x+2)(x-i)(x-1/3)
two players are to be selected out of five named a, b , c, d, e. What is the probability that a and b or and c and d or b and d are
The probability that (a and b) or (c and d) or (b and d) are selected is 3/25
How to determine the probability that a and b or and c and d or b and d are selected?
To find the probability that a and b or c and d or b and d are selected, we can use the formula for probability:
Probability = Number of favorable outcomes / Total number of outcomes
Probability of a = 1/5
Probability of b = 1/5
Probability of a and b = 1/5 × 1/5 = 1/25
Probability of c = 1/5
Probability of d = 1/5
Probability of c and d = 1/5 × 1/5 = 1/25
Probability of b = 1/5
Probability of d = 1/5
Probability of b and d = 1/5 × 1/5 = 1/25
The probability that (a and b) or (c and d) or (b and d) are selected will be:
Probability of (a and b) or (c and d) or (b and d) = P(a and b) + P(c and d + P(b and d)
Probability of (a and b) or (c and d) or (b and d) = 1/25 + 1/25 + 1/25 = 3/25
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The following expressions (-9a3b2 + 13ab5) and (-10ab5 + 12a3b2) represents the length and width of the pizza box respectfully. Find the perimeter of the pizza box. Express the perimeter of the pizza box in the order of descending exponents of a. Please use the palette below to input your answer.
The perimeter of the box has been obtained as 6a^3b^2 + 6ab^5.
What is the perimeter of the box?We know that a box has the shape of a rectangle thus we would have to apply the formula for the area of a rectangle in this case and we would have;
P = 2(l + b)
P = perimeter
l =length
b = breadth
Then we have;
2[(-9a^3b^2 + 13ab^5) + (-10ab^5 + 12a^3b^2)]
Collect the like terms
2[(-9a^3b^2) + 12a^3b^2 + 13ab^5 +(-10ab^5)]
2[3a^3b^2 + 3 ab^5]
6a^3b^2 + 6ab^5
In order of descending exponents of a, the perimeter is 6a^3b^2 + 6ab^5.
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ILL GIVE BRAINLIEST PLS I REALLY NEED question is in the photo attached
The domain is (0, 2), staying the same will be (2, 4), decreasing the fastest will be (6, 10), and the height of the water balloon at 16 seconds the will be 0.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Part A:
We can see from the graphic, increase from 0 to 2 sec.
The domain is equal to (0, 2), where the height of the water balloon increases.
Part B:
The water balloon is the same from 2 to 4 sec.
The field state that the height of the water balloon remains the same (2, 4).
Part C:
Now Height decreasing fasted at 4 to 6 sec.
Since the slope is steepest downward from 4 to 6 sec as comfort to 6 to 10 sec.
The domain is the height of the water balloon decreases rapidly (6, 10).
Part D:
The balloon's height is almost near the ground as resistance will play its role. But will almost touch the ground.
Therefore height of the water balloon will be 0 in 16 seconds.
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Which of these expressions is equivalent to log(16 • 14)?
CA. 16 log (14)
OB. log(16)+ log(14)
C. log(16) log(14)
D. log(16)-log(14)
The equivalent expression of log(16 × 14) is log 16 + log 14.
How to find equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Equivalent expressions are expressions that have similar value or worth but do not look the same.
Therefore, the equivalent expression of log(16 × 14) can be found as follows:
using logarithm law,
The log of a product is the sum of the logs.
logₐ xy = logₐ x + logₐ y
Therefore,
log(16 × 14) = log 16 + log 14
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If x + 3y^(1/3) = y what is dy/dx at the point (2,8)
The dy/dx at point (2,8) is 4/3
How to find dy/dx at a point?From the information illustrated, x + 3y^(1/3) = y and point (2,8)
Find the derivative of this equation with respect to x and solve for dy/dx:
x + 3y^(1/3) = y
1 + [3 × 1/3 × y^(-2/3)]dy/dx = dy/dx
1 + [y^(-2/3)]dy/dx = dy/dx
dy/dx - [y^(-2/3)]dy/dx = 1
dy/dx [1- y^(-2/3)] = 1
dy/dx = 1/ [1 - y^(-2/3)]
At point (2,8), x = 2 and y = 8.
Substitute into dy/dx:
dy/dx = 1/ [1 - y^(-2/3)]
dy/dx = 1/ [1 - 8^(-2/3)]
dy/dx = 1/ [1 - 1/4)]
dy/dx = 4/3
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Leia is setting up 417 toy cars. Each car needs 3 batteries to drive.
How many batteries does Leia need for her cars?
Answer:
Leia needs 3 * 417 = <<3*417=1251>>1251 batteries for her cars.
Step-by-step explanation:
To find out how many batteries Leia needs for her cars, we need to multiply the number of toy cars by the number of batteries needed for each car. Since each car needs 3 batteries and Leia has 417 toy cars, the total number of batteries she needs is 3 * 417 = 1251.
Find the term t of each continuously compounded account below rounded to the nearest tenth of a year. In the chart, B is the
ending balance, P is the principal, and r is the interest rate expressed as a percent.
Therefore , the term t of each continuously compounded account is 23.1 years.
What is compound interest ?Compound interest is the practice of adding interest to the principal of a loan or deposit. It happens when interest is reinvested, added to the lent capital rather than paid out, or when the borrower is forced to pay it, resulting in interest being generated on the principal amount plus any accumulated interest the following period. Compound interest is frequently used in economics and finance.
Here,
A) To determine the account's annual growth rate, we must calculate the impact of continual compounding. Similar to the nominal rate (APR) and actual yield (APY) on a bank's interest-bearing account, the yield will be marginally greater due to compounding and indicate actual growth rather than growth rate. Note e is a very lengthy number that can be entered with as many digits as your calculator allows if you don't have a financial calculator handy. e = 2.71828183
A = P[tex]e^{rt}[/tex] But for this, we only need to calculate growth or ert; we don't need to worry about P. When rounding in accordance with the instructions, we set t = 1 for a year and have er (or 2.71828183.03), which equals 1.03045, therefore the account increases by 3.05% annually.
B) 3000 = 1500[tex]e^{0.3t}[/tex] [Divide both sides by 1500]
To isolate t, we must determine the natural logarithm of each side (e's natural logarithm is 1 and 2's natural logarithm is 0.693). 2 = e.03t
0,693 =.03t [Subtract both sides from .03]
23.1 = t
C) Using the formula from section A, first determine the original investment's worth after ten years. A = P A = 1500e.03*10 A = 1500e.3 A = 2,024.79
Next, use the yearly compounding formula to get the value of the second investment.
A = P(1+r)t
A = 1200(1+.045)10
A = 1,863.56
After ten years, the initial investment would be worth more.
Therefore , the term t of each continuously compounded account is 23.1 years.
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segments in circles maze
Answer:
x = 6
Step-by-step explanation:
You want to know the value of x given a tangent to a circle from an external point has length x, while a secant from that point has length x-2 to the first intersection with the circle, and an additional 5 to the second intersection.
Secant/Tangent relationThe product of the segments of the secant to the two points of intersection with the circle is equal to the square of the tangent segment.
(x -2)(x -2 +5) = (x)² . . . . . use given values
x² +x -6 = x² . . . . . . simplify
x -6 = 0 . . . . . . subtract x²
x = 6 . . . . . . add 6
__
Additional comment
There are rules for two secants, for a tangent and secant (as here), and for two chords internal to the circle. These can be easier to remember if you generalize them to a single rule: the product of the distance from the common point to the first circle intersection and the distance to the second circle intersection is the same for each segment.
For a tangent, the two circle intersections are the same point, hence the distance is squared. For chords, the two circle intersections are at the ends of the chords, and the common point is where the chords cross.
Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, how much baking soda did they use?
Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, he used 19/4 baking soda.
Define subtraction.To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.
Given,
Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment.
Converting mixed fraction to improper function
1 3/4 = 7/4
If his students performed the experiment 6 1/2 times,
Converting mixed fraction to improper function
6 1/2 = 13/2
Subtracting,
7/4 - 13/2
7/4 - 26/4
19/4
Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, he used 19/4 baking soda.
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Graph the solution set to this inequality.
-2(x + 6) > -4x
Answer:
x > 6. graph this on the number line.
Step-by-step explanation:
-2x-12 > -4x
-12 > -2x
12 < 2x
6 < x
Answer:
x > 6
Step-by-step explanation:
Write an expression for the height, h, of a cylinder with a volume of 547 cubic inches
in terms of its radius, r.
The expression for the height (h) in terms of radius r is h = 547/(∏r²).
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
Given that the volume of the cylinder is 547 cubic inches.
The volume of a cylinder is V = ∏r²h
Where r is the radius of the cylinder.
h is the height of the cylinder.
Putting V = 547, r = r and h = h in V = ∏r²h
547 = ∏r²h
∏r²h = 547
Divide both sides by ∏r²:
h = 547/∏r².
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Carla divided 28 bracelets equally among 4 friends. Then, she gave Megan 3 more bracelets. Which equation shows how many bracelets, b, Megan has now?
The required number of bracelets that in the given question are 10.
What is equation?In math, the meaning of a equation is a numerical explanation that shows that two numerical articulations are equivalent. For example, 3x + 5 = 14 is a condition, where 3x + 5 and 14 are two articulations isolated by an 'equivalent' sign.
According to question:Carla divided 28 bracelets equally among 4 friends.
Number of bracelets each friends has = 28/4 = 7 bracelets
Then Carla gave 3 more bracelets to Magan.
So, Total bracelets Magan has = 7 + 3 = 10 bracelets
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Marquis sold gift-wrapping paper for a school fundraiser. He sold at least 15 rolls of paper. Write an inequality to represnet the amount of money, d, Marquis earned for the fund-raiser
The inequality to represent the amount of money, Marquis earned for the fund-raiser is d ≥ 15p
What is the inequality to represent the information?
Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the cost of each paper be p.
Since Marquis sold gift-wrapping paper for a school fundraiser and he sold at least 15 rolls of paper.
An inequality to represent the amount of money, Marquis earned for the fund-raiser is:
d ≥ (15 × p)
d ≥ 15p
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Pa help po please... Mas mahalaga pa to sa baon ko jk
Solve 3x^4-16x³+21²+4x-78=0
Answer:
Step-by-step explanation:
Solve for x:
3 x^4 - 16 x^3 + 4 x + 363 = 0
Eliminate the cubic term by substituting y = x - 4/3:
363 + 4 (y + 4/3) - 16 (y + 4/3)^3 + 3 (y + 4/3)^4 = 0
Expand out terms of the left-hand side:
3 y^4 - 32 y^2 - (476 y)/9 + 3059/9 = 0
Divide both sides by 3:
y^4 - (32 y^2)/3 - (476 y)/27 + 3059/27 = 0
Add 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27 to both sides:
y^4 + 2/3 sqrt(3059/3) y^2 + 3059/27 = 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27
y^4 + 2/3 sqrt(3059/3) y^2 + 3059/27 = (y^2 + sqrt(3059/3)/3)^2:
(y^2 + sqrt(3059/3)/3)^2 = 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27
Add 2 (y^2 + sqrt(3059/3)/3) λ + λ^2 to both sides:
(y^2 + sqrt(3059/3)/3)^2 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2
(y^2 + sqrt(3059/3)/3)^2 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (y^2 + sqrt(3059/3)/3 + λ)^2:
(y^2 + sqrt(3059/3)/3 + λ)^2 = (476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2
(476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (2 λ + 32/3 + (2 sqrt(3059/3))/3) y^2 + (476 y)/27 + 2/3 sqrt(3059/3) λ + λ^2:
(y^2 + sqrt(3059/3)/3 + λ)^2 = y^2 (2 λ + 32/3 + (2 sqrt(3059/3))/3) + (476 y)/27 + 2/3 sqrt(3059/3) λ + λ^2
Complete the square on the right-hand side:
(y^2 + sqrt(3059/3)/3 + λ)^2 = (y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)))^2 + (4 (2 λ + 32/3 + (2 sqrt(3059/3))/3) (λ^2 + 2/3 sqrt(3059/3) λ) - 226576/729)/(4 (2 λ + 32/3 + (2 sqrt(3059/3))/3))
To express the right-hand side as a square, find a value of λ such that the last term is 0.
This means 4 (2 λ + 32/3 + (2 sqrt(3059/3))/3) (λ^2 + 2/3 sqrt(3059/3) λ) - 226576/729 = 8/729 (729 λ^3 + 243 sqrt(9177) λ^2 + 3888 λ^2 + 864 sqrt(9177) λ + 165186 λ - 28322) = 0.
Thus the root λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3)) allows the right-hand side to be expressed as a square.
(This value will be substituted later):
(y^2 + sqrt(3059/3)/3 + λ)^2 = (y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)))^2
Take the square root of both sides:
y^2 + sqrt(3059/3)/3 + λ = y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)) or y^2 + sqrt(3059/3)/3 + λ = -y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) - 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3))
Solve using the quadratic formula:
y = 1/6 (sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) + sqrt(2) sqrt(48 - sqrt(9177) - 9 λ + 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) or y = 1/6 (sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) - sqrt(2) sqrt(48 - sqrt(9177) - 9 λ + 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) or y = 1/6 (sqrt(2) sqrt(48 - sqrt(9177) - 9 λ - 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177))) - sqrt(2) sqrt(9 λ + 48 + sqrt(9177))) or y = 1/6 (-sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) - sqrt(2) sqrt(48 - sqrt(9177) - 9 λ - 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) where λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3))
Substitute λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3)) and approximate:
y = -2.83639 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Substitute back for y = x - 4/3:
x - 4/3 = -2.83639 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Add 4/3 to both sides:
x = -1.50306 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Substitute back for y = x - 4/3:
x = -1.50306 - 2.06535 i or x - 4/3 = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Add 4/3 to both sides:
x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Substitute back for y = x - 4/3:
x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x - 4/3 = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Add 4/3 to both sides:
x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or y = 2.83639 + 1.07606 i
Substitute back for y = x - 4/3:
x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or x - 4/3 = 2.83639 + 1.07606 i
Add 4/3 to both sides:
Answer: x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or x = 4.16972 + 1.07606 i
A new crew of painters takes two times as long to paint a small apartment as an experienced crew. Together, both
crews can paint the apartment in
6 hours. How many hours does it take the experienced crgy
paint the
apartment?
It takes
hours for the experienced crew to paint the apartment.
The solution is
Answer: Hence, the time taken by the experienced crew would be 9 hours.
Step-by-step explanation:
A pipeline has to be laid along the boundry of the garden.What do we need to know to find the total length of the pipe needed
Answer:
Step-by-step explanation:
To find the total length of the pipe needed to lay a pipeline along the boundary of a garden, you will need to know the following:
The shape and size of the garden: The total length of the pipe needed will depend on the shape and size of the garden. For example, if the garden is rectangular, you will need to measure the length and width of the garden to calculate the total length of the pipe needed. If the garden has a more complex shape, you will need to measure the lengths of all the straight sections of the boundary and add them together to find the total length.
The type of pipe being used: The total length of the pipe needed will also depend on the type of pipe being used. Different types of pipes come in different lengths and may require different quantities of fittings and connectors.
The route of the pipeline: The total length of the pipe needed will also depend on the route that the pipeline takes. If the pipeline has to go around obstacles or make sharp turns, it may require more pipe than if it follows a straight path.
The desired width of the pipeline: The total length of the pipe needed will also depend on the desired width of the pipeline. If the pipeline needs to be wider to accommodate multiple pipes or cables, it will require more pipe than if it is only a single pipe.
Any other specific requirements: There may be other specific requirements that will affect the total length of the pipe needed. For example, if the pipeline needs to be buried, you will need to account for the depth of the trench in your calculations.
Select all the expressions that are equivalent to 8-12-(6+4).
(Select all that apply.)
8-(6+4)-12
(6+4)-8-12
8-12-6-4
8-6-12+4
Answer:
8-(6+4)-12
8-12-6-4
Step-by-step explanation:
8-(6+4)-12 and 8-12-6-4 are equivalent expressions because they both compute to -6. This is because in both expressions, the 6+4 is calculated first, yielding 10. Then, the 8 is subtracted from 10, yielding -2. Finally, the 12 is subtracted from -2, yielding -6.
6+4)-8-12 is not an equivalent expression because it does not compute to -6. In this expression, the 6+4 is calculated first, yielding 10. Then, the 8 is subtracted from 10, yielding 2. Finally, the 12 is subtracted from 2, yielding -10.
8-6-12+4 is not an equivalent expression because it does not compute to -6. In this expression, the 8 is subtracted from 6, yielding -2. Then, the 12 is subtracted from -2, yielding -14. Finally, 4 is added to -14, yielding -10.
a right triangle has a leg that measures 1. the other leg measures 2. calculate the length of the hypotenuse. round the answer to the nearest hundredth
The length of the hypotenuse is √5 with sides of 1 cm and 2 cm.
Define hypotenuse.A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilise specific terminology. The side opposite the right angle is always the hypotenuse of a right triangle. Stretching under is what the Greek word hypoteinousa signifies. In mathematics, the term "hypotenuse" is used to describe the side of a right triangle that is opposite the right angle. The hypotenuse extends below the right angle if the right angle is positioned at the top of the triangle.
Given
Lengths = 1 cm and 2 cm
For length of the hypotenuse,
c = √a² + b²
c = √1² + 2²
c = √ 1 + 4
c = √5
The length of the hypotenuse is √5 with sides of 1 cm and 2 cm.
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In order to add
3/4 and 7/10
you need to find equivalent fractions that have the same denominators. What is a common denominator?
Thus ,after adding 3/4 and 7/10 we get 29/20 where 20 is common denominator
Describe the common denominator.The smallest common multiple among the denominators of a group of fractions is known as the lowest common denominator (least common denominator) in mathematics. Fraction comparison, addition, and subtraction are made easier.
Here,
In order to add 3/4 and 7/10
we have to find LCM of 4 and 10
which comes out to be = 20
Thus,
addding => 15+`14 /20
=>29/20
Thus ,after adding 3/4 and 7/10 we get 29/20 where 20 is common denominator
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