Answer:
Step-by-step explanation:
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:
NO LINKS!! Write the first 5 terms of the geometric sequence
a1 = 2, r = -1/4
a1=
a2=
a3=
a4=
a5=
Step-by-step explanation:
since it is geometric sequence we will use the formula
[tex]tn = {a \times r}^{n - 1} [/tex]
a = 2
[tex]r = - \frac{1}{4} [/tex]
The first term
T1(a) = 2
The second Term
[tex]t2 = {a \times r}^{2 - 1} = {a \times r}^{1} [/tex]
[tex]t2 = {2 \times - \frac{1}{4} }^{1} = - \frac{1}{2} [/tex]
The third term
[tex]t3 = {a \times r}^{3 - 1} = {a \times r}^{2} [/tex]
[tex]t3 = {2 \times - \frac{1}{4} }^{2} = 2 \times - \frac{1}{16} = \frac{1}{8} [/tex]
The fourth term
[tex]t4 = {a \times r}^{4 - 1} = {a \times r}^{3} [/tex]
[tex]t4 = {2 \times - \frac{1}{4} }^{3} = 2 \times - \frac{1}{64} = - \frac{1}{32} [/tex]
The fifth term
[tex]t5 = {a \times r}^{5 - 1} = {a \times r}^{4} [/tex]
[tex]t5 = {2 \times - \frac{1}{4} }^{4} = 2 \times - \frac{1}{256} = - \frac{1}{128} [/tex]
i hope all these helped
Answer:
[tex]2,\; -\dfrac{1}{2},\; \dfrac{1}{8},\; -\dfrac{1}{32},\; \dfrac{1}{128}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
[tex]a=2[/tex][tex]r=-\dfrac{1}{4}[/tex]Substitute the given values of a and r into the formula to create an equation for the nth term:
[tex]a_n=2\left(-\dfrac{1}{4}\right)^{n-1}[/tex]
To find the first 5 terms of the geometric sequence, substitute n = 1 through 5 into the equation.
[tex]\begin{aligned}\implies a_1 & =2\left(-\dfrac{1}{4}\right)^{1-1}\\& =2\left(-\dfrac{1}{4}\right)^{0}\\& =2\left(1\right)\\&=2\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_2 & =2\left(-\dfrac{1}{4}\right)^{2-1}\\& =2\left(-\dfrac{1}{4}\right)^{1}\\& =2\left(-\dfrac{1}{4}\right)\\&=-\dfrac{1}{2}\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_3 & =2\left(-\dfrac{1}{4}\right)^{3-1}\\& =2\left(-\dfrac{1}{4}\right)^{2}\\& =2\left(\dfrac{1}{16}\right)\\&=\dfrac{1}{8}\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_4 & =2\left(-\dfrac{1}{4}\right)^{4-1}\\& =2\left(-\dfrac{1}{4}\right)^{3}\\& =2\left(-\dfrac{1}{64}\right)\\& =-\dfrac{1}{32}\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_5 & =2\left(-\dfrac{1}{4}\right)^{5-1}\\& =2\left(-\dfrac{1}{4}\right)^{4}\\& =2\left(\dfrac{1}{256}\right)\\& =\dfrac{1}{128}\end{aligned}[/tex]
Therefore, the first 5 terms of the given geometric sequence are:
[tex]2,\; -\dfrac{1}{2},\; \dfrac{1}{8},\; -\dfrac{1}{32},\; \dfrac{1}{128}[/tex]
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 = 1/8what is the ratio in the series 4, 6, 9...
The ratio in the series is 1.5.
Step-by-step explanation:The ratio consists on making the division of a value from a series, divided by its previous value. In this case you have 2 options for finding the ratio, and you will get the same answer:
6/4= 1.5
9/6= 1.5
Hence, the ratio in the series is 1.5.
In the Orthogonal Decomposition Theorem, each term in formula (2) for Å· is itself an orthogonal projection of y onto a subspace of W.
True/False
The statement that in the Orthogonal Decomposition Theorem, each term in formula (2) for Å, is itself an orthogonal projection of y onto a subspace of W is true .
What is Orthogonal Decomposition Theorem?The orthogonal decomposition of the vector of is the sum of the vectors of the subspaces of and the vectors of the orthogonal complements of . The orthogonal decomposition theorem states that each vector in can be uniquely described in the form , if W is a subspace of V then ecah vector in can be written in uniquely. Therefore z belongs to W⊥ because it is orthogonal to the spanning set of W. To keep the decomposition y = p + z unique, assume another decomposition y = q + w such that q ∈ W and w ∈ W⊥. Both decompositions are equal to y, so we have p − q = w − z. where p − q is in W and w − z is in W⊥.
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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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A person invests 200,000 into a saving account yielding 8% per annum compounded monthly. After 2 years
the interest rate is raised to 12% p.a. compounded quarterly and further 11⁄2 year later the interest rate raised to
16% compounded semi-annually.
(a) How much interest the person would earn, if he keeps his money in the account for a total of six years?
(b) What was the effective rate of interest received by the person during the final year of his investments?
Answer:
(a) 211,555.72
(b) 16.64%
Step-by-step explanation:
You want to know the total interest earned on a 200,000 investment at ...
8% compounded monthly for 2 years12% compounded quarterly for 1.5 years16% compounded semiannually for 2.5 yearsAnd you want to know the effective rate for the last period.
MultiplierThe multiplier of the investment at rate r compounded n times per year for t years is ...
k = (1 +r/n)^(nt)
ApplicationUsing this multiplier for the rates and periods given the balance of the account at the end of 6 years will be ...
200,000(1 +.08/12)^(12·2) × (1 +.12/4)^(4·1.5) × (1 +.16/2)^(2·2.5)
≈ 411,555.72
(a) InterestThe interest earned is the difference between the account balance and the principal invested:
411,555.72 -200,000 = 211,555.72 . . . . interest earned in 6 years
(b) Effective rateThe annual multiplier for the last term is ...
(1 +.16/2)^(2·1) = 1.1664
The effective interest rate is 1 less than this:
16.64% = effective rate during final year
__
Additional comment
The repetitive math can be less tedious if you let a calculator or spreadsheet do it.
No currency units are given in the problem statement.
Charles needs to determine whether x+2 is a factor of f(x)=2x^4 -3x^3 +5x -16 .
How can Charles use the factor theorem to determine whether x+2 is a factor of f(x)?
Fill in the blanks using the word bank below:
f(-2) f(2) f(4) 30 2 320 is is not
Charles evaluates ________________ and determines its value to be______________Charles concludes that ______________ factor of .
Charles evaluates f(-2) and determines its value to be 30 Charles concludes that is not factor of f(x).
What is Factor theorem?
The factor theorem in algebra establishes a connection between a polynomial's factors and zeros. The polynomial remainder theorem has this particular special instance. A polynomial f(x) has a factor if and only if f=0, according to the factor theorem.
Given : f(x)=2x^4 -3x^3 +5x -16
By Factor theorem, If x+2 is a factor of f(x), then f(-2) should be equal to 0.
So, Charles can use factor theorem to determine whether x + 2 is a factor of f(x) by putting x=-2 in f(x),
f(x) = 2x^4 -3x^3 +5x -16
= 2×(-2)^4 - 3×(-2)^3 + 5(-2) - 16
= 2×16 + 3×8 - 10 - 16
= 32 + 24 -10 -16
= 56 -26
= 30.
Since, f(-2) ≠ 0, (x +2) is not a factor of f(x).
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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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In college, we study large volumes of information - information that, unfortunately, we do not often retain for very long. The functionf(x)=80e^{-0.5x}+20describes the percentage of information, f(x), that a particular person remembers x weeks after learning the information. Find the percentage of information that is remembered after one year (52 weeks).
The percentage of information that is remembered by a particular person after one year (52 weeks) is 20%
The function f(x)=80e-0.5x+20 describes the percentage of information that a particular person remembers after x weeks.
To find the percentage of information that is remembered by a particular person after one year (52 weeks), we need to substitute x=52 in the given f(x).
f(x)=80[tex]e^{-0.5x}[/tex]+20
x=52, f(52)= 80[tex]e^{(-o.5\times 52)}[/tex]+20
=80[tex]e^{-26}[/tex]+20
=80(5.109 [tex]E^{-12[/tex])+20
= 4.087[tex]E^{-20}[/tex]+20
f(52)= 20
The percentage of information that is remembered by a particular person after one year (52 weeks) is 20%
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what is 5,000,374 * 2,000
My son James weighed 11 lbs 9 oz when he was born. convert both the
pounds and ounces separately into kilograms and add them together
One lb = one pound.
and 11 lb is 11 pound
Is 8 oz the same as 1 lb?
Each pound has 16 ounces or oz.
5,44311
What do you mean by pounds?
a unit for measuring weight: One pound is approximately equal to 454 grams. One kilogram is roughly the same as 2.2 lbs. There are 16 ounces in one pound.
What is a pound and examples?
Image result for What do you mean by pounds?
In simpler words, pounds tell us how heavy an object is. For example, the weight of a soccer ball is about one pound. A pound is expressed as lb or lbs, where “lb” stands for libra. It is a Latin word that means “balance” or “scale”.
Its name derives from the Latin word "poundus" meaning "weight". The £ symbol comes from an ornate L in Libra. The pound was a unit of currency as early as 775AD in Anglo-Saxon England, equivalent to 1 pound weight of silver.
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How much do you have to invest today at 2% compounded monthly to obtain $1,000 in return in 4 years?
Answer:6 dollars
Step-by-step explanation:
Cuz u going to need to buy 3 mc flurries :D
Roulette Wheel: The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball.
You watch a roulette wheel spin 8 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin?
You watch a roulette wheel spin 210 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin?
Part (a)
There are 18 red slots out of the total 38, so the probability is [tex]18/38=\boxed{9/19}[/tex]. Note that the previous spins don't impact the result.
Part (b)
Similar to part (a), the answer is [tex]\boxed{9/19}[/tex].
the p-value for the hypothesis test about factor b is . multiple choice less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 greater than 0.05
The p-value for the hypothesis test about factor b is greater than 0.05.
What is Hypothesis?
In effect, a theory is a hypothesis or group of hypotheses that refers to a particular issue or problem.
Thus, a hypothesis is a set of possible explanations or resolutions applicable to a situation. In other words, the hypotheses pose different scenarios in which the aim is to explain the origin and eventual resolution of the problem.
The p-value for the hypothesis test about factor b is greater than 0.05.
The p-value is a measure of statistical significance used in hypothesis testing. It represents the probability of obtaining a result at least as extreme as the one observed in the sample, given that the null hypothesis is true.
In general, a p-value less than 0.05 is considered statistically significant and indicates that the observed result is unlikely to have occurred by chance. A p-value between 0.01 and 0.025 is considered moderately significant, while a p-value between 0.025 and 0.05 is considered borderline significant. A p-value greater than 0.05 is not considered statistically significant and indicates that the observed result is likely due to chance.
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Describe hypothesis.
A theory is, in essence, a hypothesis or set of hypotheses pertaining to a certain subject or issue(s).
Consequently, a hypothesis is a group of potential explanations or solutions that could be applied to a situation. In other words, the hypotheses present many possibilities with the intent of illuminating the problem's origin and potential solutions.
The p-value for the factor b hypothesis test is higher than 0.05.
A statistical significance indicator used in hypothesis testing is the p-value. Given that the null hypothesis is true, it represents the likelihood of obtaining a result that is at least as extreme as the one seen in the sample.
A p-value of less than 0.05 is typically regarded as statistically significant and denotes the likelihood that the observed result did not arise by chance. While a p-value between 0.025 and 0.05 is regarded as borderline significant, one between 0.01 and 0.025 is regarded as moderately significant. The observed result is most likely the result of chance if the p-value is greater than 0.05, which is the threshold for statistical significance.
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What is |4|? I need help
Answer: It is just 4
Step-by-step explanation: That means the absolute value of 4 and it is just 4
Which is the largest ratio?
StartFraction 5 Over 36 EndFraction, 2:9, 3 to 18, 1:3
StartFraction 5 Over 36 EndFraction
2:9
3 to 18
1:3
Comparing the ratios in form of fraction, the ratio 1:3 is the largest.
RatiosThe ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.
In the ratios given, we have 2:9, 3:18 and 1:3
Let's write these in form of fraction to the decimal and determine which is the largest.
i)
2:9 = 2/9 = 0.22
ii)
3:18 = 3/18 = 0.1666 ≅ 0.17
iii)
1:3 = 1/3 = 0.33
From the above fractions, the ratio 1:3 is the largest.
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tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar how much flour and sugar coral will be use to make the cookies
The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.
The flour and sugar coral that will be use to make the cookies will be:
= 1 3/4 + 1/2
= 2 1/4
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Identify the graph of y= -2^x+3
Q23: Problem-solving
Work out the area of this triangle.
The area of the triangle is 11.1 square cm
How to determine the area of the triangle?From the question, we have the following parameters that can be used in our computation:
Legs = 3cm and h cm
Hypotenuse = 8 cm
The area of the triangle is calculated using
Area = 0.5 * b * h
Where
h = √(8² - 3²) --- this is gotten from the Pythagorean theorem
So, we have
h = 7.4
The area is then calculated as
Area = 0.5 * b * h
So, we have
Area = 0.5 * 3 * 7.4
Evaluate
Area = 11.1
Hence, the area is 11.1 square cm
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in order to compare the means of two populations, independent random samples of 457 observations are selected from each population, with the following
On solving the provided question, we can say that - 95 confidence interval Z alpha 2 = 1.96, CI = (4.1 , 53.9)
What is the 95 confidence interval Z alpha 2?The z critical value is 1.96 for a test with a 95% confidence level (e.g. = 0.05). The z critical value is 5.576 for a test with a 99% confidence level (for instance, with = 0.01).
Why is Z alpha 2 significant?The two red tails represent the alpha level split by two. Finding the z-score for an alpha level for a two-tailed test is what is meant when a question asks you to determine z alpha/2. The confidence interval may be subtracted from 100% to calculate alpha, which is connected to confidence levels.
for 95% confidence,
[tex]Z_{\frac{\alpha }{2} }[/tex] = 1.96
CI = (5279 - 5250) ± 1.96[tex]\sqrt{\frac{140^2}{395} + \frac{210^2}{395} } \\[/tex]
CI = (4.1 , 53.9)
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. $84 for 6 carnival tickets. Find the unit price for 1 ticket. *
Answer: $14 for 1 ticket
Step-by-step explanation: 84 divided by 6 is 14. hope this helps
Can somebody help me with this pls pls need it asap
Don’t just give me the answer add the steps to it too pls and Thank-You
1/6 because $160 as a fraction is 1/6
Solve the equation.
7h-5(3h-8)=-72
Answer:
4 hours
Step-by-step explanation:
7h - 5(3h - 8) = -72 Distribute the -5
7h - 5(3h )(-5)(-8) = -72 A negative times a negative is a positive
7h - 15h + 40 = -72 Combine like terms
-8h + 40 = -72 Subtract 40 from both sides
-8h +40 - 40 = -72 - 40
-8h = -32 Divide both sides by -8
[tex]\frac{-8h}{-8}[/tex] = [tex]\frac{-32}{-8}[/tex]
h = 4
The graph of two functions is shown. graph of f of x equals x squared and g of x equals 2 times x minus 3 If f(x) = x2 and g(x) = 2x − 3, why is f(x) ≠ g(x)? a f(x) ≠ g(x) because the graphs do not intersect. b f(x) ≠ g(x) because the x-intercept of the two graphs is not the same. c f(x) ≠ g(x) because the y-intercept of the two graphs is not the same. d f(x) ≠ g(x) because f(x) is a curve and g(x) is a straight line.
The correct statement regarding why f(x) ≠ g(x) is given as follows:
a. f(x) ≠ g(x) because the graphs do not intersect.
When are two functions different?
Two functions are classified as different when they do not intersect.
The functions in this problem are given as follows:
f(x) = x².g(x) = 2x - 3.For them to intersect, it is needed that:
f(x) = g(x).
x² = 2x - 3.
x² - 2x + 3 = 0.
Which is a quadratic function with the coefficients given as follows:
a = 1, b = -2, c = 3.
The number of solutions of the quadratic function depends on the discriminant, given as follows:
Discriminant = b² - 4ac.
Hence the numeric value for the discriminant in this problem is given as follows:
Discriminant = (-2)² - 4 x 1 x 3 = -8.
As the discriminant is negative, the quadratic function has no solutions, meaning that the functions do not intersect and statement a is correct.
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Question #2
0 of 3 points
Cynthia has a watch that counts the number of steps she takes every
day. When she goes for a casual walk, she can get 50 steps every
minute. She has already walked for 236 steps today and she wants to
get to 950 steps before she goes to school.
Which inequality represents the number of minutes (m) Cynthia would
need to walk to reach her goal before she gets to school?
X
0/3
The inequality that represents the number of minutes Cynthia would need to walk to reach her goal before she gets to school is;
50m + 236 ≥ 950
How to solve inequality word problems?We are told that;
Cynthia has a watch that counts the number of steps she takes every
day.
She can get 50 steps every minute for a casual walk.
Number of steps she has walked today = 236 steps
Number of steps she wants to get to before going to school = 950 steps
Now, if m represents the number of minutes Cynthia would need to walk to reach her goal before she gets to school, then the inequality equation her is;
50m + 236 ≥ 950
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Graph AABC with vertices A(0, 2), B(3, 2), and C(2, 1) and its image after a reflection in the x-axis.
To graph the triangle AABC, we can plot the coordinates of the three vertices and then connect them to form the triangle. The coordinates of the vertices are (0, 2), (3, 2), and (2, 1), so we can plot these points on a coordinate grid and connect them with line segments to form the triangle:
|
|
| (2,1)
| /
| /
| /
|/
(0,2) __________ (3,2)
To reflect the triangle in the x-axis, we can multiply the y-coordinate of each vertex by -1. This will cause the triangle to be flipped over the x-axis. The coordinates of the reflected triangle are (0, -2), (3, -2), and (2, -1), so we can plot these points on the same coordinate grid and connect them with line segments to form the reflected triangle:
|
|
|
| /\
| / \
| / \
|/ \
(0,2) __________ (3,2)
|
|
| (2,-1)
|
The resulting graph shows the original triangle AABC and its image after reflection in the x-axis.
Answer:
A' = (0, -2)
B' = (3, -2)
C' = (2, -1)
Step-by-step explanation:
Given vertices of triangle ABC:
A = (0, 2)B = (3, 2)C = (2, 1)The mapping rule for a reflection in the x-axis is:
(x, y) → (x, -y)Therefore, the vertices of ΔA'B'C' are:
A' = (0, -2)B' = (3, -2)C' = (2, -1)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:
Which tile is missing?
By Logical reasoning, missing tile in the given figure is Option C.
How to answer these type of logical reasoning questions?
Initially find the similarity in each row or column. Get the logic relation between the blocks/tiles. Then try to apply the same logic on the missing tile/block to get the answer.
In the given question there are 9 tiles with 1 missing tile.
Now Check the first row:(As we go to the right one-by-one)
1) Normal circle is changing its square side in anti clockwise direction and also it goes in and out every time we pass a block/tile.
2)Dark circle is at corners of the squares as we pass the block it goes out or in tile by tile and also it changes the corner every time one corner is visited.
3)Triangle is at corners of the square and always inside the square, it changes the corner tile by tile in anti clockwise direction.
Similarly the same logic applies to remaining two rows.
Now for third row:
1) As the normal circle is at right side of square and inside the square, as we pass the tile it goes up(anti clockwise) and to outside of square.
2)The dark circle changes the corner once it visits a corner as it visited the down corner once it changes the corner to top right of square
3)Triangle just changes the corner as we pass, so it goes to bottom left corner of the square.
By Logical reasoning, missing tile in the given figure is Option C.
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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