prove that 1³+2³+....n³=n²(n+1)²/4. principle of mathematics induction
Answers
\(\sf 1^3+2^3\dots n^3=\dfrac{n^2(n+1)^2}{2}\)
\(\\ \sf\longmapsto 1^3+2^3+\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2\)
Solution:-Let
\(\\ \sf\longmapsto P(n)=1^3+2^3\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2\)
For n=1
\(\\ \sf\longmapsto P(1)=\left(\dfrac{1(1+1)}{2}\right)^2\)
\(\\ \sf\longmapsto P(1)=\left(\dfrac{1(2)}{2}\right)^2\)
\(\\ \sf\longmapsto P(1)=\left(\dfrac{2}{2}\right)^2\)
\(\\ \sf\longmapsto P(1)=(1)^2\)
\(\\ \bf\longmapsto P(1)=1=1^3\)
Let k be any positive integer.
\(\\ \sf\longmapsto P(k)= 1^3+2^3\dots k^3=\left(\dfrac{k(k+1)}{2}\right)^2\)
We have to prove that p(k+1) is true.
consider
\(\sf 1^3+2^3\dots k^3+(k+1)^3\)
\(\\ \sf\longmapsto \left(\dfrac{k(k+1)}{2}\right)^2+(k+1)^3\)
\(\\ \sf\longmapsto \dfrac{k^2(k+1)^2}{4}+(k+1)^3\)
\(\\ \sf\longmapsto \dfrac{k^2(k+1)^2+4(k+1)^3}{4}\)
\(\\ \sf\longmapsto \dfrac{k+1)^2\left\{k^2+4k+4\right\}}{4}\)
\(\\ \sf\longmapsto \dfrac{(k+1)^2(k+2)^2}{4}\)
\(\\ \sf\longmapsto \dfrac{(k+1)^2(k+1+1)^2}{4}\)
\(\\ \sf\longmapsto \left(\dfrac{(k+1)(k+1+1)}{2}\right)^2\)
\(\\ \sf\longmapsto (1^3+2^3+3^3\dots k^3)+(k+1)^3\)
Thus P(k+1) is true whenever P(k) is true.
Hence by the Principal of mathematical induction statement P(n) is true for \(\bf n\epsilon N.\)
Note:-
We can solve without simplifying the Question .I did it for clear steps and understanding .
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Answer:
Step-by-step explanation:
\(1^3=1=\dfrac{1^2*(1+1)^2}{4} =\dfrac{4}{4} =1\\\\\\\displaystyle \sum_{i=1}^{n+1}\ i^3=(\sum_{i=1}^{n}\ i^3) + (n+1)^3\\\\\\=\dfrac{n^2*(n+1)^2}{4} +(n+1)^3\\\\\\=(n+1)^2*(\frac{n^2}{4} +n+1)\\\\\\=(n+1)^2*\dfrac{n^2+4n+4}{4} \\\\\\=\dfrac{(n+1)^2*(n+2)^2}{4}\)
Related Questions
help meeeeeee pleaseee !!!!
Answers
So, we are writing a function. c(x) is the manufacturing costs, and x is the amount of bikes manufactured. The y-intercept is 1908 because when no bikes are manufactured it still costs 1908 to run the factory. The slope is 75 because it costs $75 to create a bike. So, y = mx + b, where m is the slope and b is the y-intercept is:
c(x) = 75x + 1908
how many solutions does the system of equations have?
Answers
Step-by-step explanation:
The ONE solution to this system of two lines is the point where the two lines cross at (1,4)
I WILL GIVE BRAINERLEST ABD LIKE AND 5 STARS IF YOU ANSWER
How many people n would be seated in
each section if there were 27 total
people in the gym?
Answers
Answer:
IT SAYS IT 27 PEOPLE WOULD BE SEATED
Step-by-step explanation:
A gardener made a scale drawing of a lawn with a scale
factor of 1:4. The dimensions of her drawing are 15 inches
long by 10 inches wide. Her partner plans to make another
scale drawing of the lawn, but with a scale factor of 1:20.
What are the dimensions of her scale drawing?
A. The length is 3 inches and the width is 2 inches.
B. The length is 50 inches and the width is 75 inches.
O c. The length is 2 inches and the width is 3 inches.
O D. The length is 75 inches and the width is 50 inches.
Answers
Answer: A.
Step-by-step explanation:
I just took the exam
can i get brainlyiest?
12
Solve for x.
9
X+4
2x
will give brainliest
Answers
The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.
What is the quadratic equation?
A quadratic equation is a type of polynomial equation of degree 2, that can be written in the form of ax^2 + bx + c = 0 where x is the variable, a,b,c are constant and a is not equal to zero.
To solve for x in the equation 9/(x+4) = 2x, we can first clear the fractions by multiplying both sides of the equation by (x+4). This gives us:
9 = 2x*(x+4)
Then we can simplify the right side of the equation:
9 = 2x^2 + 8x
Next, we can move all the x terms to one side of the equation and all the constants to the other side:
2x^2 + 8x - 9 = 0
Now we can use the quadratic formula to solve for x:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
where a = 2, b = 8, and c = -9
So we have:
x = (-8 +/- sqrt(8^2 - 42-9)) / 2*2
x = (-8 +/- sqrt(64 + 72)) / 4
x = (-8 +/- sqrt(136)) / 4
x = (-8 +/- 4*sqrt(17)) / 4
x = (-2 +/- sqrt(17))
So the solutions for x are x = -2 + sqrt(17) and x = -2 - sqrt(17)
The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.
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Uma folha de papel foi dobrada como mostra o esquema abaixo. Determine o valor do ângulo alfa.
Answers
Answer:
\(\alpha = 35º\)
Step-by-step explanation:
Primeiro, vamos dizer que essa folha tem extremidades nos pontos \(A, B, C, D\).
E vamos chamar os vértices do triângulo que contém o ângulo \(\alpha\) de \(E, F, G\).
Na semireta de baixo, formada por \(DC\), a gente tem um ângulo de \(70º\) e um outro ângulo de \(90º\) (porque ele indica um ângulo reto).
Vamos dizer que estes dois ângulos se encontram no ponto \(E\), que combinamos antes, como vértice (extremidade) do triângulo de cima.
Como os dois ângulos, estão num mesmo ponto, \(E\), podemos dizer que existe um terceiro ângulo para o qual sua soma seja \(180º\). E tem, seria o ângulo à esquerda de
Vamos chamar este ângulo de \(\beta _{I}\). Portanto:
\(\beta _{I} + 90º + 70º = 180º\\\beta _{I} = 180º - 160º\\\beta _{I} = 20º\)
Agora, temos um outro triângulo no canto inferior esquerdo da folha, cujos ângulos são \(\beta x_{I}\), \(90º\) e um outro ângulo, que vamos chamar de \(\beta x_{II}\)
Esse último vai ser o ângulo superior deste triângulo, tá legal?
Então, vamos ter que:
\(\beta _{I} + 90º + \beta _{II} = 180º\\\beta _{I} + \beta _{II} = 90º\\\)
Como \(\beta _{I} = 20º\),
\(\beta _{I} + \beta _{II} =20º + \beta _{II}\)
\(20º + \beta _{II} = 90º\\\beta _{II} = 90º - 20º\\\beta _{II} = 70º\)
Ou seja, o ângulo superior do triângulo no canto inferior esquerdo, é 70º.
Vamos concordar, que este mesmo triângulo tem vértices nos pontos \(F, D, E\). Onde \(F\) é o ponto superior, \(D\) é a extremidade inferior esquerda do retângulo e \(E\) é aquele mesmo ponto em que se encontram os ângulos de \(90º\)e \(70º\).
Mais à frente, você vai entender o porquê é importante nomear estes pontos, eu fiquei 40 minutos tentando fazer essa questão sem fazer isso e não conseguia porque empacava numa parte da resolução.
Então, agora, sabemos que o ângulo \(\beta _{II}\), que é o encontro dos seguimentos \(FD\) e \(EF\) vale \(70º\).
Até aqui, foi só aplicar propriedades. Mas, a partir desse ponto, você vai precisar usar a criatividade.
Então, você entende que o ângulo \(\beta _{II}\) está inserido numa reta com outros dois ângulos concentrados no ponto \(F\).
Então, pode dizer que esse ângulo externo é o suplemento de \(\beta _{II}\).
Vamos chamar todo ele de \(\beta _{III}\)
\(\beta _{II} + \beta _{III} = 180º\\70º + \beta _{III} = 180º\\\beta _{III} = 180º - 70º\\\beta _{III} = 110º\)
Agora, vamos elevar o nível de criatividade no raciocínio e ver também que temos um quadrilátero formado pelos pontos \(A, G, F, E\)
A soma dos ângulos de qualquer quadrilátero é 360º.
E temos que esse mesmo quadrilátero é formado por dois ângulos retos, além do ângulo de 110º que calculamos.
A última extremidade que falta é um ângulo formado pela soma de \(\alpha\) a um outro ângulo, que vamos chamar de \(\beta _{IV}\).
Então, temos que:
\(90º + 110º + 90º + \alpha + \beta _{IV} = 360º\\\alpha + \beta _{IV} +290º = 360º\\\alpha + \beta _{IV} = 360º + 290º\\\alpha + \beta _{IV} = 70º\\\)
De todas, as etapas dessa resolução essa é a mais importante de entendermos os pontos que definimos. Eu refiz ela várias vezes porque não fiz isso antes.
Mas, veja, quando a gente dobra a folha, pegamos um formato qualquer e destacamos do resto dela.
Isso quer dizer que o formato que ficou dobrado é o mesmo que falta na folha. Do contrário, estaríamos criando folha ou excluindo matéria, o que não é possível no caso de uma simples dobra.
Em outras palavras, os triângulos \(AGF\) e \(EFG\) são os mesmos. (Eu recomendo que você construa esse desenho e coloque as letras em cada ponto, pra visualizar melhor.)
Isso é o mesmo que dizer que os ângulos de um vão ser os ângulos do outro.
Portanto, os ângulos são equivalentes. (Mesmos ângulos para ambos os triângulos, mudando só de posição.)
Assim, você pode afirmar que \(\alpha\) = \(\beta _{IV}\)
Se subirmos um pouco a resolução, vamos lembrar que encontramos que \(\alpha + \beta _{IV} = 70º\\\)
Se \(\alpha = \beta _{IV}\)
Temos:
\(\alpha + \alpha = 70º\\2\alpha = 70º\\\alpha = \frac{70º}{2} \\\)
e TCHARAAN!
\(\alpha = 35º\)
-------------------------
Força, guerreiro(a). Sucesso e que Deus te abençoe nos estudos.
One number is eight less than five times another. If the sum of the two numbers is 28, findthe two numbers.(separate your answers using commas)
Answers
Problem
One number is eight less than five times another. If the sum of the two numbers is 28, find
the two numbers.(separate your answers using commas)
Solution
for this case we can define the following notation:
Let x and y the two numbers and we have:
x= 5y -8
and we also know that:
x+ y = 28
Replacing we got:
5y -8 +y = 28
6y = 28+8
6y= 36
And y = 6
And for x we got:
x= 5*6 -8= 30 -8 = 22
What is 3-3×6+2 please?
Answers
Answer:
-13Step-by-step explanation:
What is 3-3×6+2 please?
remember PEMDAS
3 - 3 × 6 + 2 = (solve multiplication)
3 - 18 + 2 = (solve addition)
3 - 16 = (solve subtraction)
-13 (result)
Ashanti Goldfields, wanted to undertake a project which will costs GH 30,000 now and is expected to generate year –end cash inflows of GH 9000, GH 8000, GH 7000, GH 6000, GH5000 and GH 4000 in years 1 through 6.The opportunity cost of capital may be assumed to be 10 percent.
Answers
Answer:
I strongly believe that NPV of the project is the requirement of this question:
NPV is -$486.82
Step-by-step explanation:
The NPV is the present value of the future cash flows from year 1 through year 6 minus the initial capital investment of GH30,000
The cash flow discount factor =1/(1+r)^n
r is the opportunity cost of capital at 10%
n is the relevant year of each cash flow
NPV=-30,000+9000/(1+10%)^1+8000/(1+10%)^2+7000/(1+10%)^3+6000/(1+10%)^4+5000/(1+10%)^5+4000/(1+10%)^6=-$486.82
The project is not viable since NPV is negative
Solve the system. -3x-y=10; y-4z=-13; x-4y+z=4
Answers
9514 1404 393
Answer:
(x, y, z) = (-3, -1, 3)
Step-by-step explanation:
Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.
Use the last equation to write an expression for z.
z = 4 -x +4y
Substitute this into the second equation:
y -4(4 -x +4y) = -13
y -16 +4x -16y = -13
4x -15y -3 = 0
In genera form, the first equation can be written as ...
3x +y +10 = 0
Now, the solution to these two equations can be found to be ...
x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"
y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation
z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z
The solution to the system is (x, y, z) = (-3, -1, 3).
_____
Additional comment
Written as an augmented matrix, the system of equations is ...
\(\left[\begin{array}{ccc|c}-3&-1&0&10\\0&1&-4&-13\\1&-4&1&4\end{array}\right]\)
...........................
Answers
Answer:
x= 88
Step-by-step explanation:
PLEASE ANSWER QUICKLY
What is the correct definition for sec 0? A. sec 0 = cos-1 0 B. sec 0 = sin-1 0 C. sec 0 = 1/sin 0 D. sec 0 = 1/cos 0 E. sec 0 = 1/tan 0
Answers
sec(theta) = 1/cos(theta)
I believe that is your option D
Write and solve an inequality to find the possible values of x.
Answers
The inequality tha calculates the possible values of x is x < 2
How to determine the inequality tha calculates xFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
3x + 2 < 10
And, we have
2x + 6 < 10
Evaluate the expressions
So, we have
3x < 8 and 2x < 4
Evaluate
x < 8/3 and x < 2
Hence, the inequality tha calculates x is x < 2
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A test to determine whether a certain antibody is present is 99.3% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.3% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.007 . Suppose the test is given to six randomly selected people who do not have the antibody.
(a) What is the probability that the test comes back negative for all six people?
(b) What is the probability that the test comes back positive for at least one of the six people?
Answers
a) The probability that the test comes back negative for all six people is 95.8%,
b) The probability that the test comes back positive for at least one of the six people is 4.2%.
(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.
Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:
P(negative for all 6) = (0.993)^6 ≈ 0.958
Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.
(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.
The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.
The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:
P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042
Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.
In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.
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A package of 88 batteries costs $ 4 . 724.72 .
What is the cost per battery?
Answers
We get that the cost of the battery is $ 8.24 per battery.
We are given that the cost of 88 batteries = $ 724.72
We need to find the cost of one battery.
We will do this by diving the cost of 88 batteries by 88.
Using division, we get that:
cost of one battery = $ 724.72 ÷ 88
Simplifying the expression, we get that:
cost of one battery = $ 8.24 per battery.
Therefore, we get that the cost of the battery is $ 8.24 per battery.
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A rectangular picture frame has a length of 20 inches and a width of 15 inches. The perimeter of the frame can be found using the formula 2l+2w, where l is the length and w is the width. What is the perimeter of the picture frame in inches
Answers
Answer:
70
Step-by-step explanation:
The diagram shows a triangle.
31° / 6x / x+16°
What is the value of x?
Answers
Step-by-step explanation:
31 + 6x + x + 16 = 180
7x + 47 = 180
7x = 180 - 47
x = 133/7
x = 19
A contractor hired 150 workers to pave 30 miles of highway how many workers will they need to hire to pave 20 miles of highway in the same amount of time?
Answers
Answer: 100
Step-by-step explanation:
First, we need to know how many workers must be hired to pave one mile.
Which is 5 workers per 1 mile ( 150 / 30 )
Then you can either do
(5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5)
OR
5 x 20 = 100
( if I'm wrong it's like 3 am so I'm a bit slow but I hope I helped )
There were 15 students running in a race. How many different arrangements of first, second, and third place are possible?
Answers
Answer:
The area 2730 possible arrangements of first, second, and third place.
Step-by-step explanation:
The order in which the students finish is important. For example A, B and C is a different finishing order(outcome) than B, A and C. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
\(P_{(n,x)} = \frac{n!}{(n-x)!}\)
In this question:
3 from a set of 15. So
\(P_{(15,3)} = \frac{15!}{(15-3)!} = 2730\)
The area 2730 possible arrangements of first, second, and third place.
I'm in the 4th grade and having a little problem.
Question:
A painter mixed 1/4 quart of red paint with 3/4 blue paint to make purple paint. How much purple paint did the painter make?
Answers
Answer:yea Jen he d Jen Jen. Djd
Step-by-step explanation:Kim ke. Me k
Answer:
1
Step-by-step explanation:
the painter made 1 of purple paint
Relative intensity of 9 decibels is how many times higher than that of 8 decibels
Answers
Answer:
what do you mean by land ?
The intensity of sound is proportional to the square of its amplitude.
Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:
I9/I8 = (10^(9/10))/(10^(8/10))
I9/I8 = 10^(0.1)
I9/I8 = 1.2589
Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.
May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
Suppose that the force acting on an object can be expressed by vector (-8,14), where each
measure in the ordered pair represents the force in pounds. What is the magnitude of the force? Round
your answer to the nearest hundredth.
Answers
Answer:
Magnitude of force is \(||v||\approx16.12\text{ lbs}\)
Step-by-step explanation:
\(||v||=\sqrt{x^2+y^2}\\||v||=\sqrt{(-8)^2+(14)^2}\\||v||=\sqrt{64+196}\\||v||=\sqrt{260}\\||v||\approx16.12\text{ lbs}\)
A 42 gallon hot water tank hose 350 pounds of water what weight of water at 53 gallon tank hold
Answers
Answer:
441.66667 pounds
Step-by-step explanation:
divide 350/42 then multiply the quotient by 53
If f (p) = 3p – 1 andg(n)=n? + 2,what is (f.g)(x)?
Answers
This is a composition function, so:
\(\begin{gathered} f(p)=3p-1 \\ g(n)=n^2+2 \\ (f\circ g)(x)=f(g(x))=3\cdot g(x)-1 \\ (f\circ g)(x)=3(x^2+2)-1=3x^2+3\cdot2-1 \\ (f\circ g)(x)=3x^2+5 \end{gathered}\)The monthly profit for a company that makes decorative picture frames depends on the price per frame. The company determines that the profit is approximated by f(p)= -80p + 3440p -36,000, where p is the price per frame and f(p) is the monthly profit based on that price.
Requried:
a. Find the price that generates the maximum profit.
b. Find the maximum profit.
c. Find the price(s) that would enable the company to break even.
Answers
Answer:
a. $21.50
b. $980
c. $25 and $18
Step-by-step explanation:
a. The price that generates the maximum profit is
In this question we use the vertex formula i.e shown below:
\((-\frac{b}{2a}, f(-\frac{b}{2a} ))\\\\\)
where a = -80
b = 3440
c = 36000
hence,
P-coordinate is
\((-\frac{b}{2a}, (-\frac{3440}{2\times -80} ))\\\\\)
\(= \frac{3440}{160}\)
= $21.5
b. Now The maximum profit could be determined by the following equation
\(f(p) = 80p^2 + 3440p - 36000\\\\f($21.5) = -80(21.5)^2 + 3440(21.5) - 36000\\\\\)
= $980
c. The price that would enable the company to break even that is
f(p) = 0
\(f(p) = -80p^2 + 3440p - 36000\\\\-80p^2 + 3440p - 36000 = 0\\\\p^2 -43p + 450 = 0\\\\p^2 - 25p - 18p + 450p = 0\\\\p(p - 25) - 18(p-25) = 0\\\\(p - 25) (p - 18) = 0\)
By applying the factoring by -50 and then divided it by -80 and after that we split middle value and at last factors could come
(p - 25) = 0 or (p - 18) = 0
so we can write in this form as well which is
p = 25 or p = 18
Therefore the correct answer is $25 and $18
The table below shows the number of dog licenses
issued in the town of Palmer over a 5-year period.
On the blank graph to the right, label and number
the axes. Then plot the ordered pairs.
Year (input)
Number of Dog Licenses
Issued (output)
1
75
2
100
3
125
4
125
5
150
y
Answers
The graph of the given order pairs is attached below.
What is graph of a function?
In mathematics, the set of ordered pairs where f(x) = y exists is known as the graph of a function. These pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane in the typical case where x and f(x) are real numbers.
Given:
The table below shows the number of dog licenses issued in the town of Palmer over a 5-year period.
We have to plot the graph for the given order pairs.
The graph of the given order pairs is attached below.
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let C be the curve y=5sqrtx for 1.1
Answers
We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
We have,
To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:
S = ∫(a to b) 2πy√(1 + (f'(x))²) dx
In this case,
f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).
Let's calculate the surface area:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx
Simplifying the expression inside the integral:
S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx
Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
To find the surface area of revolution about the x-axis of the function
f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx
Let's calculate the integral:
S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx
To simplify the calculation, let's simplify the expression inside the integral first:
S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx
Next, we can distribute the square root and simplify further:
S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx
Thus,
We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
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Order the values from least (on top) to greatest (on bottom).
64%
0.65
5/8
Answers
Convert them all into decimals. Percent is just 0.--, and the fraction you can calculate out which gives: 0.625=5/8,0.64=64%
5/8
64%
0.65
\( {x}^{2} - 4 \div x - 2\)
Answers
Step-by-step explanation:
\(\dfrac{x^2-4}{x-2}\)
Apply identity a²-b² = (a-b)(a+b)
So, it will be
\(\dfrac{(x-2)(x+2)}{x-2}\)
Where x-2 gets cancelled from numerator and denominator.
Hence, x+2 is the answer.
Hope it helps :)
What is the sin B?
/21
B
5
2
sin (B) =
[?]
![What is the sin B?/21B52sin (B) =[?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/bJqEBQdNtkeNzRPqszdQkxPqXUYlMPak.png)
Answers
Answer:
Step-by-step explanation:
sin (B) = \(\frac{2}{5}\)