find the greatest common divisor of the following pair of integers. 60,90 220,1400 3273∙11, 23∙5∙7
Answers
We found that the GCD of the following pairs of integers is:6 for 60 and 90.10 for 220 and 1400.21 for 3273∙11 and 23∙5∙7.
Greatest Common Divisor is also known as GCD. It is defined as the highest number that divides two or more integers completely. Let's solve the given pairs of integers:1. To find the GCD of 60 and 90, first, we have to factorize both numbers into their prime factors.60 = 2² × 3 × 590 = 2 × 3² × 5Now we will select the common factors and multiply them. Here, 2 and 3 are common factors.
GCD(60,90) = 2 × 3 = 6Therefore, the GCD of 60 and 90 is 6.2. To find the GCD of 220 and 1400, first, we have to factorize both numbers into their prime factors.220 = 2² × 5 × 111400 = 2³ × 5² × 7Now we will select the common factors and multiply them. Here, 2 and 5 are common factors.
GCD(220,1400) = 2 × 5 = 10Therefore, the GCD of 220 and 1400 is 10.3. To find the GCD of 3273∙11 and 23∙5∙7, first, we have to factorize both numbers into their prime factors.3273∙11 = 3 × 7 × 13 × 1123∙5∙7 = 3 × 5 × 7 × 23Now we will select the common factors and multiply them.
Here, 3 and 7 are common factors. GCD(3273∙11, 23∙5∙7) = 3 × 7 = 21Therefore, the GCD of 3273∙11 and 23∙5∙7 is 21. Therefore, we found that the GCD of the following pairs of integers is:6 for 60 and 90.10 for 220 and 1400.21 for 3273∙11 and 23∙5∙7.
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Related Questions
help please this assignment is due in a few minutes
Answers
Answer:
C. 200 hours
Step-by-step explanation:
According to the given Question ,
Speed of Aeroplane is 400miles/hourIt means that the aeroplane covers 400 miles in 60 minutes.
and it is asked for 30 minutes , so
We know that 30 minutes is equal to 0.5 hours
By the formula ,
Distance = Speed × Time
putting the values given , we get
= 400×0.5
Distance = 200 miles
How do you find the end behavior of a polynomial?
Answers
The end behavior of this the end behavior of this polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity.
The end behavior of a polynomial can be determined by looking at the degree (highest exponent) and the leading coefficient (coefficient of the highest degree term). If the degree is even and the leading coefficient is positive, the end behavior of the polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity. Similarly, if the degree is even and the leading coefficient is negative, the end behavior of the polynomial is negative, meaning that as x approaches positive and negative infinity, the y values approach negative infinity. If the degree is odd and the leading coefficient is positive, the end behavior of the polynomial is positive, and if the degree is odd and the leading coefficient is negative, the end behavior of the polynomial is negative.For example, consider a polynomial of degree 5, f(x) = 3x5 + 2x4 - 3x2 + 4. The leading coefficient is 3, which is positive, and the degree is 5, which is odd. Therefore, the end behavior of this polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity. This can be verified by using the formula: End Behavior = Leading Coefficient x ∞limitx→±∞ End Behavior = 3 x ∞limitx→±∞ End Behavior = +∞.
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4/7 divided by 7/2 this is dividing fraction
Answers
Final Answer:
8/49!
Step-by-step explanation:
4/7 ÷ 7/2
4/7 ÷ 2/7
4/7 × 2/7 = 8/49
Express the definite integral as an infinite series in the form ∑=0[infinity]an. ∫ 0 1 ,3 tan-1 (x²) dx (Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answers
To express the definite integral ∫ 0 1 ,3 tan-1 (x²) dx as an infinite series in the form ∑=0[infinity]an, we can use the Taylor series expansion of the arctangent function:
arctan(x) = ∑n=0[infinity] (-1)ⁿ x^(2n+1) / (2n+1)
Substituting x² for x and multiplying by 3, we get:
3 arctan(x²) = 3 ∑n=0[infinity] (-1)ⁿ (x²)^(2n+1) / (2n+1)
= 3 ∑n=0[infinity] (-1)ⁿ x^(4n+2) / (2n+1)
Integrating this series with respect to x from 0 to 1, we get:
∫ 0 1 ,3 tan-1 (x²) dx = ∫ 0 1 3 ∑n=0[infinity] (-1)ⁿ x^(4n+2) / (2n+1) dx
= 3 ∑n=0[infinity] (-1)ⁿ ∫ 0 1 x^(4n+2) / (2n+1) dx
= 3 ∑n=0[infinity] (-1)ⁿ (1/(4n+3)) / (2n+1)
= 3 ∑n=0[infinity] (-1)ⁿ / [(4n+3)(2n+1)]
Therefore, the infinite series representation of the definite integral ∫ 0 1 ,3 tan-1 (x²) dx in the form ∑=0[infinity]an is:
∑n=0[infinity] (-1)ⁿ / [(4n+3)(2n+1)]
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Solve 2^x+1=1/8
The solution is x =
Answers
Fill in the missing step for this number trick
operation
1.pick a number
2.,
3.,
4.,
5.
6. Subtract the original number
Answers
Answer:
1 pick a number
2mutiply that number by 5
3 mutiply it by 20
4 then double that number
5 divide it by 100
6 subtract the orginal number
Step-by-step explanation:
HELP!!!
An area model with 12 shaded parts and 6 unshaded parts. The shaded part is labeled two-thirds. Adela divided Two-thirds of a cup of bird food equally among 6 birds. How much food did she give each bird? The dividend is The divisor is . The division expreesion is Rewrite the division expression to get Each bird receives -cup of bird food.
Answers
Each bird would receive 1/9 cup of bird food.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
We have been given an area model with 12 shaded parts and 6 unshaded parts. The shaded part is labeled two-thirds. Adela divided Two-thirds of a cup of bird food equally among 6 birds.
The dividend would be
⇒ 2/3
The divisor would be
⇒ 6
The division expression would be
⇒ 2/3
Divided by 6
Rewrite the division expression to get
⇒ 2/3 × 1/6
⇒ 2 / 18
⇒ 1/9
Therefore, each bird would receive 1/9 cup of bird food.
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Write the linear equation in slope-intercept form. 4x+y=1
Answers
Answer:
y = -4x + 1
\(\sf{\#FromThePhilippines}\)
Find the relation between backwards finite difference and
average operator.
Answers
The backward finite difference operator and the average operator are related in that they both approximate derivatives of a function.
The backward finite difference operator is a numerical approximation technique used to estimate the derivative of a function at a specific point. It involves considering the difference between the function values at the current point and a preceding point. By dividing this difference by the step size between the two points, the backward finite difference operator provides an approximation of the derivative.
On the other hand, the average operator calculates the average value of a function over an interval. It involves dividing the integral of the function over the interval by the length of the interval. The result is a single value that represents the average behavior of the function over the given interval.
The connection between the backward finite difference operator and the average operator lies in their underlying principles. Both operators involve taking the difference or average of function values to approximate the behavior of the function. While the backward finite difference operator focuses on estimating the derivative at a single point, the average operator provides an overall summary of the function's behavior over an interval. Therefore, the backward finite difference operator can be seen as a specific case of the average operator, where the interval is reduced to a single point.
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1) f(x) = 5x^4+ 49x^2+ 36
Answers
Answer:
That's the simplest I could do, sorry
Determine whether the series converges or diverges. (n+4)! a) 4!n!4" b) 1 \n(n+1)(n+2) =
Answers
We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.
The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.
`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`
As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `
lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`
Since the limit of the ratio test is less than one, the given series converges.
The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).
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For each of the differential equations in Problems 9 through 11, find the first four nonzero terms in each of two power series solutions about the origin. Show that they form a fundamental set of solutions. What do you expect the radius of convergence to be for each solution? 9. y'' + (sin x)y = 0 10. e^xy'' + xy = 0 11. (cos x)y'' + xy'- 2y = 0
Answers
We will solve the differential equation and find the power series solutions for each problem.
Problem 9: y'' + (sin x)y = 0
Assuming the power series solution: y = a0 + a1x + a2x^2 + ...
Differentiating twice, we have:
y' = a1 + 2a2x + 3a3x^2 + ...
y'' = 2a2 + 6a3x + 12a4x^2 + ...
Substituting these expressions into the differential equation, we get:
2a2 + 6a3x + 12a4x^2 + ... + (sin x)(a0 + a1x + a2x^2 + ...) = 0
Grouping the terms by powers of x, we get:
a0(sin x) = 0
a1(sin x) + 2a2 = 0
a2(sin x) + 6a3 = 0
a3(sin x) + 12a4 = 0
...
From the first equation, we have a0 = 0, since sin(0) = 0. From the second equation, we have a2 = -a1(sin x)/2. From the third equation, we have a3 = -a2(sin x)/6 = a1(sin x)^2/12. From the fourth equation, we have a4 = -a3(sin x)/12 = -a1(sin x)^3/288.
Thus, we have the power series solution:
y = a1x - a1(sin x)^3/288 + ...
This solution is nontrivial, and the ratio of consecutive coefficients is:
-a1(sin x)^3/288 / (a1x) = -(sin x)^3 / (288x)
The ratio approaches zero as x approaches infinity, so the radius of convergence is infinite. Therefore, we expect the solution to be valid for all values of x.
Problem 10: e^xy'' + xy = 0
Assuming the power series solution: y = a0 + a1x + a2x^2 + ...
Differentiating twice, we have:
y' = a1 + 2a2x + 3a3x^2 + ...
y'' = 2a2 + 6a3x + 12a4x^2 + ...
Substituting these expressions into the differential equation, we get:
e^x(2a2 + 6a3x + 12a4x^2 + ...) + x(a0 + a1x + a2x^2 + ...) = 0
Grouping the terms by powers of x, we get:
a0 + (a1 + a0)x + [(2a2 + a1)x^2 + (6a3 + 2a2)x^3 + (12a4 + 6a3)x^4 + ...] = 0
Since the coefficient of x^0 is nonzero, we must have a0 = 0. Then, the coefficient of x^1 gives:
a1 + a0 = 0
a1 = 0
This means that the power series solution is identically zero, which is trivial. Therefore, we cannot form a fundamental set of solutions using power series.
Problem 11: (cos x)y'' + xy' - 2y = 0
Assuming the power series solution: y = a0 + a1x + a2x^2 + ...
Differentiating twice, we have:
y' = a1 + 2a2x + 3a3x
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14 divided by 1883 i need to understand this answer can any of you guys please help me It would be highly appreciated .
Answers
Answer:
0.00743494423 or 0.007
Step-by-step explanation:
The solution to a linear programming problem is (x1,x2,x3)=(5,0,10) and the objective function value is 45,000. The constraints of this linear program are: i. 2x1 + x2 – 0.5x3 <= 5 ii. 0.9x1 - 0.1x2 - 0.1x3 <= 10 iii. X1 <= 14 iv. X2 <= 20 v. X3 <= 10 vi. 3x1 + x2 + 2x3 <= 50 The dual to this LP is: Min 5y1+10y2 + 14y3 + 20y4 +10y5 + 15,000y6 s.t. 2y1 + 0.9y2 + y3 + 3y6 >= 5000 y1 - 0.1y2 + y4 + y6 >= 2000 -0.5y1 - 0.1y2 + y5 + 2y6 >= 2000 Nonnegativity Use the strong duality and/or complementary slackness theorem to solve this problem [do not use solver to find the solution].
PLEASE SOLVE BY USING EXCEL. THANK YOU!
Answers
Life Insurance Corporation (LIC) issued a policy in his favor charging a lower premium than what it should have charged if the actual age had been given. the optimal solution of the primal problem is (x1,x2,x3)=(5,0,10) and the objective function value is 45,000.
The optimal value of the given LP problem is 45,000. In this problem, x1 = 5,
x2 = 0 and
x3 = 10.
Therefore, the objective function value = 7x1 + 5x2 + 9x3 will be 45,000, which is the optimal value.
problem is Minimize z = 7x1 + 5x2 + 9x3
subject to the constraints: i. 2x1 + x2 – 0.5x3 ≤ 5ii. 0.9x1 - 0.1x2 - 0.1x3 ≤ 10iii. x1 ≤ 14iv. x2 ≤ 20v. x3 ≤ 10vi. 3x1 + x2 + 2x3 ≤ 50
Duality: Maximize z = 5y1 + 10y2 + 14y3 + 20y4 + 10y5 + 15,000y6
subject to the constraints:2y1 + 0.9y2 + y3 + 3y6 ≥ 7y1 - 0.1y2 + y4 + y6 ≥ 0.5y1 - 0.1y2 + y5 + 2y6 ≥ 0y3, y4, y5, y6 ≥ 0 Now, we will solve the dual problem using the Simplex method. Using Excel Solver, As per complementary slackness theorem, the value of the objective function of the dual problem = 45,000, which is same as the optimal value of the primal problem. Therefore, the optimal solution of the primal problem is (x1,x2,x3)=(5,0,10) and the objective function value is 45,000.
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A rocket is launched in the air. Its height in feet is given by h(t)= -16t^2+88t where t represents the time in seconds after launch. How long is the rocket in the air?
Answer: ___ seconds
Answers
For the given height function h(t)= -16t²+88t the rocket is in the air for 5.5 seconds.
Height of the launched rocket is equal to :
h(t)= -16t²+88t
Time is represented by 't' in seconds after launch
'h' represents the height of the rocket.
For how long time rocket is in the air :
h(t) = 0
⇒ -16t²+88t = 0
⇒ t ( -16t+88 ) = 0
⇒ t = 0 or ( -16t+88 ) = 0
value of time 't' cannot be equal to zero.
This implies ( -16t+88 ) = 0
⇒16t = 88
⇒ t = 88 / 16
⇒ t = 5.5 seconds
Therefore, the time for which rocket is in the air as per given height function is equal to 5.5 seconds.
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4(2x+1)
what is the answer
Answers
Answer:
8x + 4
Step-by-step explanation:
4(2x+1)
4*2x + 4*1
8x + 4
Can't figure this out please help
Answers
Felix has two pet snakes the first snake is 6/10 meters long. the second snake is 8/100 I Felix lays the snakes together. How many meters will a two snakes be all together
Answers
\(\frac{68}{100}\) is the length of both the snakes all together in fraction.
Meaning of Fractions:A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
To Add two fractions with Different Denominators:
First make the denominators of the fractions same, by finding the LCM of denominators and rationalising them. Add the numerators of the fractions, keeping the denominator common.
Simplify the fraction to get final sum.
According to the given information :
The length of first snake = \(\frac{6}{10}\)
[ multiplying numerator and denominator by \(10\) ]
length of first snake =\(\frac{60}{100}\)
The length of second snake =\(\frac{8}{100}\)
length of both snakes all together =
length of first snake + length of second snake
\(\frac{60}{100} +\frac{8}{100} \\=\frac{68}{100}\)
Therefore length of both the snakes is \(\frac{68}{100}\)
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Simplify Expression
3/5b - 2 + 7b - 12 - 2/5b + 14
Answers
Answer:
The answer is 7 1/5 b
Step-by-step explanation:
1/3+2/3x=-5/6x-1/24
step by step pls
Answers
Answer:
x = -1/4, or -0.25
Step-by-step explanation:
1/3 + 2/3x = -5/6x - 1/24
first lets write everything in the common denominator of 24
8/24 + 16/24x = -20/24x - 1/24
now we take all our x's onto 1 side, and all our numbers onto the other side
36/24x = -9/24
lets cancel out all the 24's
36x = -9
x = -9/36
now lets simplify
x = -1/4, or -0.25
The diagnols of sqaure LMNP intersect at K. Given that LK= 1, find MP.
Answers
if LK = 1, then MP =1, since the diagonals of a square are equal and intersect at the center of the square
This follows that KN = 1 and KP = 1
Therefore, MP = MK + KP = 1 + 1 = 2
A merchant mixed 8 lb of a cinnamon tea with 6 lb of spice tea. The 14-pound mixture cost $38. A second mixture included 16 lb of the cinnamon tea and 4 lb of the spice tea. The 20-pound mixture cost $52. Find the cost per pound of the cinnamon tea and of the spice tea.
cinnamon ___ dollars per pound
spice ____ dollars per pound
Answers
The cost per pound of the cinnamon tea and of the spice tea would be = cinnamon $31.76 dollars per pound
spice $58.24 dollars per pound.
How to calculate the cost of the two different teas?For the first mixture ;The volume of the cinnamon tea = 8 Ib
The volume of the spice tea = 6 Ib
The total volume of mixture = 14 Ib
For the second mixture:The volume of the cinnamon tea = 4 Ib
The volume of the spice tea = 16 Ib
The total volume of mixture = 14 Ib
Add the both constitutes of the mixture;
Total volume of cinnamon tea in both mixture = 8+4 = 12 Ib.
Total volume of spice tea in both mixture = 6+16 = 22 Ib
Total weight of the both mixture = 12+22 = 34 Ib
Total price for both mixture = 38+52 = $90
The cost of cinnamon alone;
= 12/34 × 90/1
= 1080/34
= $31.76
The cost of spice tea = 90- 31.76 = $58.24.
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pleasse help me out with this
Answers
Answer:
2 cos (x + pi/2)
Step-by-step explanation:
Of the choices given, this looks like a cos curve that is shifted to the Left by pi / 2 and multiplied to give an amplitude of 2
What else do I do?
(btw I'm The one with the black and white pfp!
Answers
Answer:
if u don't want them to have your insta/snap, tell them that you don't like sharing them. I just wouldn't respond after that
If they are bothering you say "Thank you for being nice to me, I am going to say this in the most the nicest way possible, but you're kind of bothering me right now. If you keep messaging me/ bothering me I'm going to have to block you" or you could say "Please stop asking me for my insta/snap if you keep asking me I am going to have to block you. Thank you have a nice day :)"
you could say something like that
Find the slope of the line through the given points.
(1, 3) and (0, -9)
Answers
Select the correct answer.
Which inequality represents the values of x that ensure triangle ABC exists?
Answers
the soup shack usually makes tomato soup with 9 99 tomatoes for every 12 1212 bowls of soup. today, they used 6 66 tomatoes to make 8 88 bowls of soup. how does the tomato taste in today's soup compared to the usual recipe?
Answers
The taste of the tomato in today's soup compared to the usual recipe is same .
We find the tomato to soup ratio for each day to compare the taste of tomato in today's soup with the usual recipe,
For the usual recipe, the soup shack uses 9 tomatoes for every 12 bowls of soup, which can be simplified to a ratio of 9:12 ⇒ 3:4 .
This means that for every 3 parts of tomato, there are 4 parts of soup.
For today's soup, the soup shack used 6 tomatoes to make 8 bowls of soup, which can be simplified to a ratio of 6:8 ⇒ 3:4.
This means that for every 3 parts of tomato, there are 4 parts of soup, which is the same as the usual recipe.
Therefore, based on the tomato to soup ratio, the taste of tomato in today's soup is same as the usual recipe.
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The given question is incomplete , the complete question is
The soup shack usually makes tomato soup with 9 tomatoes for every 12 bowls of soup. today, they used 6 tomatoes to make 8 bowls of soup.
How does the tomato taste in today's soup compared to the usual recipe ?
A baker needs 15 lb of cream cheese that contains 20% fat to fill a big order. But his supplier delivers one cream cheese that contains 10% fat, and another that contains 35% fat. How many pounds of each should the baker combine to fill the order?
Answers
Answer:
6 2/3 lbs of each
Step-by-step explanation:
.10x + .35x = 15(.20)
.45x = 3
x = 3/4.5
x = 6.67
Answer:
Step-by-step explanation:
[.1x+.35(15-x)]/15=.2
.1x+5.25-.35x=3
-.25x+5.25=3
-.25x=-2.25
x=9
So he will use 9lbs of 10% and 6lbs of 35%.
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY
Answers
Answer:
15\(\sqrt{2}\)
Step-by-step explanation:
The given is a special right triangle and an isosceles
The angles are 45-45-90 and side lengths are represented by a-a-a\(\sqrt{2}\)
Here as we can see the side length which sees angle measure 45 is 15 (that is represented by a) so a = 15
if a is 15 then x = 15\(\sqrt{2}\)
Answer:
15\(\sqrt{2}\)
Step-by-step explanation:
This is a 45-45-90 triangle the rules are in the image below.
16/8 would be classified as a/an?
A:whole number
B:integer
C:Rational Number
Answers
Answer:
Whole Number
Step-by-step explanation:
Numerator. This is the number above the fraction line. For 16/8, the numerator is 16.
Denominator. This is the number below the fraction line. For 16/8, the denominator is 8.
Improper fraction. This is a fraction where the numerator is greater than the denominator.
Mixed number. This is a way of expressing an improper fraction by simplifying it to whole units and a smaller overall fraction. It's an integer (whole number) and a proper fraction.
Now let's go through the steps needed to convert 16/8 to a mixed number.
Step 1: Find the whole number
We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
16/8 = 2
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numerator
To work this out we'll use the whole number we calculated in step one (2) and multiply it by the original denominator (8). The result of that multiplication is then subtracted from the original numerator:
16 - (8 x 2) = 0
Step 3: Our mixed fraction
We've now simplified 16/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
2 (0/8)
You maybe have noticed here that our new numerator is actually 0. Since there is no remainder, we can remove the entire fraction part of this mixed number, leaving us with a final answer.