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aivan3 [116]
3 years ago
4

Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6,

10, and 15. Is there a direct variation between a triangular number and its position in the sequence? Explain your reasoning.
Mathematics
2 answers:
MissTica3 years ago
8 0

Answer:

No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and its position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.

Hope this helps!!! :)

uranmaximum [27]3 years ago
4 0
Nth triangular number = n* (n+1) / 2
Basically, input the triangular number's  position in the sequence (for example four) then input the number position into the equation and you get the triangular number's value.
Example:
4 * (5/2) = 10
So, the 4th triangular number has a value of 10.


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Si un proyectil asciende verticalmente, y después de 3 segundos alcanza su altura máxima, calcule la velocidad que lleva a la mi
lys-0071 [83]

Answer:

The speed is 20.8  m/s

Step-by-step explanation:

If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory

Let the maximum height is h and initial velocity is u.

From first equation of motion

v = u + at

0 = u - g x 3

u = 3 g.....(1)

Use third equation of motion

v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g

Let the speed at half the height is v'.

v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s

8 0
3 years ago
The opening balance of the January billing cycle for Megan's credit card was $4,805 if she makes a new purchase of 300 on the 20
Nookie1986 [14]

Answer:

$4911.45

Step-by-step explanation:

To find Megan's average daily balance, we first need to assume that the billing cycle begins at January 1st.

Now we know that there are 31 days in the month of January, we will use that as our basis.

20 days x 4805 = First 20 days of the billing cycle.

11 days 4805 + 300 = 21st day of the billing cycle.

31 days in the month

So now we simply add the first 20 days and the days after the 21st day and divide it by the number of days in the month since we're looking for the average.

(20 x 4805 + 11(4805+300))/31

(20 x 4805 + 11(5105))/31

(96100 + 56155)/31

152255/31

This then gives us:

$4911.45

5 0
3 years ago
Read 2 more answers
Are the irrational numbers closed under addition?
Arte-miy333 [17]

Answer:

Irrational numbers are not closed under addition.

Step-by-step explanation:

Irrational numbers are the numbers that cannot be expressed in the form of a fraction \frac{x}{y}. In other words we can say that irrational number,s decimal expantion does not cease to end.

The closure property of addition in irrational numbers say that sum of two irrational number is always a rational number, But this is not true. It is not necessary that the sum is always irrational some time it may be rational.

This can be understood with the help of an example:

let (2+√2) and (-√2) be two irrational number. Their sum is (2+√2)+(-√2) = 2, which is clearly a rational number.

Hence, irrational numbers are not closed under addition.

4 0
3 years ago
25 POINTS Trina's Toy Company charges $0.85 per pound to ship toys.
d1i1m1o1n [39]

Answer:

Part A

C = $.85p

For 2 pounds , the charge is $1.70

Part B

C = $.05 * p

Step-by-step explanation:

Part A

Cost = charge per pound * pounds

We know the charge per pound is $.85

C = $.85 * p

We want to ship 2 pounds

C = .85*2

C = 1.70

Part B

Cost = charge per pound * pounds

We know the charge per pound is now $.05

C = $.05 * p


3 0
3 years ago
Solve for
Varvara68 [4.7K]

Answer:

t = 1, but please check to see if I correctly interpreted your formatting.

Step-by-step explanation:

The format of the question is too confusing.

I'll assume this is the equation to be solved:

<u>16−2t=t+9+4t</u>

<u></u>

16−2t=t+9+4t

16-9 = t + 2t + 4t

7 = 7t

t = 1

7 0
2 years ago
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