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2 years ago

The sum of the first 15 terms of an arithmetic series

Mathematics

1 answer:

ale4655 [162]2 years ago

7 0

Answer:

d=4

Step-by-step explanation:

SUM OF 15 terms = 615

T5 = 53

T5 = a+(n-1)d

53 = a + 4d

4d = 53 - a

d = (53-a)/4

S15 = 15/2 (2a+14d) =615

15/2 [2a + 14×(53-a)/4 ]

=15/2 [ 2a +(53×14 - 14a )/4 ]

=15/2 [ (8a +742 - 14a ) /4]

615×8 = 15(-6a +742)

-6a+72=615×8/15 =41

-6a+72=42

-6a = - 72 + 42 = -30

a = 30/6= 5

a = 5

T5 = 5 + 4×d = 53

4d= 53 - 5 = 48

4d=48

d=4

Common difference is 4

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tres hermanos danvueltas circuito en bicicleta. el mayor tarda 18 en dar Una vuelta el del medio 24 minutos yel menos 36 minutos

hodyreva [135]

Tienes que hallar el mínimo común múltiplo de las 3 cantidades.

18= 2×3²
24= 2³×3
36= 2²×3²

mcm(18,24,36) = 2³×3²=8×9= 72

Eso quier decir que si partieron a la misma hora se encontraran de nuevo en el punto de partida 72 minutos después de la salida.

Las vueltas que habrán realizado será el resultado de dividir 72 entre el tiempo que tardan en dar una vuelta

Mayor: = 4

Mediano: = 3

Pequeño: = 2

Soluciónes:

se vuelven a encontrar a los 72 min de la salida
El mayor dió 4 vueltas, el mediano 3 y el pequeño 2

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3 years ago

Les is measuring the border of her bulletin

borishaifa [10]

Answer:

Perimeter of the board

Step-by-step explanation:

That measurement of "the border of her bulletin board" is actually the perimeter of the board.

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3 years ago

Line XY is perpendicular to line CD at D. Which conclusion can be drawn?

guapka [62]

I have attached the choices given for this question

Answer:
measure angle XDC = 90 degrees

Explanation:
The term "perpendicular" implies that the angle formed between the two lines is 90 degrees.
These two lines do not have to be equal in length, they just intersect forming a 90-degree angle.

Comparing the explanation with the given choices, we would find that the only correct choice is:
measure angle XDC = 90 degrees

Hope this helps :)

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4 years ago

What is the equation of a line that has a slope of - 1/2 and a y intercept of 3

Alla [95]

y = ½x +3

Step-by-step explanation:

Slope = m = ½

y-intercept = 3

Substitute values into Slope intercept form :

$y = mx + b$

Where m = slope

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3 years ago

Question Help

klasskru [66]

Answer:

16 times

Step-by-step explanation:

$\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.

$\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h$

Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so 16 times greater than the smaller cone.

<h3>Proof</h3>

Given: