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2 years ago

A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula?

Mathematics

2 answers:

Flauer [41]2 years ago

6 0

Answer:

Option C. 3, -2, -7, -12....

Step-by-step explanation:

The sequence is defined recursively using the formula f(n+1) = f(n) - 5

We have to identify the sequence generated by this formula.

B). 1, -5, 25, -125.....

f(n+1) = -5 and f(n) = 1

Therefore - 5 = 1 - 5

⇒ -5 ≠ -4

This sequence is not following the formula.

B). 2, 10, 50, 250.........

f(n+1) = 10 and f(n) = 2

Now we use the formula

10 = 2 - 5

10 ≠ -3

This sequence is not following the formula.

C). 3, -2, -7, -12

f(n+1) = -2 and f(n) = 3

We put this value in the formula

-2 = 3 - 5

-2 = -2

Therefore , the sequence is following the formula.

D). 4, 9, 14, 19........

f(n+1) = 9 and f(n) = 4

9 = 4 - 5

9 ≠ -1

Therefore the formula is not applicable to form this sequence.

Option C. is the answer.

MariettaO [177]2 years ago

5 0

The answer is 3, –2, –7, –12

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kumpel [21]

Answer:

(i) Debemos apilar 5 dados para construir el cubo de mayor tamaño.

(ii) Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.

Step-by-step explanation:

(i) Sabemos por la Geometría Euclídea del Espacio que un cubo es un sólido regular con 6 caras cuadradas y longitudes iguales. Cada dado tiene un volumen de 1 dado cúbico y 125 dados dan un volumen total de 125 dados cúbicos.

El volumen de un cubo está dado por la siguiente fórmula:

$V = L^{3}$

Donde:

$L$ - Longitud de la arista, medida en dados.

$V$ - Volumen del cubo, medido en dados cúbicos.

Ahora, necesitamos despejar la longitud de la arista para calcular la altura máxima posible:

$L = \sqrt[3]{V}$

Dado que $V = 125\,dados^{3}$ , encontramos que la altura del cubo de mayor tamaño sería:

$L =\sqrt[3]{125\,dados^{3}}$

$L = 5\,dados$

Debemos apilar 5 dados para construir el cubo de mayor tamaño.

(ii) El área cuadrada formada por cubos está determinada por la siguiente fórmula:

$A = L^{2}$

Donde:

$L$ - Longitud de arista, medida en dados.

$A$ - Área, medida en dados cuadrados.

Puesto que la longitud de arista se basa en un conjunto discreto, esto es, el número de dados disponibles, debemos encontrar el valor máximo de $L$ tal que no supere 125 y de un área entera. Es decir:

$L \leq 125\,dados$

Si cada cubo tiene un área de 1 dado cuadrado, entonces un cuadrado conformado por 125 dados tiene un área total de 125 dados cuadrados. Entonces:

$L^{2}< 125\,dados^{2}$

Esto nos lleva a decir que:

$L < 11.180\,dados$

Entonces, la longitud máxima del cuadrado con la mayor cantidad de cubos posible es de 11 dados. El número total requerido de cubos es el cuadrado de esa cifra, es decir:

$n = (11\,dados)^{2}$

$n = 121\,dados$

Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.

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2 years ago

The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0. The equation of this circle in standard form is

Ede4ka [16]

Answer:

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Step-by-step explanation:

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What is 2 (log Subscript 3 Baseline 8 + log Subscript 3 Baseline z) minus log Subscript 3 Baseline (3 Superscript 4 Baseline min

Ilya [14]

Answer:

Value of expression in single logarithm is $\log_3\left(2z^2\right)$ .

Step-by-step explanation:

Given expression is,

$2\left(\log_3\left(8\right)+\log_3\left(z\right)\right)-\log_3\left(3^4-7^2\right)$

Now using logarithmic rule to solve the expression as follows,

Applying product rule of logarithmic,

$\log_c\left(a\right)+\log_c\left(b\right)=\log_c\left(ab\right)$

Therefore,

$2\log_3\left(8z\right)-\log_3\left(3^4-7^2\right)$

Applying power rule of logarithmic,

$a\log_c\left(b\right)=\log_c\left(b^a\right)$

Therefore,

$\log_3\left(\left(8z\right)^2\right)-\log_3\left(3^4-7^2\right)$

$\log_3\left(\left(64z^2\right)\right)-\log_3\left(3^4-7^2\right)$

Applying quotient rule of logarithmic,

$\log_c\left(a\right)-\log_c\left(b\right)=\log_c\left(\frac{a}{b}\right)$

Therefore,

$\log_3\left(\dfrac{\left(64z^2\right)^2}{3^4-7^2}\right)$

Simplifying,

$\log_3\left(\dfrac{\left(64z^2\right)^2}{81-49}\right)$

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2 years ago

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Elenna [48]

Answer:

Only A, E, and F are correct.

Step-by-step explanation:

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The distance between two points is just the absolute value of the difference between them. Between the Pelican and the Heron it is $|P_p-p_h|= 33ft$ , and the distance between the Pelican and the Trout is $|P_p-P_t|=40ft$ .

Therefore,

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C is incorrect (distance cannot be negative);

D is incorrect (difference is not positive);

E is correct;

F is correct;

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2 years ago

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1 year ago

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