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hoa
1 month ago
15

This sequence represents the diameters of circles used to create an art project:2.5 cm, 3.1 cm, 3.7 cm, 4.3 cmLet f(n) represent

diameter in centimeters and n the term number in the sequence. Which equation represents the sequence of diameters?
Mathematics
1 answer:
PIT_PIT [12.4K]1 month ago
7 0
For this specific question, we need to formulate an equation that accurately reflects the provided data concerning the diameters of specific circles. From the information given, the first term is 2.5 cm, and the difference between the first two terms is 0.6 cm. This same difference applies to the following terms, indicating that the sequence is arithmetic, with the first term as 2.5 cm and a common difference of 0.6 cm. Based on the variables specified in this problem, the equation representing the given sequence is: f(n) = 2.5 + (n - 1)(0.6).
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Which fraction is equivalent to StartFraction 2 Over 6 EndFraction? StartFraction 3 Over 7 EndFraction, because StartFraction 2
babunello [11817]
Which equivalent fraction corresponds to \frac{2}{6}? - \frac{3}{7} since \frac{2}{6}= \frac{2 + 1}{6 + 1} - \frac{3}{9} as \frac{2}{6}= \frac{1}{3} and \frac{1}{3} = \frac{3}{9}

- \frac{3}{12} because \frac{2}{6}= \frac{1}{3} and \frac{1}{3} = \frac{3}{9}

- \frac{3}{8} since \frac{2}{6}= \frac{1}{2} = \frac{2+1}{6+2} = \frac{3}{8}

The answer is

- \frac{3}{9} because \frac{2}{6}= \frac{1}{3} and \frac{1}{3} = \frac{3}{9}

A fraction is deemed equivalent if it maintains the same value when expressed in simplest terms. The equivalent to \frac{2}{6} is found in the chosen option;

First, halve both the numerator and denominator by 2

\frac{2/2}{6/2}

Then reduce further

2/2 = 1 and 6/2 = 3; Thus;

\frac{2/2}{6/2} = \frac{1}{3}

Next, multiply both the numerator and denominator by 3

\frac{1*3}{3*3} = \frac{3}{9}

Therefore, \frac{2}{6} equals \frac{3}{9}.

7 0
1 month ago
Read 2 more answers
Below is an attempt to derive the derivative of sec(x) using product rule, where x is in the domain of secx. In which step, if a
tester [12383]

The mistake is present in step 3. According to the product rule, we find

\dfrac{\mathrm d}{\mathrm dx}(\sec x\times\cos x)=\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x+\sec x\times\dfrac{\mathrm d}{\mathrm dx}(\cos x)

=\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x\boxed{+\sec x\times(-\sin x)}

=\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x\boxed{-\sec x\times\sin x}

(meaning that a factor of \sin x is overlooked)

Then

\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x-\sec x\times\sin x=0

\implies\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x=\sec x\times\sin x

\implies\dfrac{\mathrm d}{\mathrm dx}(\sec x)=\dfrac{\sec x\times\sin x}{\cos x}

\implies\dfrac{\mathrm d}{\mathrm dx}(\sec x)=\sec x\times\tan x

6 0
1 month ago
A gold, a silver, and a bronze medal are awarded in an Olympic event. In how many possible ways can the medals be awarded for a
Leona [12618]

Answer:

720 formas posibles

Explicación paso a paso:

La medalla de oro se otorga al primer lugar, la medalla de plata al segundo lugar y la medalla de bronce al tercero.

Cualquier corredor entre los 10 puede ocupar la primera posición.

La segunda posición puede ser ocupada por los 9 corredores restantes.

Mientras que la tercera posición puede ser ocupada por los 8 corredores que quedan.

Por lo tanto, el número de formas en que se pueden otorgar estas medallas es = 10 * 9 * 8 = 720 formas.

3 0
3 months ago
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