4 years ago

What is the largest value in the sequence generated by the formula an = –n2 + 6n – 7?

2 answers:

5 0

Derive the equation and equate the derivative to zero.
dan/dt = -2n + 6 = 0
The value of n in the equation is 3. We substitute 3 to the original equation,
an = -(3)² + 6(3) - 7 = 2
The answer to this item is letter B.

alexandr402 [8]4 years ago

3 0

Answer:

Step-by-step explanation:

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It's not an arithmetic sequence.

3 0

4 years ago

The following figure is made of six semicircles with the same diameter, and of four congruent equilateral triangles represented

Oxana [17]

6 semicircles = 3 circles

The formula of the area of a equilateral triangle:

$A_\triangle=\dfrac{a^2\sqrt3}{4}$

We have a = |AE| = 3cm. Substitute:

$A_\triangle=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}\ cm^2$

The formula of the area of a circle:

$A_O=\pi r^2$

We have 2r = |AE| =3cm → r = 1.5cm. Substitute:

$A_O=\pi\cdot1.5^2=2.25\pi\ cm^2$

The area of the figure:

$A=4A_\triangle+3A_O\\\\A=4\cdot\dfrac{9\sqrt3}{4}+3\cdot2.25\pi=9\sqrt3+6.75\pi=6\dfrac{3}{4}\pi+9\sqrt3\\\\=\dfrac{27}{4}\pi+\dfrac{36\sqrt3}{4}=\dfrac{9}{4}\cdot3\pi+\dfrac{9}{4}\cdot4\sqrt3=\dfrac{9}{4}(3\pi+4\sqrt3)\ cm^2$