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3 years ago

What is the value of a1 in the sequence?

Mathematics

2 answers:

zhannawk [14.2K]3 years ago

6 0

$a_1,\ a_2,\ a_3,\ a_4,\ ...-\text{the sequence}\\\\\text{We have}\\\\-4,\ -2,\ -12,\ -14,\ ...\\\\\boxed{a_1=-4}$

Otrada [13]3 years ago

5 0

Answer:

Option B.

Step-by-step explanation:

The given sequence is

-4, -2, -12, -14, ...

We need to find the value of a₁.

We know that $a_n$ represents the nth term of a sequence. So, a₁ represents the first term of the sequence.

From the given sequence it is clear that the first term of the sequence is -4. So, we conclude that

$a_1=-4$

The value of a₁ in the sequence is -4.

Therefore, the correct option is B.

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3 years ago

Which of the following expressions results in a positive number?

arlik [135]

Answer:

-30(-8)

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A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (ha

Neko [114]

Answer:

Volume: $\frac{2}{3}\pi r^3$

Ratio: $\frac{2}{9}r$

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

where

r is the radius of the sphere

V is the volume

Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is

$A'=2\pi r^2 + \pi r^2 = 3 \pi r^2$

Therefore, the ratio betwen the volume and the surface area of the hemisphere is

$\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r$

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