Manuel's gas tank is

1 answer:

6 0

X represents the full tank
so 2/9x+12=2/3x
solve for x
2/9x+12=2/3x
try to convert 2/3 to a commom denomenator (bottom numer )
2/3=6/9
2/9x+12=6/9x
subtract 2/9x from both sides
12=4/9x
mulitply both sides by 9 to get rid of fraciton
108=4x
divide by 4
27=x

it can hold 27 gallons

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What are the first five terms of the recursive sequence

Sedaia [141]

Answer: Choice D

9, 30, 93, 282, 849

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Explanation:

The notation $a_1 = 9$ tells us that the first term is 9

The notation $a_n = 3*(a_{n-1})+3$ says that we multiply the (n-1)st term by 3, then add on 3 to get the nth term $a_n$

So if we wanted the second term for instance, then we'd say

$a_n = 3*(a_{n-1})+3\\\\a_2 = 3*(a_{2-1})+3\\\\a_2 = 3*(a_{1})+3\\\\a_2 = 3*(9)+3\\\\a_2 = 27+3\\\\a_2 = 30\\\\$

If we want the third term, then,

$a_n = 3*(a_{n-1})+3\\\\a_3 = 3*(a_{3-1})+3\\\\a_3 = 3*(a_{2})+3\\\\a_3 = 3*(30)+3\\\\a_3 = 90+3\\\\a_3 = 93\\\\$

and so on.

The terms so far are: 9, 30, 93

You should find the fourth and fifth terms are 282 and 849 respectively if you keep this pattern going.

Therefore, the answer is choice D

6 0

3 years ago

The formula for the volume of a cone is V = jarh, where V is the volume, r is the radius, and h Is the heightWhat is the volume

olga nikolaevna [1]

Given:

The radius, r=4x

The height,

$h=21xy^2$

To find the volume of the cone:

The volume of the cone formula is,

$V=\frac{1}{3}\pi r^2h$

Substitute the values of r and h in the above formula we get,

$\begin{gathered} V=\frac{1}{3}\pi\times(4x)^2\times21xy^2 \\ =\frac{1}{3}\pi\times16x^2\times21xy^2 \\ =\pi\times16x^2\times7xy^2 \\ =112\pi x^3y^2 \end{gathered}$

Hence, the volume of the cone is