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4 years ago

Formulate the recursive formula for the following geometric sequence. {-16, 4, -1, ...}

1 answer:

8 0

4 / -16 = -1/4. (also -1/4 = -1/4).

The general form of the sequence is:
a, ar, ar^2, ar^3....

Where r is the ratio: 1/4, and a is first term: -16.

You can see each term is just ar^n where n is the term number, starting where the first term n=0.

So the general formula would be:

-16(-1/4)^n

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Preview Activity 3.5.1. A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. How fast is the

ArbitrLikvidat [17]

Answer:

The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.

Because $\frac{dr}{dt}=\frac{5}{36\pi }>\frac{dr}{dt}=\frac{5}{64\pi }$ the radius is changing more rapidly when the diameter is 12 inches.

Step-by-step explanation:

Let $r$ be the radius, $d$ the diameter, and $V$ the volume of the spherical balloon.

We know $\frac{dV}{dt}=20 \:{in^3/s}$ and we want to find $\frac{dr}{dt}$

The volume of a spherical balloon is given by

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

Taking the derivative with respect of time of both sides gives

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

We now substitute the values we know and we solve for $\frac{dr}{dt}$ :

$d=2r\\\\r=\frac{d}{2}$

$r=\frac{12}{2}=6$

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=\frac{20}{4\pi(6)^2 } =\frac{5}{36\pi }\approx 0.044$

The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.

When d = 16, r = 8 and $\frac{dr}{dt}$ is:

$\frac{dr}{dt}=\frac{20}{4\pi(8)^2}=\frac{5}{64\pi }\approx 0.025$

The radius is increasing at a rate of approximately 0.025 in/s when the diameter is 16 inches.

Because $\frac{dr}{dt}=\frac{5}{36\pi }>\frac{dr}{dt}=\frac{5}{64\pi }$ the radius is changing more rapidly when the diameter is 12 inches.

8 0

3 years ago

Henry has a new album for his baseball cards. Some of the pages hold 6 cards and the other pages hold 3 cards. If Henry has 36 c

shepuryov [24]

6y + 3y = 36
9y = 36
y = 36/9
y = 4
There're 4 ways he can put cards in his album

5 0

4 years ago

a tree is 42 feet tall. its shadow is 26 feet long, if a man nearby is 5.5 feet tall how long would his shadow be

prohojiy [21]

Answer:

x/6=42/5

5x=252

x=50.4

Step-by-step explanation:

3 0

3 years ago

How can you determine the congruent triangles?

Levart [38]

If they have exactly the same sides, and if they have exactly three angles

5 0

4 years ago

You have decided both to open a savings account and to purchase a vehicle. You would like a savings account with the highest int

Law Incorporation [45]

Bank B for the car loan and Bank A for the savings account open a savings account and purchase a vehicle. Option C

This is further explained below.

<h3>Bank B for the car loan and Bank A for the savings account open a savings account and to purchase a vehicle.?</h3>

Generally, A deposit account that is kept at a financial institution and used for the purpose of conserving money often offers a low-interest rate as well as protection for the principle.

A person or other entity may rack up a loan debt if they borrow money from another party. A quantity of money is generally advanced to the borrower by the lender, which might be a business, a financial organization, or even the government.

In conclusion, Bank B will provide the financing for the automobile, while Bank A will manage the savings account. Together, they will establish a savings account and buy a vehicle. Alternative C