The faucet in my kitchen has a leak and is constantly dripping. At 7:00 a.m., I placed a

Mathematics

1 answer:

Stolb23 [73]3 years ago

6 0

Answer:

1.3125 gallons would have been wasted in 7 days

Step-by-step explanation:

mathematically, there are 0.0625 gallons in a measuring cup

So within the time frame, 0.0625 of liquid was lost

The time frame is 8 hours difference

The number of hours in 7 days will be;

7 * 24 = 168 hours

0.0625 gal in 8 hours

x gal in 168 hours

x * 8 = 168 * 0.0625

8x = 10.5

x = 10.5/8

x = 1.3125 gallons

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What is the first term of the geometric sequence whose fifth term is 1/24 and tenth term is 1/768

Neporo4naja [7]

An=a1r^(n-1)

given
a5=1/24
a10=1/768

we know that
a5=1/24=a1r^(5-1) and
a10=1/768=a1r^(10-1)

so
1/24=a1r^4
1/768=a1r^9

(a1r^9)/(a1r^4)=r^5=(1/768)/(1/24)=1/32

r^5=1/32
take 5th root of both sides
r=1/2

we have
a5=a1r^4=1/24
evaluate r^4 or (1/2)^4
1/16
a1(1/16)=1/24
times both sides by 16/1
a1=16/24
a1=2/3

the first term is 2/3

7 0

3 years ago

Hey guys I need your help on this!!

kogti [31]

Answer:

Domain: (-∞, ∞) or All Real Numbers

Range: (0, ∞)

Asymptote: y = 0

As x ⇒ -∞, f(x) ⇒ 0

As x ⇒ ∞, f(x) ⇒ ∞

Step-by-step explanation:

The domain is talking about the x values, so where is x defined on this graph? That would be from -∞ to ∞, since the graph goes infinitely in both directions.

The range is from 0 to ∞. This where all values of y are defined.

An asymptote is where the graph cannot cross a certain point/invisible line. A y = 0, this is the case because it is infinitely approaching zero, without actually crossing. At first, I thought that x = 2 would also be an asymptote, but it is not, since it is at more of an angle, and if you graphed it further, you could see that it passes through 2.

The last two questions are somewhat easy. It is basically combining the domain and range. However, I like to label the graph the picture attached to help even more.

As x ⇒ -∞, f(x) ⇒ 0

As x ⇒ ∞, f(x) ⇒ ∞