P = ab^2
q = a^3 b
p = a * b * b
q = a*a*a * b
Pairing the duplicates we have LCM = a*a*a*b*b = a^3 b^2 answer
Answer:
9 units
Step-by-step explanation:
because if the y-axis is 5 and the x-axis is 9, the line is 9 units.
A=Value of investment.
A=12000(1+0.015)^2
A= <span>£12362.70</span>
Answer:
The answer to the question: "Will Hank have the pool drained in time?" is:
- <u>Yes, Hank will have the pool drained in time</u>.
Step-by-step explanation:
To identify the time Hank needs to drain the pool, we can begin with the time Hank has from 8:00 AM to 2:00 PM in minutes:
- Available time = 6 hours * 60 minutes / 1 hour (we cancel the unit "hour")
- Available time = 360 minutes
Now we know Hank has 360 minutes to drain the pool, we're gonna calculate the volume of the pool with the given measurements and the next equation:
- Volume of the pool = Deep * Long * Wide
- Volume of the pool = 2 m * 10 m * 8 m
- Volume of the pool = 160 m^3
Since the drain rate is in gallons, we must convert the obtained volume to gallons too, we must know that:
Now, we use a rule of three:
If:
- 1 m^3 ⇒ 264.172 gal
- 160 m^3 ⇒ x
And we calculate:
(We cancel the unit "m^3)- x = 42267.52 gal
At last, we must identify how much time take to drain the pool with a volume of 42267.52 gallons if the drain rate is 130 gal/min:
- Time to drain the pool =
(We cancel the unit "gallon") - Time to drain the pool = 325.1347692 minutes
- <u>Time to drain the pool ≅ 326 minutes</u> (I approximate to the next number because I want to assure the pool is drained in that time)
As we know, <u><em>Hank has 360 minutes to drain the pool and how it would be drained in 326 minutes approximately, we know Hank will have the pool drained in time and will have and additional 34 minutes</em></u>.
a. Parameterize
by

with
.
b/c. The line integral of
over
is




d. Notice that we can write the line integral as

By Green's theorem, the line integral is equivalent to

where
is the triangle bounded by
, and this integral is simply twice the area of
.
is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.