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Zina [86]
3 years ago
6

A pool contains 3600 cubic feet of water. If the length of the pool is 30 feet, the width is 16 feet, and the depth of the pool

is the same throughout, how deep is the pool?
Mathematics
1 answer:
IgorLugansk [536]3 years ago
6 0
30 times 16 is 480
3600/480=7.5 (the depth of the pool)
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kenny6666 [7]
(8x+7y)(x-y) is the answer.
4 0
3 years ago
Calculate 3217. km + 13.1 km + 1.30 km. round off if necessary to apply the rule of significant figures for addition and subtrac
QveST [7]
3217 + 13.1 + 1.3 can also be written as

3217.0
+ 13.1
     1.3
----------
<span>3231.4
</span>
Your final answer should be <span>3231.4 or option 4. Hope this helps!</span>
6 0
3 years ago
Prove for any positive integer n, n^3 +11n is a multiple of 6
suter [353]

There are probably other ways to approach this, but I'll focus on a proof by induction.

The base case is that n = 1. Plugging this into the expression gets us

n^3+11n = 1^3+11(1) = 1+11 = 12

which is a multiple of 6. So that takes care of the base case.

----------------------------------

Now for the inductive step, which is often a tricky thing to grasp if you're not used to it. I recommend keeping at practice to get better familiar with these types of proofs.

The idea is this: assume that k^3+11k is a multiple of 6 for some integer k > 1

Based on that assumption, we need to prove that (k+1)^3+11(k+1) is also a multiple of 6. Note how I've replaced every k with k+1. This is the next value up after k.

If we can show that the (k+1)th case works, based on the assumption, then we've effectively wrapped up the inductive proof. Think of it like a chain of dominoes. One knocks over the other to take care of every case (aka every positive integer n)

-----------------------------------

Let's do a bit of algebra to say

(k+1)^3+11(k+1)

(k^3+3k^2+3k+1) + 11(k+1)

k^3+3k^2+3k+1+11k+11

(k^3+11k) + (3k^2+3k+12)

(k^3+11k) + 3(k^2+k+4)

At this point, we have the k^3+11k as the first group while we have 3(k^2+k+4) as the second group. We already know that k^3+11k is a multiple of 6, so we don't need to worry about it. We just need to show that 3(k^2+k+4) is also a multiple of 6. This means we need to show k^2+k+4 is a multiple of 2, i.e. it's even.

------------------------------------

If k is even, then k = 2m for some integer m

That means k^2+k+4 = (2m)^2+(2m)+4 = 4m^2+2m+4 = 2(m^2+m+2)

We can see that if k is even, then k^2+k+4 is also even.

If k is odd, then k = 2m+1 and

k^2+k+4 = (2m+1)^2+(2m+1)+4 = 4m^2+4m+1+2m+1+4 = 2(2m^2+3m+3)

That shows k^2+k+4 is even when k is odd.

-------------------------------------

In short, the last section shows that k^2+k+4 is always even for any integer

That then points to 3(k^2+k+4) being a multiple of 6

Which then further points to (k^3+11k) + 3(k^2+k+4) being a multiple of 6

It's a lot of work, but we've shown that (k+1)^3+11(k+1) is a multiple of 6 based on the assumption that k^3+11k is a multiple of 6.

This concludes the inductive step and overall the proof is done by this point.

6 0
3 years ago
Read 2 more answers
3. What is the radius of a circle whose area is 64π cm squared?
nataly862011 [7]

Answer:

Area = 64π

Area \: = \pi {r}^{2}Area=πr

2

64 \: \pi \: = \pi {r}^{2}64π=πr

2

{r}^{2} = \dfrac{64\pi}{\pi}r

2

=

π

64π

{r}^{2} = 64r

2

=64

r \: = \: \sqrt{64} = 8r=

64

=8

Radius = 8 units

Finding the Diameter -

Diameter = Radius x 2 = 8 x 2 = 16 .

\bold{Diameter \: is \: 16 \: units}Diameteris16units

8 0
2 years ago
Riley ordered a snow cone with 4 flavors.
frosja888 [35]
Riley has 4 flavors
caleb had 2 flavors
4-2 equals 2
6 0
3 years ago
Read 2 more answers
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