Simplify <br> √(8+2√15)<br><br> Please hurry

The fish tank has side lengths 20in, 10in and height 15in. The water level is two inches below the top of the tank. A glass sphe

Kitty [74]

Answer:

Part 1) The new distance from the water to the top of the tank is $1.979\ in$

Part 2) The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Step-by-step explanation:

step 1

Find the total volume of the tank

$V=20*10*15=3,000\ in^{3}$

step 2

Find the volume of the tank if the water level is two inches below the top of the tank

$V=20*10*(15-2)=2,600\ in^{3}$

step 3

Find the volume of the glass sphere

The volume of the glass sphere is equal to

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

we have

$r=1\ in$

assume

$\pi=3.14$

substitute

$V=\frac{4}{3}(3.14)(1)^{3}$

$V=4.2\ in^{3}$

step 4

What is the new distance from the water to the top of the tank?

we know that

$2 in -----> represent (3,000-2,600)=400\ in^{3}$

so

using proportion

Find how many inches correspond a volume of $4.2\ in^{3}$

$\frac{2}{400}\frac{in}{in^{3}}=\frac{x}{4.2}\frac{in}{in^{3}}\\ \\x=4.2*2/400\\ \\x=0.021\ in$

The new distance from the water to the top of the tank is

$2-0.021=1.979\ in$

step 5

Find how many of these balls can be put into the tank with the tank not overflowing

we know that

The volume of one ball is equal to $4.2\ in^{3}$

using proportion

$\frac{1}{4.2}=\frac{x}{400}\\ \\x=400/4.2\\ \\x=95.23\ balls$

therefore

The maximum number of balls that can be put into the tank with the tank not overflowing is 95

4 0

3 years ago

A^2−8ab+16b^2=81, find a–4b

neonofarm [45]

Answer:

-9, 9

Step-by-step explanation:

a² − 8ab + 16b² = 81

(a - 4b)² = 81 Wrote the left-hand side as a square

a - 4b = ±9 Took the square root of each side

All values of a - 4b are -9 and +9.

4 0

3 years ago

How do you factor this in the form (x+b)(x+c)

faust18 [17]

So you have your polynomial. To factor this out, you need to find the factors of -45 that will add up to 3. These two factors would be -5 and 8. So, you have factored your polynomial! (x-5)(x+8). If you are still unsure, simply use the FOIL method to check and see if you get the same polynomial back. Hope this helps!

7 0

3 years ago

PLEASE HELP ME WITH THIS QUESTION

Alla [95]

Answer:
Step by step explanation:help

6 0

3 years ago

State what additional information is required in order to know that the triangles are congruent by AAS. part 2

SVEN [57.7K]

Answer:

Step-by-step explanation:

The trick is to find the third angle

180 - A - <BCA = <CBA

180 - X - <BCX = <CBX

Everything else is OK

<CBA = <CBX Equals equated to an equal express = an equal expression.

Now by a little slight of hand, you get the two triangles to be equal by ASA, which always works.

Cheating you say? There is no such thing as cheating if it correct and it works.

8 0

3 years ago

Simplify √(8+2√15) Please hurry