PLSS HELP WILL BE MARKED BRAINLIEST

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

Use Long Division to answer number 4. Please show all work!

skelet666 [1.2K]

Answer:

2x² + 3x + 4 + (17x + 9) / (x² − 4)

Step-by-step explanation:

Start by setting up the division. Make sure to write all the coefficients, even the zero ones.

x² + 0x − 4 | 2x⁴ + 3x³ − 4x² + 5x − 7

Start by dividing the first term of the dividend (2x⁴) by the first term of the divisor (x²). That's 2x²; it'll be the first term in quotient. Multiply the divisor by 2x²:

2x⁴ + 0x³ − 8x²

Subtract that from the first three terms of the dividend:

3x³ + 4x²

Drop down the next term from the dividend, and start the process all over again.

3x³ + 4x² + 5x

When you finish, the quotient will be 2x² + 3x + 4, and the remainder will be 17x + 9.

4 0

3 years ago

Karen wrote a six digit number that only has one 8 in it . Kim also wrote a six digit number. The 8 in karens number is worth 10

Dahasolnce [82]

the 8 could be tens spot, Hundreds spot, Thousands ... till the end for karens spot

Step-by-step explanation:

Sorry if im wrong.

3 0

3 years ago

Which is the best estimate for the average rate of change for the quadratic function graph on the interval 0 ≤ x ≤ 4?

tatuchka [14]

Answer:

The best estimate for the average rate of change is $-2$

Step-by-step explanation:

we know that

the average rate of change using the graph is equal to

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$f(a)=f(0)=0$

$f(b)=f(4)=-8$

$a=0$

$b=4$

Substitute

$\frac{-8-0}{4-0}=-2$

4 0

3 years ago

Read 2 more answers

If the initial amount of iodine-131 is 537 grams , how much is left after 10 days?

viktelen [127]

Answer:

225.78 grams

Step-by-step explanation:

To solve this question, we would be using the formula

P(t) = Po × 2^t/n

Where P(t) = Remaining amount after r hours

Po = Initial amount

t = Time

In the question,

Where P(t) = Remaining amount after r hours = unknown

Po = Initial amount = 537

t = Time = 10 days

P(t) = 537 × 2^(10/)

P(t) = 225.78 grams

Therefore, the amount of iodine-131 left after 10 days = 225.78 grams

4 0

3 years ago