A graduated cylinder has a mass of 50 g when empty. When 30 ml of water is added the graduated cylinder has a mas of 120 If a rock is added to the graduated cylinder, the water level rises to 75 ml, and the total mass is now 250g. What is the density of the rock?
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The rate of change of the depth of water in the tank when the tank is half

filled can be found using chain rule of differentiation.

When the tank is half filled, the depth of the water is changing at  1.213 ×

10⁻² ft.³/hour.

Reasons:

The given parameter are;

Height of the conical tank, h = 8 feet

Diameter of the conical tank, d = 10 feet

Rate at which water is being pumped into the tank, = 3/5 ft.³/hr.

Required:

The rate at which the depth of the water in the tank is changing when the

tank is half full.

Solution:

The radius of the tank, r = d ÷ 2

∴ r = 10 ft. ÷ 2 = 5 ft.

Using similar triangles, we have;

[tex]\dfrac{r}{h} = \dfrac{5}{8}[/tex]

The volume of the tank is therefore;

[tex]V = \mathbf{\dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}[/tex]

[tex]r = \dfrac{5}{8} \times h[/tex]

Therefore;

[tex]V = \dfrac{1}{3} \cdot \pi \cdot \left( \dfrac{5}{8} \times h\right)^2 \cdot h = \dfrac{25 \cdot h^3 \cdot \pi}{192}[/tex]

By chain rule of differentiation, we have;

[tex]\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \cdot \dfrac{dh}{dt}}[/tex]

[tex]\dfrac{dV}{dh}=\dfrac{d}{h} \left( \dfrac{25 \cdot h^3 \cdot \pi}{192} \right) = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64}}[/tex]

[tex]\dfrac{dV}{dt} = \dfrac{3}{5} \ ft.^3/hour[/tex]

Which gives;

[tex]\dfrac{3}{5} = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64} \times \dfrac{dh}{dt}}[/tex]

When the tank is half filled, we have;

[tex]V_{1/2} = \dfrac{1}{2} \times \dfrac{1}{3} \times \pi \times 5^2 \times 8 =\mathbf{ \dfrac{25 \cdot h^3 \cdot \pi}{ 192}}[/tex]

Solving gives;

h³ = 256

h = ∛256

[tex]\dfrac{3}{5} \times \dfrac{64}{25 \cdot h^2 \cdot \pi} = \dfrac{dh}{dt}[/tex]

Which gives;

[tex]\dfrac{dh}{dt} = \dfrac{3}{5} \times \dfrac{64}{25 \cdot (\sqrt[3]{256}) ^2 \cdot \pi} \approx \mathbf{1.213\times 10^{-2}}[/tex]

When the tank is half filled, the depth of the water is changing at  1.213 × 10⁻² ft.³/hour.

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Answer:

the answer is -Xax.

Step-by-step explanation:

Hey man! I understand why it might be a little frustrating with those bots. Recently there has been an upsurge with them. The moderators are dealing with it. Also the answer to the question is 28994137165

Answer:

104. Explanation: There are 4 10 s to multiply.

Step-by-step explanation:

Step-by-step explanation:

the answer is in the image above

Answer:

Step-by-step explanation:

Convert improper fraction to mixed fraction.

[tex]\dfrac{5}{3}=1\dfrac{2}{3}[/tex]

1 2/3 is between 1 and 2. denominator is three. Divide into 3 parts.

Answer:

55/63

Step-by-step explanation:

Answer:

16/52 or 16/54

Step-by-step explanation:

2 blacks 2 reds

4 colours

4 kings

4 queens

4 jacks

4 ace

16 total of ‘em

and number of cards in Deck is 52, 54 if counted 2 jokers

Answer:

For the first question she would get 400 miles total by 5 PM and for the second question, he gets $25 dollars per lawn (at least I think that's what the question means)

Step-by-step explanation:

1st question: Since they get 50 miles per hour because 4-1 equals 3. 350-200 equals 150. 150/3 = 50 miles per hour

2nd question: 100/4 = 25

Answer:

When x = -2 in (x² + 4)/2, 4 is the result.

Step-by-step explanation:

(x² + 4)/2

Substitute value into varaible.

((-2)² + 4)/2

Square -2. Remeber that (-x)² = x²

(4 + 4)/2

Add 4 and 4.

8/2

Divide 8 by 2.

4

1. Each if them would get 20 fruits

[tex]23 + 37 = 60[/tex]

[tex]60 \div 3 = 20[/tex]

2. There should be 5 rows of tables needed to sit all the invited guests

On every row there would be 26 people, so then we need to divide 130 by 26 and we get 5. Then if we check, 26 times 5 equals 130.

Hope that helped:)

Answer:

decrease 3%

Step-by-step explanation:

sana makatulongggg

Answer:

Step-by-step explanation:

(2.2×10^4)*(7.1×10³)

=(2.2×7.1)×10{4+3}

=15.62×10^7

=1.562×10^8

We want to find the absolute difference between the greatest and the least of 3 consecutive terms of an arithmetic sequence that meet some given criteria. We will get that the difference is 3.88 or 12.88.

We know that the difference between any pair of two consecutive terms in an arithmetic sequence is a constant.

So if that difference is D, we can write 3 consecutive terms as:

A, A + D, A + 2*D

The sum must be equal to 27, then we have:

A + (A + D) + (A + 2*D) = 27

And the sum of their squares is equal to 293, then we have:

A^2 + (A + D)^2 + (A + 2*D)^2 = 293

If we simplify these two equations we get:

3*A + 2*D = 27

3*A^2 + 6*D*A + 5*D^2 = 293

To solve this, we just need to isolate one of the variables in the first equation and then replace that in the other one.

3*A = 27 - 2*D

A = (27 - 2*D)/3 = 9 - (2/3)*D

Replacing that on the other equation we get:

3*(9 - (2/3)*D)^2 + 6*(9 - (2/3)*D)*D + 5*D^2 = 293

Now we can solve this for D:

3*(81 - 2*9*(2/3)*D + D^2) + 54*D - 4*D^2 + 5*D^2 = 293

(243 - 293) + 18*D + 4*D^2 = 0

-50 + 18*D + 4*D^2 = 0

That is just a quadratic equation, the solutions are given by:

[tex]D = \frac{-18 \pm \sqrt{18^2 - 4*4*(-50)} }{2*4} \\\\D = \frac{-18 \pm 33.53}{8}[/tex]

Then we have two possible values for D, we take the positive one to get:

D = (-18 + 33.53)/8 = 1.94

And the difference between the greatest and least of these 3 numbers is twice the common difference, so is equal to 2*D = 2*1.94 = 3.88

If instead we take the other solution, we get:

D = (-18 - 33.53)/8 = -6.44

Then the absolute difference is -2*D = -2*-6.44 = 12.88

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Answer:

a

Step-by-step explanation:

just took the test

Answer:

$0.55 for one can

Step-by-step explanation:

16 cans of lemonade = $8.80

1 can of lemonade = $8.80 / 16 = $0.55

9514 1404 393

Answer:

  1/8

Step-by-step explanation:

1 pound is 16 ounces, so 2 pounds is 32 ounces.

  (4 oz) / (2 lb) = (4 oz) / (32 oz) = 4/32 = 1/8

Answer:

Step-by-step explanation:

$794.95(1.0875) = 864.508125 = $864.51

Answer:

.40

Step-by-step explanation:

move the decimal over 2 times

Answer:

40%=0.4

Step-by-step explanation:

Answer:

if you remember the bell curve 32 32 13.5 13.5 2.35 2.35 and .15 put the mean in the middle of the bell curve we find that 13.5 + 2.35 + .15 so

16% is your probablility

Answer:

$740.86

Step-by-step explanation:

Let me know if you need the steps.

Answer:

https://www.symbolab.com/

Step-by-step explanation:

it will help trust me

Answer:

the answer is a

Step-by-step explanation:

2/6=1/3 therefore 4/6+1/3=6/6

Answer:

Six sixths or 1

Step-by-step explanation:

Hope this helps

Answer:

3

Step-by-step explanation:

5 percent * 60 =

(5:100)* 60 =

(5* 60):100 =

300:100 = 3

Answer: 57

Step-by-step explanation:

5% of 60 is 3 and 60-3 is 57

Answer:

The area of the dilated figure is the area of the original figure multiplied by the square of the scale factor.

Step-by-step explanation:

g ( x ) = -f-4

I'm sorry if this is wrong I think that's it but I kinda suck at functions

Answer:

Step-by-step explanation:

For the shown triangle we use the tangent of 60° angle to find the value of x:

Angle A and 60° are complementary.

The measure of angle A:

Step-by-step explanation:

[tex] \tan(60) = \frac{x}{14} \\ \\ \sqrt{3} = \frac{x}{14} \\ \\ x = \sqrt[14]{3} [/tex]

the measure of angel A

m < a = 90-60 = 30

IF there was only 5/8 of the pizza left, and each person gets 1 slice for 5 friends, then each friend gets A - 1/8 of the pizza.

I hope this helps! :)

Answer:

1 /8

Step-by-step explanation:

Answer:

37.5

Step-by-step explanation: