How many times larger is 220 than 22

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer: choice D) 18

Explanation:

M is the midpoint of QR, so QM = MR, meaning that the two smaller pieces are equal (the two pieces combine back to QR)

Use substitution and isolate x

QM = MR

2x+5 = 5x-1

2x-5x = -1-5

-3x = -6

x = -6/(-3)

x = 2

If x = 2, then QM is

QM = 2x+5 = 2*2+5 = 9

and MR is

MR = 5x-1 = 5*2-1 = 9

both are 9 units long. Both are the same length as expected, so this helps confirm the answer.

The last thing we do is add up the two pieces QM and MR to get the length of QR. This is using the segment addition postulate.

QR = QM + MR

QR = 9 + 9

QR = 18

note: a negative length is never possible in any situation, so you can immediately eliminate choice B from the list of possible answers without even doing any math.

The correct answer is:

An identity is an equation that is true for all real numbers.

Explanation:

An identity is a mathematical statement that is always true. It does not matter what numbers you substitute in for the variables, the result will be the same.

Answer:

756 m²

Step-by-step explanation:

The surface area is the function of 2 dimensions.

Scale factor is

• 6/4 = 1.5

Surface are for the bigger solid will be 1.5*1.5 times the area of the smaller one

• S = 336*1.5*1.5 = 756 m²

b is the correct answer