Consider two people where one person is 20​% taller than the other but proportioned in exactly the same way.​ (That is, the tall

Answer:

Here’s the response provided

Step-by-step explanation:

Referring to the flask diagram, the diameter of the cylinder measures 1 inch and its height (h) is 3 inches. Thus, the radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder can be calculated as πr²h = π(0.5)² × 3 = 2.36 in³

As for the sphere, its diameter is 4.5 in. Hence, the radius of the sphere R = diameter / 2 = 4.5/2 = 2.25 in

The volume of the sphere is calculated as 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

The total volume of the flask = Volume of the cylinder  + Volume of the sphere = 2.36 + 47.71 = 50.07 in³

<pWhen the cylinder and the sphere are expanded by a scale factor of 2, the height (h') of the cylinder becomes 3/2 = 1.5 inches and the radius (r') becomes 0.5/2 = 0.025 inches.

The new volume for the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

For the sphere, the new radius is R' = 2.25 / 2 = 1.125 in.

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

Thus, the new volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

<pThe ratio of the new volume to the original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125<pThe resulting volume will thus be 0.125 times the original volume

Answer:

The rotation angle measures 2.11 °

Step-by-step explanation:

Stated as follows:

The radius of the circular path = r = 18 feet

The distance rolled by the wheel = l = 38 feet

Let us denote the angle of rotation as Ф

Now, according to the problem:

∵ the length of an arc at the center corresponds to an angle Ф

Thus,

distance rolled by the wheel = π × radius ×

As 180° represents π radians

And π approximates to 3.14

Thus, distance rolled by the wheel = 180 °× radius ×

That is l = r × Ф

So, Ф =

Consequently, Ф =

Therefore, Ф = 2.11 °

Thus, the rotation angle is Ф = 2.11 °

Hence, the rotation angle is 2.11 ° Answer

T<span>he area of a figure signifies the measure of space within a two-dimensional shape, typically expressed as square units based on the figure's dimensions.

For instance, with a shape having dimensions of k, its area can be given by .
</span>
<span>Consider that one similar figure possesses an area nine times that of another.

As these figures are similar, their areas correspond to the proportionality of their dimensions.

Let the smaller shape's dimensions be k, while the larger is p times the dimensions of the smaller shape. The smaller shape's area is and the larger shape's area is .

Now, knowing the larger figure's area is nine times the area of the smaller figure, we have:

</span>
Thus, the dimensions of the larger figure must be 3 times those of the smaller figure.

The variable representing the total number of songs is x, hence twice that quantity is 2x, and subtracting three results in -3, which leads to the expression 2x - 3.

A) The speed of pedestrian BC is 5 km/h

    The speed of pedestrian CD is 0 km/h

    The speed of pedestrian DE is 5 km/h

B) He reached E since the stop after 6 hours

C) The formula for section BC is d(t) = 40 - 5t

    The formula for section CD is d(t) = 20

    The formula for section DE is d(t) = 50 - 5t

Step-by-step breakdown:

A)

In the time-distance graph, speed represents the change in distance with respect to time

this means speed = Δd/Δt ⇒ (slope of the line)

For line BC:

1. Δd = 40 - 20 = 20 km

2. Δt = 4 - 0 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed of pedestrian BC stands at 5 km/h

For line CD:

1. Δd = 20 - 20 = 0 km

2. Δt = 6 - 4 = 2 hours

3. The speed = 0 ÷ 2 = 0 km/h

The speed of pedestrian CD is 0 km/h

For line DE:

1. Δd = 20 - 0 = 20 km

2. Δt = 10 - 6 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed for pedestrian DE is 5 km/h

B)

∵ He stopped at t = 4 hours

∵ He reached point E at t = 10 hours

∵ 10 - 4 = 6 hours

He arrived at E since the stop took 6 hours

C)

<pthe line="" equations="" are="" characterized="" by:=""><pthe general="" form="" of="" a="" line="" equation="" is="" f="" mx="" c="" where="" m="" represents=""><pthe slope="" and="" c="" is="" the="" y-intercept="" value="" of="" y="" when="" x="" equals="">

1. f(x) is referenced as d(t)

2. m is the speed

3. x corresponds to t

4. You can calculate c by substituting any coordinates of a point along the line into the formula

<pline bc="">

Line BC has a negative slope because d decreases as t increases

∵ m = -5 and c = 40

Thus, d(t) = 40 - 5t

The equation for section BC is d(t) = 40 - 5t

Line CD

Line CD is a horizontal line (which follows the form of any horizontal line represented as y = c)

Thus, m = 0 and c = 20

Therefore, d(t) = 20

The equation for section CD is d(t) = 20

Line DE

Line DE features a negative slope as d decreases along with an increase in t

∵ m = -5

Thus, d(t) = -5t + c

The value of c can be determined by substituting point D's coordinates into the equation

∵ D's coordinates are (6, 20)

Thus, 20 = -5(6) + c

So, 20 = -30 + c

Adding 30 to both sides yields

∴ c = 50

Thus, d(t) = 50 - 5t

The equation for section DE is d(t) = 50 - 5t

Further Learning:

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