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3 years ago

What is the relationship between the two shapes?

Mathematics

2 answers:

Goryan [66]3 years ago

7 0

Answer:

They are Congruent but not similar.

Explanation:

We speak about congruence when we talk about state of coinciding or agreeing among two figures.

Congruent segments have the same length, the congruent angles have the same measure; two figures can be congruent if they have the same shape and size; but when some figures have the same shape but different size, they are similar.

Having saying this, the relationship between both shapes is that: They are Congruent but not similar.

guapka [62]3 years ago

4 0

They are similar but not congruent.

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Both the La Plata river dolphin (Pontoporia blainvillei) and

Citrus2011 [14]

Answer:

1. A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin; 2. The radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball; 3. The volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

Step-by-step explanation:

If we expressed a number as:

$\\ N = a * 10^{b}$ (1)

Where

$\\ \frac{1}{\sqrt{10}} \leq a < \sqrt{10}$ (2)

$\\ 1 \leq a < 10$ (3)

Then, b represents the order of magnitude of such a number (Order of magnitude (2020), in Wikipedia).

The order of magnitude can be defined as "...the smallest power of ten needed to represent a quantity" (Weisstein, Eric W. "Order of Magnitude". From MathWorld--A Wolfram Web Resource).

Having gathered all this information, we can proceed as follows:

<h3>First case</h3>

The La Plata river dolphin weighs between 30 and 50kg and the sperm whale weighs between 35,000 and 40,000kg.

Then, considering (1) and (3) to express the dolphin and whale's weight (since in this way the order of magnitude is the same as the exponent part in the scientific notation):

$\\ 30kg \leq Dolphin_{weight} \leq 50kg$

$\\ 3*10^{1}kg \leq Dolphin_{weight} \leq 5*10^{1}kg$

$\\ 35000kg \leq Whale_{weight} \leq 40000kg$

$\\ 3.5*10^{4}kg \leq Whale_{weight} \leq 4.0*10^{4}kg$

Since the range for the weights are in the same order of magnitude for both dolphin and whale (considering the definition above):

$\\ Dolphin_{weight} = 10^{1}\;(order\;of\;magnitude=1)$

$\\ Whale_{weight} = 10^{4}\;(order\;of\;magnitude=4)$

Then

$\\ \frac{Whale_{weight} = 10^{4}}{Dolphin_{weight} = 10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = \frac{10^{4}}{10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{4-1}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{3}$

Thus

A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin.

<h3>Second case</h3>

Following the same reasoning, we can conclude that the radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball:

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = \frac{10^{1}}{10^{0}}$

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = 10^{1-0} = 10^{1}$

<h3>Third case</h3>

For this case, we need to calculate the volume of a sphere for both radii (1cm and 10cm).

The volume of a sphere is

$\\ V_{sphere} = \frac{4}{3}*\pi*R^{3}$

Then, the volume of the ball of radius 1cm is:

$\\ V_{radius=1} = \frac{4}{3}*\pi*(1cm)^{3}$

$\\ V_{radius=1} \approx 4.19*10^{0}cm^{3}$

And, the volume of the ball of radius 10cm is:

$\\ V_{radius=10} = \frac{4}{3}*\pi*(10cm)^{3}$

$\\ V_{radius=10} \approx 4.19*10^{3}cm^{3}$

Thus

$\\ \frac{10^{3}}{10^{0}} = 10^{3}$

As a result, the volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

4 0

3 years ago

In ΔEFG, the measure of ∠G=90°, GE = 40 feet, and EF = 44 feet. Find the measure of ∠F to the nearest degree.

Licemer1 [7]

Answer:

42°

Step-by-step explanation:

It is always good to draw a picture to help you. In this case

tan F = 40/44

m∠F = arctan (40/44) = 42°

3 0

2 years ago

If Z is the midpoint of RT , what are x, RZ AND RT?

Novosadov [1.4K]

Since z is the midpoint, rz and zt must be equal

4x - 15 = 25

4x = 40

X = 10
Plug the answer in and rz equals 40-15 which is 25.

25 + 25 = 50

Or if you really wanted, since you know 25 is half, just add them together right off the bat. (25 and 25, I mean)

5 0

3 years ago

Read 2 more answers

Simplify -(3a-3) it’s hard

Rufina [12.5K]

-(3a-3) = -3a +3

you cannot do much more.

You can rewrite it as 3 ( -a +1) or as -3 ( a -1) but nothing more really.

7 0

1 year ago

Please help ASAP if u can!! :))))

fiasKO [112]

Answer:

the answer is 32cm squared

Step-by-step explanation:

7 0

3 years ago