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3 years ago

Berniece solved the following equation:

Mathematics

1 answer:

Ghella [55]3 years ago

6 0

Step 4 is incorrect.

This is technically another example of the subtraction property of inequality. This is because we are subtracting 8 from both sides to get the 8 to cancel and the 24 to go down to 16. This is not addition and should not be justified as such.

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The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv

kari74 [83]

The river flows at 2 miles per hour. This is the speed of the current, or the speed at which the water itself is moving.

The mass of the particles moving in river is proportional to the sixth power of 2, or $2^6 = 64$ miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship $x * 2^6 = k$ , for some constant k.

For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.

So, the key here is proportional. We can set up two proportions and cross multiply.

$\dfrac{x}{2^6} = \dfrac{15x}{y^6} \\ (x)(y^6)=(2^6)(15x)$

Cancelling our x's (because we don't need to solve for them), we have

$y^6 = 15(2^6) = 15(64)=960$

To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.

$\sqrt[6]{y^6} = \sqrt[6]{960}$

Using a calculator, we see that $\sqrt[6]{960} = 3.14 \ miles \ per \ hour$ .

6 0

4 years ago

What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?

REY [17]

The volume of the sphere of radius r is:
V1 = (4/3) * (pi) * (r ^ 3)
Where,
r: sphere radius:
The volume of the sphere of radius 0.3r is:
V2 = (4/3) * (pi) * ((0.3r) ^ 3)
Rewriting:
V2 = (4/3) * (pi) * (0.027 (r) ^ 3)
V2 = 0.027 (4/3) * (pi) * (r ^ 3)
V2 = 0.027V1
The difference is:
V1-V2 = V1-0.027V1 = V1 (1-0.027)
V1-V2 = 0.973 * (4/3) * (pi) * (r ^ 3)
Answer:
the difference in volume between a sphere with radius and a sphere with radius 0.3r is:
V1-V2 = 0.973 * (4/3) * (pi) * (r ^ 3)

8 0

3 years ago

What is the answer of This,this is is rational numbers 3.3(6)=

Svetach [21]

Answer:

19.8

Step-by-step explanation:

Since 3.3*6 is 19.8.

3 0

4 years ago

Read 2 more answers

According to the recent poll, 22 1/4% of the people polled said that they approved of the city plan to expand the library. If 10

Sphinxa [80]

Answer:

Some 224 people were in favor of the expansion.

Step-by-step explanation:

Given that, according to the recent poll, 22 1/4% of the people polled said that they approved of the city plan to expand the library, if 1004 people was polled, to determine how many were in favor of the expansion should be done the following calculation:

1/4 = 0.25

100 = 1004

22.25 = X

1004 x 22.25 / 100 = X

223.39 = X

Thus, some 224 people were in favor of the expansion.

3 0

3 years ago

Antonia is keeping track of the number of pages she reads. She started the school year having already read 95 pages her book, an

cupoosta [38]

F(x) means "function of" and x represents the day number, example: day 6 would be f(6)=(20×6)+95

4 0

3 years ago