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3 years ago

Find the dimensions of a rectangle whose perimeter is 16 meters and whose area is 15 square meters

Mathematics

1 answer:

igor_vitrenko [27]3 years ago

4 0

15 square meters, hmm...
Your answer is 47.1111

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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

3 years ago

An item that cost $5.50 is marked up %60. What is the new price of the item after the markup? Show work please

r-ruslan [8.4K]

Answer:

$8.80

Step-by-step explanation:

In order to find the new price, you need to add 60% of the original price (5.50) to the original price. You have two options:

1) multiply $5.50*0.6 to get 60% of the original price. You would get $3.30. Then add $3.30+$5.50, which equals $8.80. This way takes longer but shows you all the steps.

2) The shorter way is to simply multiply $5.50*1.6, which also equals $8.80. This works because the "1" automatically adds the 5.50 to 60% of the original price, this way you don't have to multiply then add.

If you don't understand how the second way works or your teacher taught you #1, just do it the first way.

8 0

3 years ago

It’s moving day and Lydia has packed her books into a large and small boxes. The large boxes hold 35 book and the small ones hol

Natali5045456 [20]

Answer:

4 large , 14 small

Step-by-step explanation:

35*x +20*(18-x)=420

35x +360-20x=420

35x-20x=420-360=60

15x= 60

x =4

4 large 14 small

5 0

3 years ago

An employee earns $195 for 15 hours of work. Assuming he is paid by the hour, how much will the employee earn in 8 hours?

vampirchik [111]

Answer:

$104

Step-by-step explanation:

First, find the employee’s hourly rate. You can do this by dividing the total amount earned by the total hours worked. $\frac{195}{15}=13$
Now that you know that the employee’s hourly rate is $13 per hour, you can multiply the hourly rate by the number of hours. $13*8=104$

7 0

3 years ago

How many vertices does a triangular prism have?<br> 04<br> O 5<br> 06<br> 09

ZanzabumX [31]

Answer:

It has 6 vertices. As what you listed 06.

5 0

3 years ago