you brought the meat Saturday's cookout. A package of hot dogs cost $1.60 and a package of hamburger cost $5. you bought a total
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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
miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship 
, 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.
Cancelling our x's (because we don't need to solve for them), we have
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}](https://tex.z-dn.net/?f=%20%5Csqrt%5B6%5D%7By%5E6%7D%20%3D%20%20%5Csqrt%5B6%5D%7B960%7D%20)
Using a calculator, we see that![\sqrt[6]{960} = 3.14 \ miles \ per \ hour](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7B960%7D%20%3D%203.14%20%5C%20miles%20%5C%20per%20%5C%20hour)
.
The mass of the particles moving in river is proportional to the sixth power of 2, or
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.
Cancelling our x's (because we don't need to solve for them), we have
To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.
Using a calculator, we see that
Answer:
Step-by-step explanation:
Remark
Always the easiest way to study these questions is to get a graph. The one below shows
Red: y = x^2
Blue: y= 3(x + 1)^2
You will notice that (x+1)^2 shifts the graph Left -- the opposite to what you might think.
The 3 is a little harder. It narrows the red mother graph. Which choice says that?
The choice is between b and d. Why. Because the blue graph is to the left of the red one.
You have to learn the meaning of compressed. A better word might be narrows.
Answer
B
Answer:
The answer is 10y + 48.
Step-by-step explanation:
First you have to get rid of brackets by expanding :
Next you have to collect like-terms :