Find the cost to park for a day and the hourly rate to rent a paddleboat

3.9 practice complete your assignment english 111

Citrus2011 [14]

The answer is 15.9 because 3.9+111=15.9

3 0

3 years ago

How to solve this Algebra question?

PIT_PIT [208]

Slope formula: $\frac{y_2-y_1}{x_2-x_1}$

Firstly, let's set up our equation. Place the two coordinates in the slope formula and have it equal 8: $\frac{3k-4-k}{5-(-2)}=8$

Next, combine like terms: $\frac{2k-4}{7}=8$

Next, multiply both sides by 7: $2k-4=56$

Next, add 4 onto both sides of the equation: $2k=60$

Lastly, divide both sides by 2 and <u>your answer will be $k=30$ </u>

7 0

3 years ago

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 $\sqrt[6]{960} = 3.14 \ miles \ per \ hour$ .