A ______ rate is a rate expressed as a fraction with a denominator of 1.

Maddie bought 4 gallons of ice cream for $27.20. How much does one pint cost?

murzikaleks [220]

Answer:

1 pint is 0.85 dollars or 85 cents

Step-by-step explanation:

1 pint= 0.125 gal, so 8 pints= 1 gal

27.20/4 is 6.8 (for 1 gal)

6.8/8 is 0.85 (for 1 pint)

85 cents per pint

3 0

3 years ago

- Please help this is a Rational Inequality problem

Katyanochek1 [597]

1. The solution for the equation is -16t² + 64t > 0

2. The interval notation for the equation is (0, 4)

Given,

The height of the building = 400 feet

A ball is thrown straight up from the top of the building.

The initial velocity of the ball = 64 feet/second

The height of the object is modeled by, s(t) = -16t² + 64t + 400

1. Solution for the equation:

s(t) > 400

So,

-16t² + 64t + 400 > 400

Add -400 to both sides

ie, -16t² + 64t + 400 - 400 > 400 - 400

We get,

-16t² + 64t > 0

2. Now find the interval notation for the equation:

-16t² + 64t > 0

Here, 64/16 = 4

So,

-16t (t - 4) > 0

Now,

t = 0 and t - 4 = 0

The interval notation for the equation is (0, 4)

Learn more about interval notation here:

brainly.com/question/28743524

#SPJ1

7 0

1 year ago

Find the directional derivative of the function at the given point in the direction of the vector v. h(r, s, t) = ln(3r + 6s + 9

vodka [1.7K]

Answer:

$D_\overrightarrow{\rm v}$ $h(r,s,t)=(\frac{2}{7}\overrightarrow{\rm i})*(\frac{1}{r+2s+3t})+(\frac{6}{7}\overrightarrow{\rm j})*(\frac{2}{r+2s+3t})+(\frac{3}{7}\overrightarrow{\rm k})*(\frac{3}{r+2s+3t})$

Step-by-step explanation:

First, let’s check to see if the direction vector is a unit vector:

$||v||=\sqrt{(14)^{2} +(42)^{2} +(21)^{2} } =\sqrt{2401} =49$

It’s not a unit vector. therefore let's divide the vector by its magnitude in order to convert it into a unit vector:

$\overrightarrow{\rm v}=(\frac{14}{49}\overrightarrow{\rm i})+(\frac{42}{49}\overrightarrow{\rm j})+(\frac{21}{49}\overrightarrow{\rm k})= (\frac{2}{7}\overrightarrow{\rm i})+(\frac{6}{7}\overrightarrow{\rm j})+(\frac{3}{7}\overrightarrow{\rm k})$

Now, the directional derivative is given by:

$D_\overrightarrow{\rm v}$ $h(r,s,t)=\frac{\partial h(r,s,t)}{\partial r}\overrightarrow{\rm i} + \frac{\partial h(r,s,t)}{\partial s}\overrightarrow{\rm j} + \frac{\partial h(r,s,t)}{\partial t}\overrightarrow{\rm k}$

So let's calculate the partial derivates:

$\frac{\partial }{\partial r} ln(3r+6s+9t)=\frac{3}{3r+6s+9t}=\frac{1}{r+2s+3t}$

$\frac{\partial }{\partial s} ln(3r+6s+9t)=\frac{6}{3r+6s+9t}=\frac{2}{r+2s+3t}$

$\frac{\partial }{\partial t} ln(3r+6s+9t)=\frac{9}{3r+6s+9t}=\frac{3}{r+2s+3t}$

Therefore:

$D_\overrightarrow{\rm v}$ $h(r,s,t)=(\frac{2}{7}\overrightarrow{\rm i})*(\frac{1}{r+2s+3t})+(\frac{6}{7}\overrightarrow{\rm j})*(\frac{2}{r+2s+3t})+(\frac{3}{7}\overrightarrow{\rm k})*(\frac{3}{r+2s+3t})$

3 0

4 years ago

Plz help i do not understand the question.

gavmur [86]

The question is asking you to come up with a real-life example of something that can be represented as 15+ c= 17.50. If I were you I would do sales tax. You bought an item with a 15 dollar price tag, but when you go to check out 2.50 are added in tax to equal 17.50. to solve subtract 15 from 17.50: c= 2.50. Your variable (c) represents the sales tax. Hope that helps! :)

6 0

4 years ago

On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) viru

sertanlavr [38]

Answer:

growth rate = 0.1733 per day, or 17.33% per day

Step-by-step explanation:

Since the doubling time is 4 days, the growth factor over a period of t days is ...

2^(t/4)

Then the growth factor for 1 day is

2^(1/4) ≈ 1.189207

The instantaneous growth rate is the natural log of this:

ln(1.189207) ≈ 0.1733 . . . per day

4 0

3 years ago