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1 year ago

It takes Wayne 1/10 hours to walk a 1/6 mile park loop. What is Wayne's unit rate, in miles per hour

1 answer:

5 0

To solve this problem, we should set up a proportion, letting x represent our unknown number of miles that Wayne walks in one hour.

1/6 mile / 1/10 hours = x miles / 1 hour

Now we use cross-products or the multiplication of the numerator of one fraction times the denominator of the other fraction, setting these two numbers equal. The resulting equation is:

1/6 = 1/10x

Finally, we must divide both sides by 1/10 to cancel it out on the right side of the equation and get the variable x alone.

x = 5/3 or 1 2/3

Therefore, Wayne walks 1 2/3 miles per hour.

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Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the ve

Akimi4 [234]

A three-dimensional vector field is conservative if it is also irrotational, i.e. its curl is $\mathbf 0$ . We have

$\nabla\times\mathbf f(x,y,z)=-2e^{-x}\,\mathbf k$

so this vector field is not conservative.

- - -

Another way of determining the same result: We want to find a scalar function $f(x,y,z)$ such that its gradient is equal to the given vector field, $\mathbf f(x,y,z)$ :

$\nabla f(x,y,z)=\mathbf f(x,y,z)$

For this to happen, we need to satisfy

$\begin{cases}f_x=ye^{-x}\\f_y=e^{-x}\\f_z=2z\end{cases}$

From the first equation, integrating with respect to $x$ yields

$f_x=ye^{-x}\implies f(x,y,z)=-ye^{-x}+g(y,z)$

Note that $g$ *must* be a function of $y,z$ only.

Now differentiate with respect to $y$ and we have

$f_y=-e^{-x}+g_y=e^{-x}\implies g_y=2e^{-x}\implies g(y,z)=2ye^{-x}+\cdots$

but this contradicts the assumption that $g(y,z)$ is independent of $x$ . So, the scalar potential function does not exist, and therefore the vector field is not conservative.

8 0

1 year ago

A full container that holds 96 fluid ounces developed a leak in the bottom. After 72 hours, all the liquid had emptied from the

Contact [7]

Answer
this is hard

explanation
sorry i can’t answer i’m bad at math

4 0

1 year ago

Josh has a rewards card for a movie theater. - He receives 15 points for becoming a rewards card holder. - He earns 3.5 points f

jeka94

Answer:

Option A. 3.5x + 15 ≥ 55

Step-by-step explanation:

Points Rosh received for becoming a member = 15

Points Rosh received for visiting the moving theater = 3.5

Total points needed for a free movie ticket = 55

For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.

Total points = Points received on becoming a member + Points received on x visits

So,

Total Points = 15 + 3.5x

These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:

3.5x + 15 ≥ 55

So, option A gives the correct answer

8 0

1 year ago

Read 2 more answers

mars, inc. claims that 20% of its m&m plain candies are orange. a sample of 100 such candies is randomly selected. find t

elena-14-01-66 [18.8K]

The probability p of an orangecandy is 0.2. The sample size = 100.
The mean is given by:
$n\times p=100\times0.2=20$
The standard deviation is given by:
$\sqrt{npq} = \sqrt{100\times0.2\times(1-0.2)} =4$
The answers are: Mean = 20. Standard deviation = 4.

4 0

2 years ago

Read 2 more answers

Which will have a higher effective interest rate — a payday loan for $1900 that is due in 14 days with a fee of $80, or a payday

Pie

Answer:

It's D.

Step-by-step explanation:

The shorter period loan has the same total interest for the same loan amount, so it has the higher effective interest rate: 80/12 is higher than 89/14.

6 0

1 year ago