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emmainna [20.7K]
2 years ago
11

Johnny starts run at the 2 mile mark and runs 4 miles per hour. Javier starts at the 6 mile mark and runs 2 miles per hour. How

long until Johnny catches up with Javier?
Mathematics
1 answer:
Galina-37 [17]2 years ago
7 0

Answer:

2 hours

Step-by-step explanation:

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
7nadin3 [17]

The equation of the cone should be z=\sqrt{x^2+y^2}. Parameterize S by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u\,\vec k

with 1\le u\le2 and 0\le v\le2\pi. Take the normal vector to S to be

\vec s_v\times\vec s_u=u\cos v\,\vec\imath+u\sin v\,\vec\jmath-u\,\vec k

Then the integral of \vec F across S is

\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_1^2(-u\cos v\,\vec\imath-u\sin v\,\vec\jmath+u^3\,\vec k)\cdot(u\cos v\,\vec\imath+u\sin v\,\vec\jmath-u\,\vec k)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_1^2(-u^2-u^4)\,\mathrm du\,\mathrm dv

=\displaystyle-2\pi\int_1^2(u^2+u^4)\,\mathrm du\,\mathrm dv=\boxed{-\frac{256\pi}{15}}

3 0
2 years ago
Read 2 more answers
A box of 20 Crunchy Munchy cookies costs $2.50 and a box of 40 Crunchy Munchy cookies costs $4.00. One quart of milk costs $1.50
Otrada [13]
20 crunchy munchy=2.50  this means 2.50/20=0.125 cents per candy (i assume is candy)
40 crunchy munchy=4.00  4/40=0.100 cents per candy - this is cheaper than previous one
 1 quart of milk =1.50 dollars
you cant actuality compare candy to milk
3 0
2 years ago
Read 2 more answers
Pete corporation produces bags of peanuts. It's fixed cost is $18,900. Each bag sells for $2.17 with a unit cost of $1.27. What
pentagon [3]

Answer:

in units: 18,900

in dollars: $ 41,013

Step-by-step explanation:

The break even point is the sales dollar amount or sales in unit at whichthe operating income of the firm equals to zero:\frac{Fixed\:Cost}{Contribution \:Margin} = Break\: Even\: Point_{units }

Where:

\frac{Contribution \: Margin}{Sales \: Revenue} = Contribution \: Margin \: Ratio

<em><u>Contribution margin:</u></em>

2.17 - 1.27 = 1 dollar per unit

Break even:

$18,900 fixed cost /  $1 per unit = 18,900 units

Then, in sales:

18,900 x $2.17 each = 41.013‬

break even point:

3 0
2 years ago
Read 2 more answers
Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If clare doesn't
AVprozaik [17]

We have been given that Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesn't touch the money in her account, she can find the amount she'll have the next year by multiplying her current amount 1.03.

We are asked to write an expression for the amount of money Clare would have after 30 years if she never withdraws money from her account.

We will use exponential growth function to solve our given problem.

An exponential growth function is in form y=a(1+r)^x, where

y = Final value,

a = Initial value,

r = Growth rate in decimal form,

x = Time.

3\%=\frac{3}{100}=0.03

We can see that initial value is $160. Upon substituting our given values in above formula, we will get:

y=160(1+0.03)^x

y=160(1.03)^x

To find amount of money in Clare's account after 30 years, we need to substitute x=30 in our equation.

y=160(1.03)^{30}

Therefore, the expression 160(1.03)^{30} represents the amount of money that Clare would have after 30 years.

8 0
2 years ago
Rank the following quantities in order of decreasing volume. rank from highest to lowest volume. to rank items as equivalent, ov
Anastasy [175]
This should be the data:

1ML 
<span>100L </span>
<span>5 million nL </span>
<span>1GL </span>
<span>50 mL </span>
<span>1cL </span>
<span>1mL 
</span>
Below is the answer:

the conversion into litres are next to the order of volume. 
<span>1. 1GL (10^9) </span>
<span>2. 1ML (10^6) </span>
<span>3. 100L (100) </span>
<span>4. 50mL (50*10^-3)=0.05 </span>
<span>5. 1cL (10^-2) </span>
<span>6. 5 million nL [(5*10^6)*(10^-9)]=0.005 </span>
<span>7. 1mL (10^-3) </span>
5 0
2 years ago
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