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2 years ago

10

Micah jogs on a path at the park at 5 miles per hour. He has jogged 2 miles when Luke starts running on the same path at 5 miles

per hour. If they maintain their pace, when will Luke catch up to Micah?

2 answers:

miss Akunina [59]2 years ago

3 0

Answer:

no because micah started before and they are running at the same pace.

Step-by-step explanation:

Karo-lina-s [1.5K]2 years ago

3 0

No Micah can't catch up with Luke...

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What is the value of k used to find the coordinates of a point that partitions a segment into a ratio of 5:3. Please Explain.

Dafna11 [192]

Answer:

The value of k is 5/8

Step-by-step explanation:

The value of k is found by dividing the numerator of the original ratio, 5, by the sum of the numerator and denominator of the ratio

When finding a point, P, to partition a line segment AB into the ratio a/b, we find a ratio c = a / (a + b)

According to this formula we find the value of k.

k = a/(a+b)

where a = 5

b = 3

Now plug the values in the formula:

k = 5/(5+3)

k = 5/8 ....

4 0

3 years ago

Does question 4 look correct

mars1129 [50]

I really don’t know but try it and see

6 0

2 years ago

Consider the initial value problem y′+5y=⎧⎩⎨⎪⎪0110 if 0≤t<3 if 3≤t<5 if 5≤t<[infinity],y(0)=4. y′+5y={0 if 0≤t<311 i

rosijanka [135]

It looks like the ODE is

$y'+5y=\begin{cases}0&\text{for }0\le t$

with the initial condition of $y(0)=4$ .

Rewrite the right side in terms of the unit step function,

$u(t-c)=\begin{cases}1&\text{for }t\ge c\\0&\text{for }t$

In this case, we have

$\begin{cases}0&\text{for }0\le t$

The Laplace transform of the step function is easy to compute:

$\displaystyle\int_0^\infty u(t-c)e^{-st}\,\mathrm dt=\int_c^\infty e^{-st}\,\mathrm dt=\frac{e^{-cs}}s$

So, taking the Laplace transform of both sides of the ODE, we get

$sY(s)-y(0)+5Y(s)=\dfrac{e^{-3s}-e^{-5s}}s$

Solve for $Y(s)$ :

$(s+5)Y(s)-4=\dfrac{e^{-3s}-e^{-5s}}s\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}{s(s+5)}+\dfrac4{s+5}$

We can split the first term into partial fractions:

$\dfrac1{s(s+5)}=\dfrac as+\dfrac b{s+5}\implies1=a(s+5)+bs$

If $s=0$ , then $1=5a\implies a=\frac15$ .

If $s=-5$ , then $1=-5b\implies b=-\frac15$ .

$\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}5\left(\frac1s-\frac1{s+5}\right)+\dfrac4{s+5}$

$\implies Y(s)=\dfrac15\left(\dfrac{e^{-3s}}s-\dfrac{e^{-3s}}{s+5}-\dfrac{e^{-5s}}s+\dfrac{e^{-5s}}{s+5}\right)+\dfrac4{s+5}$

Take the inverse transform of both sides, recalling that

$Y(s)=e^{-cs}F(s)\implies y(t)=u(t-c)f(t-c)$

where $F(s)$ is the Laplace transform of the function $f(t)$ . We have

$F(s)=\dfrac1s\implies f(t)=1$

$F(s)=\dfrac1{s+5}\implies f(t)=e^{-5t}$

We then end up with

$y(t)=\dfrac{u(t-3)(1-e^{-5t})-u(t-5)(1-e^{-5t})}5+5e^{-5t}$

3 0

4 years ago

The windscreen wiper of a car sweeps

AVprozaik [17]

Answer:

A ≈ 530 cm²

Step-by-step explanation:

The swept area equals the total area covered by the blade minus the unswept area.

The area of a sector with radius r and angle θ is:

A = (θ / 360) πr²

So the swept area is:

A = (θ / 360) πR² − (θ / 360) πr²

A = (θ / 360) π (R² − r²)

A = (150 / 360) π (21² − 6²)

A ≈ 530 cm²

6 0

3 years ago

Dan bought 24 pounds of sugar for $10. how many dollars did he pu per pound of sugar

siniylev [52]

Step-by-step explanation:

10÷24= .41 cents per pound

7 0

3 years ago