What is the GCF of 80 and 20?

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

stepladder [879]

When the direction is reversed velocity = 0

v = ds/dt = 6t^2 - 42t + 60 = 0

t^2 - 7t + 10 = 0

(t - 5)(t - 2) = 0

t = 2 s and 5 s which are the times when the direction is reversed
Position at t = 2 = 2(2)^3 - 21(2)^2 +60(2) + 3 = 55 feet
at t = 5 position = 28 feet

Acceleration = dv/dt = 12t - 42

At t = 2 acceleration = -18 ft s-2
At t = 5 ............... = 18 ft s-2

6 0

4 years ago

Use the substitution of x=e^{t} to transform the given Cauchy-Euler differential equation to a differential equation with consta

kherson [118]

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dt}=x\dfrac{\mathrm dy}{\mathrm dx}$

which follows from $x=e^t\implies t=\ln x\implies\dfrac{\mathrm dt}{\mathrm dx}=\dfrac1x$ .

$\dfrac{\mathrm dy}{\mathrm dt}$ is then a function of $x$ ; denote this function by $f(x)$ . Then by the product rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dt}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm df}{\mathrm dx}$

and by the chain rule,

$\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}=\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dt^2}$

so that

$\dfrac{\mathrm d^2y}{\mathrm dt^2}-\dfrac{\mathrm dy}{\mathrm dt}=x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}$

Then the ODE in terms of $t$ is

$\dfrac{\mathrm d^2y}{\mathrm dt^2}+8\dfrac{\mathrm dy}{\mathrm dt}-20y=0$

The characteristic equation

$r^2+8r-20=(r+10)(r-2)=0$

has two roots at $r=-10$ and $r=2$ , so the characteristic solution is

$y_c(t)=C_1e^{-10t}+C_2e^{2t}$

Solving in terms of $x$ gives

$y_c(x)=C_1e^{-10\ln x}+C_2e^{2\ln x}\implies\boxed{y_c(x)=C_1x^{-10}+C_2x^2}$

4 0

4 years ago

Plz help

zheka24 [161]

Answer:

a

Step-by-step explanation:

4 0

3 years ago

Every year, Alice's family runs the sand castle contest during the Fun in the Sun beach festival. Alice's job is to deliver empt

seropon [69]

Answer:

120 buckets

Step-by-step explanation:

If there are 15 teams and each team gets the same number of buckets (8 buckets as mentioned in the problem), then you can multiply 15 by 8 to get 120.

15 teams * 8 buckets = 120 total buckets

8 0

2 years ago

Spanko sells every shirt for an amount of $20.

Westkost [7]

Answer: $18

Step-by-step explanation:

We know that Spanko sells every shirt for $20 dollars.

Now, there is 10% off, so we subtract 10%.

10% of $20 = $2 off

Now, we will subtract 2 from $20.

$20 - 2 = $18

Our answer is $18.

4 0

3 years ago

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