There is 40% decreased in price on a sale it is further decreased by 5%,find the total decreased percentage.

The differential equation for the motion is given by mv' = mg - γv. We re-write as mv' + γv = mg ⇒ v' + γv/m = g. ⇒ v' + kv = g. where k = γ/m.Since this is a linear first order differential equation, We find the integrating factor μ(t)= $e^{\int\limits^ {}k \, dt }$ = $e^{kt}$ . We now multiply both sides of the equation by the integrating factor.

μv' + μkv = μg ⇒ $e^{kt}$ v' + k $e^{kt}$ v = g $e^{kt}$ ⇒ [v $e^{kt}$ ]' = g $e^{kt}$ . Integrating, we have

∫ [v $e^{kt}$ ]' = ∫g $e^{kt}$

v $e^{kt}$ = $\frac{g}{k}$ $e^{kt}$ + c

v(t)= $\frac{g}{k}$ + c $e^{-kt}$ .

From our initial conditions, v(0) = 9.55 m/s, t = 0 , g = 9.8 m/s², γ = 9 kg/s , m = 15 kg. k = y/m. Substituting these values, we have

9.55 = 9.8 × 15/9 + c $e^{-16.33 * 0}$ = 16.33 + c

c = 9.55 -16.33 = -6.78.

So, v(t)= 16.33 - 6.78 $e^{-16.33t}$ . m/s = - 6.78 $e^{-16.33t}$ + 16.33 m/s

b. Velocity of object at time t = 0.5

At t = 0.5, v = - 6.78 $e^{-16.33 x 0.5}$ + 16.33 m/s = 16.328 m/s ≅ 16.33 m/s

6 0

2 years ago

Can someone tell me if my answer to this problem is correct, please? And if it isn't how do you solve it?

Mrac [35]

Answer:

Height of tree= 13.8m

Step-by-step explanation:

When finding the value of a in your working, I suggest to leave the answer to 5 significant figures so that your final answer is more accurate. The value of a should be 26.048m to 5 s.f.

Then multiplying 26.048 with sin 32° would give you 13.8m too when rounded off to 3 significant figures :)

I have attached my working too.

3 0

3 years ago

Hey 20 points for the first person to show work and answer this

Harrizon [31]

Step-by-step explanation:

First, the pizza is 18 inches in diameter, so

$d = 18$

and, because the radium is half of the diameter,

$r = 9$

<u>Note that the units are inches.</u>

Using the equation

$a = \pi r ^{2}$

where a is the area of a circle, we know that the area of the whole pizza is approx.254.5 square inches. Divide by 8 to find the area of 1/8 of a pizza. Each slice will have an area of approx. 32 square inches. For a precise result, the answer is

$a(s)= \frac{(\pi \times 9^{2})}{s}$

where a(s) is the area of a slice of pizza, and s is the total number of slices, given they are equal in size.

5 0

3 years ago