Which point satisfies the system of equations y = 3x

The family members going are 4 mothers, 4 grand-mothers and 4 daughters. What will be the minimum number of tickets required?

iragen [17]

There are 12 tickets needed. Just add all the 4's together.

4 0

3 years ago

NO LINKS OR FILES!

Archy [21]

(a) If the particle's position (measured with some unit) at time t is given by s(t), where

$s(t) = \dfrac{5t}{t^2+11}\,\mathrm{units}$

then the velocity at time t, v(t), is given by the derivative of s(t),

$v(t) = \dfrac{\mathrm ds}{\mathrm dt} = \dfrac{5(t^2+11)-5t(2t)}{(t^2+11)^2} = \boxed{\dfrac{-5t^2+55}{(t^2+11)^2}\,\dfrac{\rm units}{\rm s}}$

(b) The velocity after 3 seconds is

$v(3) = \dfrac{-5\cdot3^2+55}{(3^2+11)^2} = \dfrac{1}{40}\dfrac{\rm units}{\rm s} = \boxed{0.025\dfrac{\rm units}{\rm s}}$

(c) The particle is at rest when its velocity is zero:

$\dfrac{-5t^2+55}{(t^2+11)^2} = 0 \implies -5t^2+55 = 0 \implies t^2 = 11 \implies t=\pm\sqrt{11}\,\mathrm s \imples t \approx \boxed{3.317\,\mathrm s}$

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

$\dfrac{-5t^2+55}{(t^2+11)^2} > 0 \implies -5t^2+55>0 \implies -5t^2>-55 \implies t^2 < 11 \implies |t|$

In interval notation, this happens for t in the interval (0, √11) or approximately (0, 3.317) s.

(e) The total distance traveled is given by the definite integral,

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt$

By definition of absolute value, we have

$|v(t)| = \begin{cases}v(t) & \text{if }v(t)\ge0 \\ -v(t) & \text{if }v(t)$

In part (d), we've shown that v(t) > 0 when -√11 < t < √11, so we split up the integral at t = √11 as

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt = \int_0^{\sqrt{11}}v(t)\,\mathrm dt - \int_{\sqrt{11}}^8 v(t)\,\mathrm dt$

and by the fundamental theorem of calculus, since we know v(t) is the derivative of s(t), this reduces to

$s(\sqrt{11})-s(0) - s(8) + s(\sqrt{11)) = 2s(\sqrt{11})-s(0)-s(8) = \dfrac5{\sqrt{11}}-0 - \dfrac8{15} \approx 0.974\,\mathrm{units}$

7 0

3 years ago

Help me out please !!!!!!!!!!!

Bad White [126]

Answer: A=2, B=5, C=4

Step-by-step explanation:

$\frac{6x^{2}+13x-5}{x^{2}-16} \cdot \frac{x+4}{3x-1}\\\frac{(3x-1)(2x+5)}{(x-4)(x+4)} \cdot \frac{x+4}{3x-1}\\\frac{2x+5}{x-4}$

So A=2, B=5, and C=4.

8 0

2 years ago

You have 5 blocks of cheese. If it takes 2/3 block of cheese to make a pizza, how many pizzas can you make with 5 blocks of chee

Vedmedyk [2.9K]

Answer:

12

Step-by-step explanation:

5 0

3 years ago

. SHOPPING Ramos went to a pizza shop and spent half of his money on lunch. If Ramos had $4.50 left after lunch, how much money

zheka24 [161]

Answer:

Looks like it's already answered

Step-by-step explanation:

lol

6 0

3 years ago

Which point satisfies the system of equations y = 3x - 2 and y = -2x + 3