Simplify 15.6 divided by negative 3..

On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s^2. A cannonball is launched from the or

almond37 [142]

Answer:

a) $\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$ , b) $\theta = \frac{\pi}{4}$ , c) $y_{max} = 84.375\,m$ , $t = 3.75\,s$ .

Step-by-step explanation:

a) The function in terms of time and the inital angle measured from the horizontal is:

$\vec r (t) = [(v_{o}\cdot \cos \theta)\cdot t]\cdot i + \left[(v_{o}\cdot \sin \theta)\cdot t -\frac{1}{2}\cdot g \cdot t^{2} \right]\cdot j$

The particular expression for the cannonball is:

$\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$

b) The components of the position of the cannonball before hitting the ground is:

$x = (90\cdot \cos \theta)\cdot t$

$0 = 90\cdot \sin \theta - 6\cdot t$

After a quick substitution and some algebraic and trigonometric handling, the following expression is found:

$0 = 90\cdot \sin \theta - 6\cdot \left(\frac{x}{90\cdot \cos \theta} \right)$

$0 = 8100\cdot \sin \theta \cdot \cos \theta - 6\cdot x$

$0 = 4050\cdot \sin 2\theta - 6\cdot x$

$6\cdot x = 4050\cdot \sin 2\theta$

$x = 675\cdot \sin 2\theta$

The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:

$\frac{dx}{d\theta} = 1350\cdot \cos 2\theta$

$1350\cdot \cos 2\theta = 0$

$\cos 2\theta = 0$

$2\theta = \frac{\pi}{2}$

$\theta = \frac{\pi}{4}$

Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:

$\frac{d^{2}x}{d\theta^{2}} = -2700\cdot \sin 2\theta$

$\frac{d^{2}x}{d\theta^{2}} = -2700$

Which demonstrates the existence of the maximum associated with the critical point found before.

c) The equation for the vertical component of position is:

$y = 45\cdot t - 6\cdot t^{2}$

The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:

$\frac{dy}{dt} = 45 - 12\cdot t$

$45-12\cdot t = 0$

$t = \frac{45}{12}$

$t = 3.75\,s$

Now, the second derivative is used to check if such solution leads to a maximum:

$\frac{d^{2}y}{dt^{2}} = -12$

Which demonstrates the assumption.

The maximum height reached by the cannonball is:

$y_{max} = 45\cdot (3.75\,s)-6\cdot (3.75\,s)^{2}$

$y_{max} = 84.375\,m$

7 0

3 years ago

4(3+2x) + 2 = 46 , solve for x I need help I'm a bit confused

Reil [10]

Answer:

x=4

Step-by-step explanation:

4(3+2x)+2=46

12+8x+2=46

12+8x=44

8x=32

x=4

8 0

3 years ago

Read 2 more answers

HELP WILL GET BRAINLIEST Select the correct answer.

irina [24]

Answer:

its 0.3

Step-by-step explanation:

i got it wrong bcuz i chose something else but trust me its 0.3

brainliest plz

8 0

2 years ago

Which expression is equivalent to 4(23)

Blizzard [7]

Answer:

the correct answer is , 4(20+3)

Step-by-step explanation:

6 0

2 years ago

Help and explanation.

Natasha_Volkova [10]

Answer:

Andrew

Step-by-step explanation:

Abby:

Since red cards are negative, a red 9 would represent the number -9. And because black cards are positive, a black 6 would represent the number 6. To get the sum, we add the two numbers together:

-9 + 6

That gives us a total of -3.

Ashley:

We can do the same thing as before. A black seven would represent 7 and a red 8 would represent -8. Next we again add them together:

7 + (-8)

That gives us a total of -1.

Andrew:

The red 4 is -4, while the black 4 is 4:

-4 + 4

That gives us a total of 0.

Anna:

Anna has a red 8 which represents -8 and another red, a three, which would represent -3. We can add the two to get:

-8 + (-3)

That gives us a total of -11.

In all, Andrew has the highest sum of 0, which means he won the game.

6 0

2 years ago