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3 years ago

Please help I will give you brainiest!!!

Mathematics

1 answer:

rusak2 [61]3 years ago

8 0

9514 1404 393

Answer:

x-intercept: -14/9

y-intercept: 7

Step-by-step explanation:

This is one of the easiest forms for finding intercepts. To find the x-intercept, set y=0 and divide both sides by the coefficient of x.

-9x = 14 . . . . . set y=0

x = -14/9 . . . . divide by -9

To find the y-intercept, set x=0 and divide both sides by the coefficient of y.

2y = 14 . . . . set x=0

y = 7 . . . . . . divide by 2

The x-intercept is -14/9; the y-intercept is 7.

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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:

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

$y_{max} = 84.375\,m$

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3 years ago

How long will the bus take to travel 300km, if it averages 60km/h?

prisoha [69]

Answer:

5 hours.

Step-by-step explanation:

5 hours * 60km = 300km in 5 hours.

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A record store has 3,108 records evenly shared among 6 rows. How many records are in each row?

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Answer:

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2 years ago

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30 POINTS FOR SIMPLE QUESTION

Komok [63]

-4 = y + 3

y = -4x - 3

Solve for Y in the first equation:

-4 = y +3

Subtract 3 from both sides:

y = -7

Now using the addition method:

rewrite the second equation as 4x+y = -3

Multiply y = -7 by - 1 to get -y = 7

Now add the two together:

4x +y = -3

-y =7

4x = 4

Divide each side by 4:

x = 4/4 = 1

Then replace x in one of the equations to solve for y which is -7

X = 1, Y = -7

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3 years ago

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Usimov [2.4K]

Answer:

second answer should be corr3ect tell em if wrong

Step-by-step explanation:

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