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2 years ago

-4.9x=9.8 what is the value of x please explain what and how you did the problem so I can learn too thanks!

2 answers:

8 0

To get x alone, you have to divide -4.9 to both sides. The reason you have to divide is because division is the opposite of multiplication

This is what you call a one step equation

-4.9x = 9.8
x = 9.8/-4.9
x= -2

Naily [24]2 years ago

7 0

-4.9x = 9.8 Divide both sides by -4.9

x = 9.8/-4.9. Use a calculator.

x = -2. Answer is - because + /- = -

I hope this helps.

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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:

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

$y_{max} = 84.375\,m$

7 0

2 years ago

Math problem help me

Ratling [72]

Answer:

$y=3x+2$

Step-by-step explanation:

To find the equation, use the slope-intercept formula:

$y=mx+b$

m is the slope and b is the y-intercept. Now, it'll really help to draw a line through the points, connecting them. If you look at point (0,2), we can see that this is the y-intercept (where a point sits on the y-axis when x=0). You can insert this into the equation by taking the y value:

$(0,2)\\y=mx+2$

Now, take any two points to find the slope. To make it easier, I'll use (1,5) and (0,2). Use the slope formula for when you know two points:

$\frac{y(2)-y(1)}{x(2)-(x1)} =\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

$(1(x1),5(y1))\\(0(x2),2(y2))\\\\\frac{2-5}{0-1}$

Solve:

$\frac{2-5}{0-1}=\frac{-3}{-1}$

Since both are negative, the result is a positive:

$\frac{-3}{-1}=\frac{3}{1} =3$

Insert this into the equation as m, the slope:

$y=3x+2$

Done.

6 0

2 years ago

A book store sells a textbook for $150. If the textbook is on sale with 12% off, and there is a sales tax of 8.25% added to the

Yuri [45]

The textbook is $150 originally, so to find the price of the textbook on sale, multiply the original price by 12% (0.12). Then subtract 12% of 150 from 150.

150 * 0.12 = 18

Subtract 18 from 150.

150 - 18 = 132

Multiply the price of the textbook on sale by the sales tax of 8.25% (0.0825). Then add the tax price onto the sale price of the textbook.

132 * 0.0825 = 10.89

Add 10.89 to 132.

132 + 10.89 = 142.89

The final price of the textbook is $142.89.

4 0

2 years ago

an architect created a scale model of a building. the length of the model is 15 inches. the scale factor used to create the mode

navik [9.2K]

The length of model is ......15 inch
if the scale factor is 1/20
it means 1/20=15/h
h=12*15=300

4 0

2 years ago

PLSS HELP

Harrizon [31]

Your answer is going to be Letter B

8 0

2 years ago