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Mass of the asteroid =m = 4.66667×10^10 kg.=Volume of the asteroid.

4.66667×10^10=4/3 x pi x r^3, solve for r

r=2,233m x 2 =4,466m =~4.5 km - diameter of the asteroid.

662

Volume of sphere=4/3 x Pi x r^3, r=radius

V =4/3 x 3.141592 x 4,000^3

V=268,082,517,333 cubic meters

Mass =268,082,517,333 kg

KE =1/2 x M x v^2

KE=1/2 x 268,082,517,333 x 30,000^2

KE=120,637,132,800,000,000,000 =~1.2 x 10^20 Joules

1 Megaton =4.2 x 10^15 Joules, therefore:

[1.2 x 10^20] / [4.2 x 10^15] =~28,723 Megatons of energy released.

Take the cubic root of 729, that's your answer.

To solve:     9x - 13  <  -22     or     -8x + 7  <  -25

                            9x  <  -9       or            -8x  <  -32

                              x  <  -1       or                x  >  4

All real numbers less than -1 or greater than 4.

               ( - infinity, -1 )     union     ( 4, infinity )

To place an equation into slope-intercept form, solve the equation for y.

                                          -3x - 2y  =  30

Add 3x to both sides:             -2y  =  3x + 30

Divide both sides by -2:             y  =  (-3/2)x - 15

because it is a negative times a positive, there are always 2 negatives in a equation

5 x 198  =  5 x (200 - 2)  =  5 x 200 - 5 x 2  =  1000 - 10  =  990

Hi LambLamb,

I am assuming that you are on the ground and that the plane is flying in your compas direction but that it ia maintainng a height of 5km

\(\frac{d\theta}{dt}=\frac{d\theta}{dx}\times \frac{dx}{dt}\\ \text{now }\frac{dx}{dt} \text{ is the velocity of the plane so it equals 600km/hour so}\\ \frac{d\theta}{dt}=\frac{d\theta}{dx}\times -600\\~\\ \)

At any point in time,  

\(sin\theta=\frac{height\; of \;plane}{x}\\ sin\theta=\frac{5}{x}\\ x=\frac{5}{sin\theta}\qquad \text{except when }sin\theta =0\\ x=5*({sin\theta})^{-1}\\ \frac{dx}{d\theta}=-5(sin\theta)^{-2}*cos\theta\\ \frac{dx}{d\theta}=\frac{-5cos\theta}{(sin\theta)^2}\\ \frac{d\theta}{dx}=\frac{-(sin\theta)^2}{5cos\theta}\\\)

SO

\(\frac{d\theta}{dt}=\frac{d\theta}{dx}*-600\\ \frac{d\theta}{dt}=\frac{-(sin\theta)^2}{5cos\theta}*-600\\ When\;\theta=30^\circ\\ \frac{d\theta}{dt}=[-(sin30^\circ)^2 \div 5cos30^\circ]*-600\\ \frac{d\theta}{dt}=[\frac{-1}{4} \div \frac{5\sqrt3}{2}]*-600\\ \frac{d\theta}{dt}=[\frac{-1}{4} \times \frac{2}{5\sqrt3}]*-600\\ \frac{d\theta}{dt}=[ \frac{-1}{10\sqrt3}]*-600\\ \frac{d\theta}{dt}= \frac{60}{\sqrt3}\;degrees/ hour\\ \frac{d\theta}{dt}=\frac{1}{\sqrt3}\;degrees/ minute\\\)

1 /sqrt(3) = 0.5773502691896258

When the angle ofelevation is 30 degrees it (the angle) is increasing at the rate of approx 0.577 degrees per minute 

-30 the larger the negative the father away it is from 0 on the number line

For negative numbers, the one closest to 0 is the largest.

-30 is closer to 0 than -47; therefore -30 is the larger number.

If you know that  x = 45,  then  x + 65  =  45 + 65  =  110

Starting with:                                      y + 1/5  =  3x

Subtract 3x from both sides:  -3x + y + 1/5  =  0

Subtract 1/5 from both sides:           -3x + y  =  -1/5

Multiply both sies by 5:                    -15x + 5y  =  -1      

It takes Jonathan 2/3 as long as it takes Juancho to paint a car. If they are together it will take 12 hours. How long will Juancho take if he will work alone?

Let the time it takes Juancho to paint a car =x, then:

The time it takes for Jonathan to paint a car =2/3x, but we have:

1/x + 1 / (2/3x) = 1 / 12, solve for x

x=30 hours for Juancho to paint a car, and:

30 x 2/3 =20 hours for Jonathan to paint a car.

To find the x-intercept, replace y with 0 and solve:  y  =  -(1/2)x - 3

                                                                                       0  =  -(1/2)x - 3

                                                                                       3  =  -(1/2)x

                                                                                      -6  =  x     --->     (-6, 0)

To find the y-intercept, replace x with 0 and solve:  y  =  -(1/2)x - 3

                                                                                       y  =  -(1/2)(0) - 3

                                                                                       y  =  -3     --->     (0, -3)

7 + -7 = 0 and -22 + 7 = -15 so x=-15 

In math you can make these problems using variables (X) easier by adding on to each side (or subtracting)

What is the radius of an asteroid for which the escape velocity is 8 meters/sec? Assume the density of the asteroid is 3000 kg/m3. (At this low escape speed, a person could “run” off the asteroid.)

Calculate the total mass of water needed to cover the entire surface of Mars to a depth of 30 meters. How many comets of average size (say, 2 km diameter) would it take to bring in this much water? What is the average time between impacts, if this number of comets struck Mars in the first billion years of the solar system?

1 Megaton of TNT has an explosive yield of 4×1015 Joules. The entire nuclear arsenal of the world has been estimated at 5,000 Megatons. Estimate the diameter of a comet with a destructive power of 5,000 Megatons (with the same density and velocity as above).

29=x

The answer is 8, you can just enter this into the calculator without asking. Its with the more complicated equations that may be Linear or involve things like EMC or M=?.

What is 7 times 21?

\(7\times21= 7 \times7\times3=3\times{7^2}={\color{blue}147}\)   !

Hello Guest!

y=x

\({\color{black}y=f(x)=x}\)

Is a linear function. The graph of the function is inclined by 45 ° against the abscissa. It goes through the coordinate origin.

Greeting asinus :- ) !