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2 years ago

Find the cube root of 216

Mathematics

2 answers:

andre [41]2 years ago

7 0

6 is the cube root of 216.

I hope this helps! :D

Shtirlitz [24]2 years ago

6 0

∛216

216 = 6 * 6 * 6

∛216 = ∛(6 * 6 * 6) = 6,

Cube root of 216 = 6

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What is the average rate of change of f(x), represented by the table of values, over the interval [-3,4]

77julia77 [94]

Answer:

Average rate of change = 3

Step-by-step explanation:

We know that the average rate of change is basically a measure of the slope of the secant line in the closed interval [a, b].

here a = -3 and b = 4

f(b) = f(4) = 27

f(a) = f(-3) = 6

⇒ Average rate of change = f(b) - f(a) / b - a

= (27 - 6) / (4 - (-3))

= 21 / 7

= 3

Therefore, Average rate of change = 3

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2 years ago

What is the slope of this line

Elenna [48]

Answer:

Step-by-step explanation:

rise/run = slope

As it goes to the left or adds by one, it goes up by 4

4/1

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2 years ago

Read 2 more answers

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 4385 feet and Plane B is at an altitude

Fantom [35]

Answer:

60 seconds, 7715 feet

Step-by-step explanation:

Plane A and B start out 615 feet apart, and we find this by subtracting the height of plane A from plane B, getting 5000-4385=615. Now we have to find how many more feet of altitude plane A is gaining per second over plane B.

To find this we subtract 45.25 from 55.5 and get 10.25 feet per second. Now to find out how many seconds until they'll be at the same altitude we simply divide 615 by 10.25, getting 60 seconds.

For the second part, to find the altitude at this point, we simply multiply the altitude gain of one of the planes per second by the time of 60 seconds to get how much altitude they gained over that time, and add it to the starting altitude. Doing this with plane B we get 45.25*60=2715, and we add that to 5000 to get the final answer of 7715.

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2 years ago

Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).

I am Lyosha [343]

Take the homogeneous part and find the roots to the characteristic equation:

$y''+4y=0\implies r^2+4=0\implies r=\pm2i$

This means the characteristic solution is $y_c=C_1\cos2x+C_2\sin2x$ .

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form $y_p=ax\cos2x+bx\sin2x$ . Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With $y_1=\cos2x$ and $y_2=\sin2x$ , you're looking for a particular solution of the form $y_p=u_1y_1+u_2y_2$ . The functions $u_i$ satisfy

$u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$

where $W(y_1,y_2)$ is the Wronskian determinant of the two characteristic solutions.

$W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2$

So you have

$u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx$
$u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x$

$u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx$
$u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x$

So you end up with a solution

$u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

but since $\cos2x$ is already accounted for in the characteristic solution, the particular solution is then

$y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x$

so that the general solution is

$y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

7 0

2 years ago

It is about 1.62×10⁶ miles from Venus to Earth. It is about 5.4×10⁷ from Earth to Mars. How far is it total from Venus to Earth

Lubov Fominskaja [6]

Answer:

-5.238- $10^{7}$

Since the exponent of the scientific notation is positive, move the decimal point 6 places to the right.

1620000

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Hope this helps :)

4 0

2 years ago