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Jim Abbott purchased a $58,000 recreational vehicle (RV) with a 45 percent markup on selling price. a. What was the amount of th

BARSIC [14]

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6 0

3 years ago

Suppose that F is an inverse square force field below, where c is a constant.

Andre45 [30]

Answer:

Forces in our Universe

Step-by-step explanation:

a)

First of all we have,

$F(r) = \frac{cr}{|r|^{3} }$

and,

$r = xi+yj+zk$

We need to define a function that allows us to find said change based on r, so one of the functions that shows that change is,

$f(r) = - c /|r|$

That is,

$\nabla f = F$

For this case F is a conservative field and the line integral is independent of the path. Thus, defining $P_{1} = (x_{1}, y_{1}, z_{1})$ and $P_{2} = (x_{2}, y_{2}, z_{2})$ . So the amount of work on the movement of the object from P1 to P2 is,

$W=\int\limits_c {F} \, dr$

$W= f(P_{1}-P_{2})$

$W= \frac{c}{(x_{2}^2+ y_{2}^2+ z_{2}^2)^{1/2} } -\frac{c}{(x_{1}^2+ y_{1}^2+ z_{1}^2)^{1/2}}$

$W= c(\frac{1}{d1}-\frac{1}{d2} )$

2) The gravitational force field is given by,

$F(r) =-\frac{mMGr}{ |r|^3}$

The maximum distance from the earth to the sun is $1.52*10 ^ 8$ km and the minimum distance is $1.47*10 ^ 8$ km. The mass values of the bodies are given by m = $5.97*10 ^ {24}$ kg, M = $1.99 *19 ^ {30}$ kg and the constant G is $6.67 * 10 ^{ -11 }$ $\frac{Nm ^ 2}{kg^2}$

In this way we raise the problem like this,

$c= -mMG$

$W= -mMG (\frac{1}{1.52*10 ^ 8} -\frac{1}{1.47*10 ^ 8} )$

$W= -(5.95*10^{24})(1.99*10^{30})(6.67*10^{-11})(-2.2377*10^{-10})$

$W \approx 1.77*10^{35}}J$

5 0

3 years ago

Factor complete −2x2 + 10x.

mezya [45]

The factors of the quadratic equation is (x + 1) and (x - 6)

Given,

The quadratic equation; -2x² + 10x + 12

We have to find the factors of this equation using quadratic formula;-

Quadratic formula;- $\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}$

Here,

a = -2, b = 10 and c = 12

Now,

$\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}$ = $\frac{-10(+-)\sqrt{10^{2} -4 . -2. 12} }{2.-2}$ = $\frac{-10(+-)\sqrt{100 +96} }{-4}$ = (-10±14) ÷ -4

Solve for,

- 10 + 14 / -4 = -4/4 = -1

That is, (x + 1)

Solve for,

- 10 - 14 / -4 = -24/-4 = 6

That is, (x - 6)

Therefore, the factors for the given quadratic equation is (x + 1) and (x - 6)

Learn more about quadratic formula here;

brainly.com/question/9300679

#SPJ1

6 0

1 year ago

A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, i

attashe74 [19]

The ball takes approximately a time of 2.041 seconds to reach its maximum height.

<h3>What time does the ball take to reach maximum height?</h3>

The height of the ball as a function of time is modelled by a <em>quadratic</em> equation, the required information can be found by transforming the expression into <em>vertex</em> form:

h = - 4.9 · t² + 20 · t + 12

h = - 4.9 · (t² - 4.082 · t - 2.449)

h + (- 4.9) · (6.615) = - 4.9 · (t² - 4.082 · t + 4.166)

h - 32.414 = - 4.9 · (t - 2.041)²

The ball takes approximately a time of 2.041 seconds to reach its maximum height.

To learn more on quadratic equations: brainly.com/question/1863222

#SPJ1

5 0

1 year ago

If 1 is 3 and 2 is 3 and 3 is 5 what is 4 # riddles

Helga [31]

Answer:

4 is 5

Hope it's right :))

7 0

3 years ago