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Paladinen [302]
3 years ago
14

What is the slope of a line perpendicular to a line with slope –9?

Mathematics
1 answer:
7nadin3 [17]3 years ago
3 0

Answer:

The answer is 1/9.

Step-by-step explanation:

When solving for the slope of a perpendicular line to a given, you have to flip the opposite reciprocal.

First take the number and flip the reciprocal, in this case -9 turns into -1/9.

Then flip the sign, like making a negative to a positive or a positive to a negative. In this case make -1/9 into 1/9

Therefore the answer is 1/9.

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At what point does she lose contact with the snowball and fly off at a tangent? That is
postnew [5]

Answer:

α ≥ 48.2°

Step-by-step explanation:

The complete question is given as follows:

" A skier starts at the top of a very large frictionless snowball, with a very small initial speed, and skis straight  down the side. At what point does she lose contact with the snowball and fly off at a tangent? That is, at the  instant she loses contact with the snowball, what angle α does a radial line from the center of the snowball to  the skier make with the vertical?"

- The figure is also attached.

Solution:

- The skier has a mass (m) and the snowball’s radius (r).

- Choose the center of the snowball to be the zero of gravitational  potential. - We can look at the velocity (v) as a function of the angle (α) and find the specific α at which the skier lifts off and  departs from the snowball.

- If we ignore snow-­ski friction along with air resistance, then the one work producing force in this problem, gravity,  is conservative. Therefore the skier’s total mechanical energy at any angle α is the same as her total mechanical  energy at the top of the snowball.

- Hence, From conservation of energy we have:

                       KE (α) + PE(α) = KE(α = 0) + PE(α = 0)

                       0.2*m*v(α)^2 + m*g*r*cos(α) = 0.5*m*[ v(α = 0)]^2 + m*g*r

                       0.2*m*v(α)^2 + m*g*r*cos(α) ≈ m*g*r

                        m*v(α)^2 / r = 2*m*g( 1 - cos(α) )

- The centripetal force (due to gravity) will be mgcosα, so the skier will remain on the snowball as long as gravity  can hold her to that path, i.e. as long as:

                         m*g*cos(α) ≥ 2*m*g( 1 - cos(α) )

- Any radial gravitational force beyond what is necessary for the circular motion will be balanced by the normal  force—or else the skier will sink into the snowball.

- The expression for α_lift becomes:

                            3*cos(α) ≥ 2

                            α ≥ arc cos ( 2/3) ≥ 48.2°

4 0
3 years ago
Twenty four is less than 10 times the number equals 64 more than 8 times a number.
Elena-2011 [213]
You would write the equation like this:
24-10n=64+8n
3 0
3 years ago
Alguien sabe que pasa con los grados de los polinomios Cúando se multiplican
allochka39001 [22]

respuesta :

eso es un ejemplo aver si te ayuda

explicacion :

polinomio en una letra                        Grado    

2x³ - 5x² +  8                       ⇒                  3

6 0
3 years ago
X,y,z and l are proportional quantites, prove that : y–x/x = l–z/z​
Vera_Pavlovna [14]

Answer:

y=24

Step-by-step explanation:

7 0
2 years ago
Find the slope of a line parallel to each given line -2/5x + 3
masha68 [24]

9514 1404 393

Answer:

  -2/5

Step-by-step explanation:

The slopes of parallel lines are the same. The slope of the given line is -2/5, the coefficient of x.

The slope of a parallel line is -2/5.

3 0
3 years ago
Read 2 more answers
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