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kumpel [21]
4 years ago
6

A line passes through (3, –2) and (6, 2).

Mathematics
1 answer:
Liono4ka [1.6K]4 years ago
3 0
A. Slope of the line = (-2 - 2) / (3 - 6)  = -4 / -3 = 4/3

the equation  required is  y - 2 = 4/3(x - 6)

b.  convert this to standard form:-

y - 2 = 4/3(x - 6)    Multiply through by 3:-
3y - 6  =  4(x - 6)
3y - 6 = 4x - 24

4x - 3y = 18  is the answer

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In a collision, a 5 kg mass moving at 2m/s transfers all of its momentum to a 1 kg mass. What is the velocity of the 1kg mass af
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Answer:
velocity = 10 m/sec in the same direction as the first body did

Explanation:
The momentum of the body can be calculated as follows:
momentum = mass * velocity

For the first body, we have:
mass = 5 kg
velocity = 2 m/sec
momentum = mass * velocity
momentum = 5 * 2 = 10 kg.m/sec

We know that this momentum is transferred completely to the second body

For the second bode, we have:
momentum = 10 Kg.m/sec
mass = 1 kg
momentum = mass * velocity
10 = 1 * velocity 
velocity = 10/1
velocity = 10 m/sec

Finally, we should get the direction of the motion:
Both the velocity of the first and second bodies have positive values. Therefore, the second body is moving in the same direction as the first body did.

Hope this helps :)
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Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!\cdot(n-k)!}

(a)

Compute the number of ways to select 9 applicants from 100 as follows:

{100\choose 9}=\frac{100!}{9!\cdot(100-9)!}

        =\frac{100!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92}{9!}\\\\=1902231808400

(b)

Compute the number of ways to select 6 people from 9 as follows:

{9\choose 6}=\frac{9!}{6!\cdot(9-6)!}

        =\frac{9!}{6!\times 3!}\\\\=\frac{9\times 8\times 7\times 6!}{6!\times 3!}\\\\=\frac{9\times 8\times 7}{3!}\\\\=84

(c)

Compute the number of ways to select top 3 candidates from 6 as follows:

{6\choose 3}=\frac{6!}{3!\cdot(6-3)!}

        =\frac{6!}{3!\times 3!}\\\\=\frac{6\times 5\times 4\times 3!}{3!\times 3!}\\\\=\frac{6\times 5\times 4}{3!}\\\\=20

7 0
3 years ago
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