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3 years ago

The sum of 8 and 5 minus 2

Mathematics

1 answer:

Masteriza [31]3 years ago

7 0

(8+5)- 2
First, add 8+5 (=13)
Then, subtract 2 (=11)
So the answer is 11

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Resolve the vector into components. 1. A vector starting at the point Q = (4, 6) and ending at the point P = (1, 2).

lesya692 [45]

Answer:

1. Horizontal component = -3 units

Vertical component = -4 units

2. Horizontal component = 3 units

Vertical component = 4 units

Step-by-step explanation:

If a vector M, starting at point A = (a, b) and ending at point B = (c, d) is given, then the vector can be resolved into x and y components as follows;

M = AB

Where;

AB = B - A

AB = (a, b) - (c, d)

AB = (a-c, b-d)

AB = (a-c)i + (b-d)k

Therefore, a-c and b-d are the x and y components of the vector M.

(1) Let the vector be M:

Starting point of M = Q = (4, 6)

Ending point of M = P = (1, 2)

So,

M = PQ

Where;

PQ = Q - P

PQ = (1,2) - (4,6)

PQ = (1-4, 2-6)

PQ = (-3, -4)

Therefore,

M = PQ = -3i - 4j

The x and y components of M are therefore, -3 and -4 respectively.

(2) Let the vector be M:

Starting point of M = P = (1, 2)

Ending point of M = Q = (4, 6)

So,

M = PQ

Where;

PQ = Q - P

PQ = (4,6) - (1,2)

PQ = (4-1, 6-2)

PQ = (3, 4)

Therefore,

M = PQ = 3i + 4j

The x and y components of M are therefore, 3 and 4 respectively.

Note: The x and y components are also called the horizontal and vertical components respectively.

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Step-by-step explanation:

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To test the impact performance of a 10 cm thick gymnastics mat, a 20 kg cylindrical

denis23 [38]

Answer:

A)196J

B)-208J

C)3467J

Step-by-step explanation:

We are given that a 20 kg cylindrical mass is dropped onto the mat from a height of 1 m above the mat. During the impact, the cylinder’s vertical velocity reaches zero at the instant the mat has compressed to only 4 cm thick.

So, The Mat gets compressed by : 10cm - 4 cm = 6 cm=0.06 m

Using Conservations of energy

Potential energy at the top = Kinetic energy at the point before touching the surface

Kinetic energy = mgh= $20 \times 9.8 \times 1 = 196 J$

Work done by the mat do to stop the fall of the cylinder = $-mg(h+0.06)=-20 \times 9.8(1+0.06)=-208 J$

Work done= $\text{Average force} \times \text{ Compression of mat}$

$208=F \times 0.06$

F=3467J

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3 years ago