Consider the picture attached.

From right triangle trigonometry:

tan(α)=(opposite side)/(adjacent side)=15/67=0.2239

using a scientific calculator we find that arctan(0.2239)=12.62°

thus α=12.62°, is the angle that the vector makes with the positive x-axis.

The angle made with the + y-axis is 12.62°+90°=102.62°.

The length of the vector v can be determined using the Pythagorean theorem:

$|v|= \sqrt{ 67^{2} + 15^{2} }= \sqrt{4489+225}= \sqrt{4714}=68.8$

Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.

This means that the x and y components will also be divided by 68.8, by proportionality.

So, the unit vector in the direction of v is:

<span>(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j
</span>

Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j

6 0

3 years ago

if the cost price of 10 tables is equal to the selling price of 16 tables , find out the gain or loss percentage

Dovator [93]

Hi,

To solve this problem, Let us take the LCM of 10 and 16 which will come 80.

Now suppose the cost price of 10 tables =₹n CP of 80 tables will be ₹ 8n

According to the question, CP of 10 tables is equal to the SP of 16 tables, then

the SP of 16 tables will also be ₹ n.

So, SP of 80 tables will be ₹ 5n

So, Loss = CP-SP

→ 8n - 5n = ₹ 3n

Loss%= (3n×100)/8n

Loss%= 37.5%.

Hence the correct answer will be a <u>loss of 37.5%.</u>

4 0

2 years ago