Aship travels 70 km on a bearing of 27 degrees, and then travels on a bearing of 147 degrees for 180 km. find the distance of the end of the trip from the starting point.

So the angle would be 123,66º and the distance will be 183,23,

Step-by-step explanation:

To solve this you need to create a triangle rectangle with the values of the vector that you are given you just need to convert them to the X and Y in the graph:

x1=70*cos27=62,37

y1=70*sin27= 31,77

x2=180cos147=-150,96

y2=180sin147=98,03

So from this you just can calculate with the calculus of the hypothenuse:

So the answer is 183,23 km from the starting point.

To calculate the angle we use sin-1, by dividing adjacent/hyphotenuse:

-150,96/183,23=-,8238

Sin-1-,8323= 123,66

So the angle would be 123,66º and the distance will be 183,23,

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x