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Answer:
The three angles of the triangle given above are 23, 73 and 84 correct to the nearest degree. The concept of dot product under vectors was applied in solving this problem. The three positions forming the triangle were taken as positions vectors. The Dot product also known as scalar product is a very good way of finding the angle between two vectors. ( in this case the sides of the triangle given above). Below is a picture of the step by step procedure of the solution.
Step-by-step explanation:
The first thing to do is to treat the given positions in space as position vectors which gives us room to perform vector manipulations on them. Next we calculate the magnitude of the position vector which is the square root of the sun of the square of the positions of the vectors along the three respective axes). Then we calculate the dot product. After this is calculated the angle can then be found easily using formula for the dot product.
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Answer:
Step-by-step explanation:
<u>Function modeling</u>
Real-life situations often require the help of mathematics to model numerically what happens when the variables involved can change. It could even be used to predict some expected outcomes from those models.
The problem states Janice receives $.40 per pound when he recycles less or equal than 99 pounds of aluminum. If x is the number of recycled pounds, then the amount of money he receives is
We also know that if he recycles more than 100 pounds of aluminum, the pay increases to $0.5 per pound. In that case, the amount of money is
This is a case where the function is defined differently depending on the conditions of the input variable x. It's called a piecewise function. The function can be written as
Note the function is not well constructed because there is a gap for x=100 where M is not defined. If we establish that for 100 pounds the payment is $0.5, then the second piece would include x=100