Find, corrrect to the nearest degree, the three angles of the triangle with the given vertices. D(0,1,1), E(-2,4,3), C(1,2,-1)
Sholpan [36]
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.
Thank you for reading this and I hope it is helpful to you.
Answer:
The GCF of 3x^4, 15x^3 and 21x is 3x^2
Step-by-step explanation:
3x^2(x^2), 3x^2(5x) , 3x^2(7)
For this case we have that by definition it is fulfilled:
Where:
a: It is the base
b: It is the exponent
So, if we have the following expression:
-6 to the power of 4, is equivalent to: 
So we have to:
-6: It is the base
4: It is the exponent
Answer:
-6: It is the base
4: It is the exponent
or 
divide both sides by 2
sinΘ = - 
Since the sin ratio is negative then Θ is in third / fourth quadrants
Θ = 
() = 
related acute angle
Θ = ( π + ) =
or Θ = ( 2π - ) =
1 - 8
2 - 16
3 - 32
x - +200
Each lemonade has a profit of $1, so the number of cups of lemonade he sells is the same as the amount of dollars he has. You just need to add each previous day's total to the next day's, doubling the amount of cups from the previous day's for each new day.
4 - (32 x 2 = ) 64
8 + 16 + 32 + 64 = 120. We need at least $80 dollars more, so we continue.
5 - (64 x 2 = ) 128
120 + 128 = $248.00 That's more than enough, so Tom will have enough money for his bike after the fifth day of selling lemonade.
