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.
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Answer:
x=15is your answer
Step-by-step explanation:
8x=120 vertically opposite angle
x=120/8=15
Multiple each number I think
Answer:
a =2.2
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2
where a and b are the legs and c is the hypotenuse
a^2+2^2 = 3^2
a^2 +4 = 9
a^2 = 9-4
a^2 = 5
Taking the square root of each side
sqrt(a^2) = sqrt(5)
a = sqrt(5)
a=2.236067977
To the nearest tenth
a =2.2
The time it will take the principal to grow to the desired amount is 0.7 years
Using the compound interest formula :
A = P(1 + r/n)^(nt)
A = final amount = 225,000
P = principal = 180,000
r = rate = 3.12%
n = Number of compounding times per period = 12(monthly)
t = time
225000 = 180000(1 + (0.0312 /12))^(12t)
Divide both sides by 180000
225000/180000 = (1 + (0.0312 /12))^(12t)
1.25 = 1.026^12t
Take the log of both sides
0.0969100 = 0.0111473 × 12t
0.0969100 = 0.1337676t
Divide both sides by 0.1337676 to isolate t
0.0969100 / 0.1337676 = t
0.7244 years
0.7 years
It will take 0.7 years for the amount to grow
Learn more : brainly.com/question/21270833?referrer=searchResults
