Answer:
Angle between vectors u and v: 26.56 degrees
Step-by-step explanation:
I just recently did this question, so here's my response and hopefully that helps you:
Vector u is <-3,-4> and vector v is <-2,-1>. To find the angle between the two vectors, you first need to find their dot product. This means that u*v = <-3,-4> * <-2,-1> = (-3)(-2) + (-4)(-1) = 6 + 4 = 10. Second, you find the product of each of the vectors' magnitudes. The magnitude for vector u is ||u|| = sqrt((-3)^2 + (-4)^2) = sqrt(9+16) = sqrt(25) = 5. The magnitude for vector v is ||v|| = sqrt((-2)^2 + (-1)^2) = sqrt(4+1) = sqrt(5). The product of the magnitudes would thus be ||u||||v|| = 5sqrt(5). Third, divide the dot product by the product of the magnitudes which would be u*v/||u||||v|| = 10/5sqrt(5) = 2sqrt(5)/5. Lastly, you take the arccosine of the result which would be theta=cos^-1(2sqrt(5)/5) = 26.56 degrees, which is the angle between vectors u and v.
Answer:
Step-by-step explanation:
Recall that the angle formed by two tangents is half the difference of the intercepted arc.
Multiply through by 2 to get:
26x+20=49x+10-180+13x+10
Group similar terms to get:
26x-13x-49x=10-180+10-20
-36x=-180
x=5
Answer:
12
Step-by-step explanation:
Largest number-smallest
13-1=12
Answer:
62.83
Step-by-step explanation:
Circumference=2 pi r
diameter=20
20*pi= about 62.83
so it sould be around 62.83
<span>The ordered pair is (5000,12). This is given from the function a at x=5000, which is written in the question as a(5000)=12. Here, a is our dependent variable and is equal to 12. The x value, or independent variable is given as 5000. Ordered pairs are written (x,y) or (independent, dependent), thus the ordered pair is (5000,12).</span>