Answer:
the answer is 7
Step-by-step explanation:
angle 30°
x=14/2
x=7
If u= (u1,u2,u3) andv= (v1,v2,v3), then the dot product of u and v is u·v=u1v1+u2v2+u3v3. For instance, the dot product of u=i−2j−3kandv= 2j−kisu·v= 1·0 + (−2)·2 + (−3)(−1) =−1.
Properties of the Dot Product.
Let u,v, and w be three vectors and let c be a real number. Then u·v=v·u,(u+v)·w=u·w+v·w,(cu)·v=c(u·v).
Further, u·u=|u|2.
Thus, if u=0is the zerovector, then u·u= 0, and otherwise u·u>0.1
Orthogonality Two vectors u and v are said to be orthogonal(perpendicular), if the angle between them is 90◦.Theorem. Two vectors u and v are orthogonal if and only if u·v= 0.
The equivalent measures to 3 yards are;
108 inches and ; 6 ft 36 inches
Here, we want to get the values of the measurements that are equivalent to 3 yards
To do this, we need to know how to convert between the various measure types
We proceed as follows;
Mathematically, 1 yard is 36 inches; also, 1 yard is 3 feet
So, 3 yards is (3*36) = 108 inches
Also, 3 yards is (3*3) = 9 feet
Also, 1 ft is 12 inches;
So, 6 ft 12 inches is 7 feet
108 inches is as seen above, so 3 yards equal this
3 yards is not 108 feet as calculated above
6 ft 36 inches
36 inches is 3 ft; so by addition; 6 ft 36 inches is 9 ft
So, the correct answers here are 108 inches and 6 ft 36 inches
Let <em>a</em> and <em>b</em> be the two numbers. Then
<em>a</em> + <em>b</em> = -4
<em>a b</em> = -2
Solve the second equation for <em>b</em> :
<em>b</em> = -2/<em>a</em>
Substitute this into the first equation:
<em>a</em> - 2/<em>a</em> = -4
Multiply both sides by <em>a</em> :
<em>a</em>² - 2 = -4<em>a</em>
Move 4<em>a</em> to the left side:
<em>a</em>² + 4<em>a</em> - 2 = 0
Use the quadratic formula to solve for <em>a</em> :
<em>a</em> = (-4 ± √(4² - 4(-2))) / 2
<em>a</em> = -2 ± √6
If <em>a</em> = -2 + √6, then
-2 + √6 + <em>b</em> = -4
<em>b</em> = -2 - √6
In the other case, we end up with the same numbers, but <em>a</em> and <em>b</em> are swapped.
Answer:
82
Step-by-step explanation:
-27 -50(-2) + (-3)^2
-27+100+9
73+9
82
