(1)Identify the surface whose equation is r = 2cosθ by converting first to rectangular coordinates...(2)Identify the surface whose equation is r = 3sinθ by converting first to rectangular coordinates...(3)Find an equation of the plane that passes through the point (6, 0, −2) and contains the line x−4/−2 = y−3/5 = z−7/4...(4)Find an equation of the plane that passes through the point (−1,2,3) and contains the line x+1/2 = y+2/3 = z-3/-1...(5)Find a) the scalar projection of a onto b b) the vector projection of a onto b given = 〈2, −1,3〉 and = 〈1,2,2〉...(6)Find a) the scalar projection of a onto b b) the vector projection of a onto b given = 〈2,1,4〉 and = 〈3,0,1〉...(7)Find symmetric equations for the line of intersection of the planes x + 2 y + 3z = 1 and x − y + z = 1...(8)Find symmetric equations for the line of intersection of the planes x + y + z = 1 and x + 2y + 2z = 1...(9)Write inequalities to describe the region consisting of all points between, but not on, the spheres of radius 3 and 5 centered at the origin....(10)Write inequalities to describe the solid upper hemisphere of the sphere of radius 2 centered at the origin....(11)Find the distance between the point (4,1, −2) and the line x = 1 +t , y = 3 2−t , z = 4 3−t...(12)Find the distance between the point (0,1,3) and the line x = 2t , y = 6 2−t , z = 3 + t...(13)Find a vector equation for the line through the point (0,14, −10) and parallel to the line x=−1+2t, y=6-3t, z=3+9t<span>...</span>
Step-by-step explanation:So we know x + y = 21 and 5x +10y = 165 We line them up in columns x + y = 21 5x +10y = 165 To eliminate the x variable, I'll multiply every element in the 1st equation by -5. -5x + -5y = -105 5x + 10y = 165 Now we combine (add) the equations, which eliminates x altogether. 5y = 60 ... y = 12 From there, x + 12 = 21 ... x = 21-12 ... x = 9 You should double check. Do 9 nickles and 12 dimes equal $1.65? A very important thing to remember using this method is to do the same thing to each element in the equation that you change! I hope that helps.
The two numbers have 1 as a common factor and nothing else. Hence 1 is the HCF. This proves that the HCF of any two consecutive numbers is always a one.
Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.
